Harnessing highly efficient coherent polariton parametric emission in quantum confined perovskite microcavities

Domain: physics
Published: 2026-04-02
Editorial outcome: minor_revision

Abstract
Microcavity exciton polaritons emerge as a versatile platform for nonlinear optical effects thanks to the
unique dispersion which enables a manifold of energy and wavevector conserved processes. However,
efficient generation of parametric emission while preserving coherence remains challenging mainly due to
lack of strong parametric interactions compared to simultaneous interaction with relaxation channels.
Herein, we report highly efficient parametric emission with sub-1-meV linewidth from quantum confined
microcavities, enabling the first observation of strong phase coherence between the two parametric species.
Quantum size effect enabled by surface disorder in confined systems acts as the microscopic mechanism
for the observed anomalous enhancement of parametric emission, playing important role in triggering
exotic parametric interactions for microcavity polaritons. Finally, we demonstrate the emergence of
polariton supersolid phase at room temperature in a coherent parametric oscillator, characterized by periodic
density modulation in real space that indicates the breaking of translational symmetry.

Introduction
Exciton-polaritons, hybrid light-matter quasiparticles formed through strong photon-exciton coupling,
have established themselves as a versatile platform for investigating nonlinear quantum optics and
collective coherent phenomena in driven-dissipative systems1-4. The inherent nonlinearity of these bosonic
quasi-particles, originating from the excitonic component, enables efficient polariton-polariton scattering
processes. Further enriched by the distinctive dispersion of multiple polariton bands, microcavity polariton
supports a manifold of parametric interactions that circumvent conventional phase-matching constraints,
enabling efficient parametric emission at reduced power consumption5-9. Among the various types of
parametric interactions, energy-degenerate optical parametric oscillation (OPO, or parametric scattering)9-
16 has garnered significant interest for its potential to generate phase-correlated or quantum-entangled
photon pairs17-19, given that the signal and idler states emerge from source polaritons sharing identical
quantum statistics. More recently, such an OPO configuration has attracted huge interest in the study of the
supersolid phase of matter20,21 , characterized by the formation of periodic density modulations in real
space22-26, thanks to the symmetric momentum-space distribution and the interacting nature of signal and
idler polaritons. Nevertheless, most experimental implementations of such configurations exhibit
suboptimal parametric emission efficiencies-typically characterized by low signal/idler-to-source polariton
intensity ratios-with reported enhancement often requiring pump powers few times above threshold11.
These improvements, however, are inevitably accompanied by spectral broadening, which degrades the
coherence and interaction properties of the signal and idler polaritons. This inefficiency may arise from
either insufficient nonlinear interaction strengths or rapid depletion of parametric states12,13, limiting the
intricate application of parametric interactions and highlighting the need for strategies that simultaneously
enhance emission efficiency while preserving spectral purity.

In this work, we report highly efficient and spectrally pure interbranch energy-degenerate polariton
parametric emission in quantum confined CsPbBr microcavities. Dispersion characteristics enabled by
3
surface disorder (refer to morphological roughness, in this context) and geometric confinement allow
enhanced parametric interactions. Such configuration further endows high-purity polariton states on
different branches to have phase-matched energy levels and increased density of states, thereby enabling
efficient parametric emission while preserving sub-1-meV linewidth. Benefiting from the efficient emission,
phase coherence between signal and idler polaritons in momentum space with clear visibility were observed,
showing the potential for coherent interactions into the quantum regime. With respect to the mechanism
that leads to strong parametric emission, corresponding experimental and theoretical studies reveal a
quantum size effect and highlight the crucial role of disorder in strongly confined regime. Finally, we
observed the room temperature supersolid phase utilizing the efficient coherent parametric oscillator. Our
findings reveal the crucial role of quantum confinement and disorder potential landscape in facilitating
exotic parametric interactions.

Results
Fig. 1a depicts the geometrical features of the CsPbBr microcavity, where an orthorhombic phase
3
single-crystalline CsPbBr microplatelet (MP) was embedded in a distributed Bragg reflector (DBR) cavity.
3
The CsPbBr was selected due to its large exciton binding energy, high photoluminescence quantum yield
3
and good structure stability, enabling robust room-temperature polaritonics27-30. The MPs were fabricated
by an anti-solvent route (Fig. 1b)31, which exhibit an anisotropic lateral dimension with L (length of x-
x
axis) > L (length of y-axis). The L is generally no less than 10 μm, while L can be as short as around2 μm
y x y
(Supplementary Fig. 2). Nevertheless, the MPs feature smooth facets and exhibit consistent optical
properties across the relevant range of lateral dimensions (Supplementary Fig. 2). Considering the polariton
thermal de Broglie wavelength (1.1–1.3 μm, Methods)32, the influence of L could be neglected, and we
x
therefore consider the spatial confinement and energy quantization according to L
y
dimension33. Since the
high-efficiency parametric emission (with a parametric ratio larger than 1 as shown in later discussions)
emerges when L decreases to 4.5 μm, we define the regime where L < 4.5 μm as strongly confined and
y y
L > 4.5 μm as weakly confined, respectively. Before evaporation of the top DBR, the MPs were transferred
y
to the bottom DBR with a viscous polydimethylsiloxane stamp to induce disordered surface potential as we
reported before (Fig. 1c)34. The surface disorder with 5–15 nanometers of depth and few-hundred
nanometers of lateral dimension poses trivial degradation on the cavity quality after top mirror
encapsulation.

Inset on the lower right part of Fig. 1a depicts the two types of potential that affect the polariton
interaction schemes: geometric confinement and surface disorder, which are reflected correspondingly in
the dispersion of such microcavity (Fig. 1d, L : 3.7 μm, excitation: CW, 405 nm). The micron-scale
y
thickness of MPs enables multiple sets of lower polariton branches (LPBs) which further split into
transverse electric (TE) and transverse magnetic (TM) branches due to material birefringence35. The
coupled oscillator model fitting in both polarizations are depicted in Supplementary Fig. 7, showing strong
coupling characteristics. To illustrate the respective roles of confinement and disorder on polariton
dispersion, TM polarized PL spectra was collected from this microcavity on sites (Supplementary Fig. 8)
with weak disorder (Fig. 1d, left panel) and moderate disorder (Fig. 1d, right panel). The spacing for lowest
two energy levels are 6.0 meV and 7.2 meV respectively for the two LPBs depicted on left panel, consistent
with the model considering L dimension and polariton effective mass in the small wavevector limit2
y
(Supplementary Fig. 7). For the moderate disorder regime, additional energy levels arise with an overall
narrowed linewidth, making the dispersion further enriched to fulfill phase matching condition and to
enhance polariton parametric interactions through lifted degeneracy34,36-39. Here the lowest energy level
associated with disorder lies 5.46 meV above the one associated with confinement, reflecting an effective
disorder height of ~8 nm (Supplementary Fig. 8)33. In such strongly confined cavity with dressed surface
disorder, polaritons are herein considered in the ‘quantum confinement’ regime where polariton interactions
are modified on de Broglie wavelength scale and give rise to anomalously strong and coherent parametric
emission (Fig. 1e). When condensation occurs on ground state, acting as ‘source’ polariton, efficient
parametric process initiates and scatters to neighboring branch with symmetric wavevector (k) position,
which are referred to as ‘signal’ and ‘idler’ polaritons, respectively.

As illustrated in Fig. 2a for a MP with L = 1.9 μm, when pumped non-resonantly (1 kHz, 100 fs, 400
y
nm) above condensation threshold, in addition to the condensate spanning the central region in angle-
resolved PL spectra, two sharp emissions corresponding to signal and idler states emerge, with intensity
rivaling that of the condensate. In the energy-degenerate interbranch parametric scattering process,
components near k = 0 would serve as the most effective source to create parametric polariton pairs at
y
opposite in-plane wavevectors, due to the highly satisfied phase matching condition5,7,40,41. Therefore, we
extracted the spectra from central region of the respective states (Supplementary Fig. 9), considering that
the source emission is broadened due to spatial confinement33. As shown in Fig. 2a right panel, strong signal
and idler emission exhibited linewidth down to ~0.78 meV, with signal emission reaching ~1.35 times the
intensity of remaining source emission. The above-unity signal-to-source ratio suggests depletion of the
source state in the stimulated regime and indicates highly efficient nonlinear parametric process, a
characteristic that has likewise been reported in pure-photonic OPOs42,43. The depletion of source state has
also been observed in intrabranch polariton OPOs in the stimulated regime44,45. In our theoretical study, an
above-unity ratio has also been observed as presented in the following discussion on quantum size effect.
An imbalance in the intensity of signal and idler emission could also be observed, which is expected in
these microcavities dressed with disorder and confinement37,46,47, considering the asymmetry in both
population and depletion pathways in the driven-dissipative system.

Furthermore, to recognize the population mechanism for nonlinear parametric emission, resonant and
non-resonant pump experiments were performed in an identical microcavity (Supplementary Fig. 10–12).
The comparable parametric ratio and intensity growth behavior suggested the dictating role of nonlinear
parametric scattering, rather than direct condensation fed by the exciton reservoir. Meanwhile, we observed
that blue shifting the source condensate via increasing pumping fluence simultaneously blueshifts the signal
and idler emissions, with their wave vectors shifting toward larger values, governed by the parabolic
dispersion of the LPB22,23 (Supplementary Fig. 13). In addition, to exclude the edge scattering effect
previously observed for the laterally confined cavities, we performed real-space-resolved spectroscopy of
a strongly confined microcavity and identified that the parametric emission solely comes from center of the
microcavity (Supplementary Fig. 14).

To estimate the parametric emission intensity and coherence, a comparison with reported values10,11,13-
16,23 was summarized and plotted in Fig. 2b, in respect of linewidth and parametric emission ratio. Our
parametric emission with intensity rivaling that of the source condensate while maintaining sub-1-meV
linewidth shows superiority as an efficient coherent polariton parametric oscillator. Such pure emission
holds promise to study coherent interactions for parametric polaritons. We use k-space interferometry as a
proof-of-concept demonstration to show its capability. Fig. 2c shows the experimental configuration: the
Michelson interference with images superimposing mirror-symmetrically were carried out in k-space, with
signal and idler polariton emission on two opposite k directions superimposed with each other. To directly
visualize the superiority of strong parametric emission with preserved coherence in quantum confinement
regime, we compare the k-space interferometry in a strongly confined microcavity and a weakly confined
cavity (both dressed with disorder) at time delay of ~0.03 ps. Fig. 2d shows the momentum space
interferogram for a strongly confined microcavity at 9 μJ cm-2 (1.5 P ) where clear interference fringes
th
were observed for overlapping signal and idler polaritons, as circled out by white dashed boxes on one side
of the Fourier plane. The visibility is calculated to be ~0.72 according to the line profile of the interference
fringes (Fig. 2e). Such visibility demonstrates strong phase coherence between signal and idler polaritons
in our microcavities. In contrast, for the weakly confined microcavity, when it was pumped at similar level
(10 μJ cm-2, 1.5 P ), parametric emission is rather weak (Supplementary Fig. 15). Therefore, higher pump
th
fluence (20 μJ cm-2, 3.0 P ) is needed for the generation of strong parametric emission comparable with
th
the strongly confined microcavities (Fig. 2f). Such pump fluence inevitably leads to dephasing processes
and broadening of the linewidth of signal and idler polaritons (Fig. 2f and g, Supplementary Fig. 16).

The role of confinement in enhancing polariton–polariton interactions can be anticipated from the
increased wavefunction overlap and thus stronger nonlinear coupling, as has been reported in a variety of
microcavity configurations36,37,39,48. However, in previously reported confined schemes13,14, the parametric
emission intensity is often not substantially improved compared to planar microcavities. In our case, the
disorder potential acts as the key enabler for the observation of strong coherent parametric emission. To
qualitatively illustrate its role, we investigated variation of parametric emission with different levels of
disorder (Supplementary Fig. 17). The markedly enhanced parametric emission in the presence of a
moderate amount of disorder highlights its crucial importance in triggering efficient parametric emission.
The disorder potential breaks overall inversion symmetry and thereby lifts the degeneracy for wavevector
selection rules36,39,49, allowing the parametric process to occur under less stringent conditions.

To further examine how confinement and disorder correlate and mediate parametric interactions, we
compiled a statistical data set with the lateral confinement size (L ) taken as the independent variable. The
y
confinement size (L ) can be accurately defined, whereas the degree of disorder is difficult to parameterize.
y
For each size, all accessible disorder configurations measured are included, effectively averaging over
random realizations and allowing the overall trends and systematic behavior to be revealed. The statistical
analysis is shown in Fig. 3 and carried out in parallel with theory based on the driven-dissipative Gross-
Pitaevskii equation as described in the Methods section. An identical trend is observed for experiments
(scatters) and theoretical results (lines) that with decreasing confinement dimension, the fluctuation in
parametric scattering ratio becomes stronger. Such phenomenon is typically observed in strongly interacting
systems such as nano-sized superconductors50-53. For small particles or thin films, trivial size variation could
lead to evident changes in number of energy levels near the Fermi energy, causing prominent fluctuations
in the spectral density and are reflected in a gradually increasing fluctuation in order parameters like
superconducting transition temperature52 or energy gap53, etc.

Adopting the scheme to our polariton OPO, we attribute such rapid fluctuation to an analogous quantum
size effect. When the system size (predominated by confinement L in CsPbBr microcavity) becomes
y 3
comparable to de Broglie wavelength32, disorder potential would induces a strong sensitivity of nonlinear
processes to system parameters like energy level position, energy level density of states, etc. In this regime,
quantization of energy and momentum becomes strong and starts playing significant roles in mediating
parametric interaction strength. Disorder in such quantum confinement configuration induce significant
fluctuations in energy positions and density of states for signal, source and idler on respective LPBs even
with small perturbations, strongly affecting the phase matching conditions and final state population density
to stimulate efficient parametric scattering. As a result, the parametric ratio becomes rapidly oscillating as
depicted by eye-guided background peaks in Fig. 3a. The fine-energy-matching mechanism could also be
reflected in the gradually decreasing energy mismatch of signal and source, idler and source with increasing
pump fluence (Supplementary Fig. 18) and acquisition of highly efficient parametric emission in strongly
confined microcavities with small mismatch (shown in Supplementary Fig. 19 in a histogram map that
correlates energy mismatch into the counted ratio).

Disorder is present in all cavities, but its impact becomes most pronounced when confinement approaches
dimension comparable to the polariton de Broglie wavelength. To quantify the fluctuations and accessible
ratios across confinement regimes, we select two confinement ranges (1.8–3.6 μm, and 10.8–12.6 μm) and
plot the corresponding fluctuation level in probability histogram. For strongly confined regime (upper
panel), the histogram distributes in a broad ‘ratio’ range and exhibits a probability amplitude that decreases
with larger ‘ratio’. However, in weakly confined systems (lower panel), such histogram mainly distributes
in a small ‘ratio’ range on the lower value side. Although the distribution shown in Fig. 3a and b refers to
the randomness in emission intensity, a statistical analysis on its maximum and average value is meaningful
in finding the expectation values in obtaining an efficient parametric oscillator, as shown in Fig. 3c. An
increasing trend is observed for both maximum (red) and average (blue) values in scattering efficiency
when decreasing confinement, indicating that the role of disorder is fully revealed in the strongly confined
regime.

The coherent interacting nature, combined with conjugated k-space position of the parametric polaritons
makes energy-degenerate OPO an ideal platform to investigate crystallized supersolid phase of the quantum
fluid of light. The recently observed supersolidity of polariton OPO in GaAs at liquid helium temperature
is a crucial step towards this goal22,23. Benefitting from the large exciton binding energy and robust light-
matter interaction of CsPbBr at room temperature27,29,30,34,54,55, we realize such supersolidity at ambient
3
conditions, substantiated by the observation of two thresholds in parametric emission growth behavior, and
coordinate space pattern formation with a period correlated with k position of the parametric polariton.
As illustrated in Fig. 4a, the evolution of intensity exhibits two nonlinear thresholds (marked by black dashed
lines), with sub-linear growth at low pump fluence and subsequent nonlinear growth of source (5.35 μJ cm-
2) and signal/idler (7.44 μJ cm-2), respectively. Different growth behavior of parametric emission with
respect to source BEC density (I) is retrieved by examining the respective intensity evolution closely near
the two thresholds, as shown in Fig. 4b and denoted by I, I0.25, and I0.9. Below the first threshold, incoherent
relaxation from the exciton reservoir, and linear scattering from source polariton is responsible for the
population at signal and idler states. Crossing the first threshold, source condensate first exhibits nonlinear
growth. With source condensate population building up, nonlinear parametric scattering was initiated and
nonlinearly increases the signal and idler intensity, accompanied by a dramatic reorganization in momentum
space as shown in the insets of Fig. 4b. The left inset depicts a uniform exciton reservoir distribution, while
the right inset highlights coherent parametric scattering between the source condensate and conjugate
signal/idler polaritons. Respective angle-resolved PL spectra and momentum space images for this
microcavity at different pump fluences are depicted in Supplementary Fig. 20.

As shown in Fig. 4c–f, for two parametric oscillators with angle-resolved PL spectra (Fig. 4c and e)
showing signal and idler polaritons centered at distinct wavevectors (8.0 μm-1 and 7.2 μm-1), corresponding
features were observed in real space emission patterns. The real space images (Fig. 4d and f, upper panels)
with striking periodic fringes confirm a ‘lattice’ constant of 0.78 μm and 0.87 μm by extracting the line
profiles (lower panels). Such spatial periodicity aligns precisely with the momentum-space emission peaks
via Fourier reciprocity, confirming the spontaneous ‘crystallization’ of the polariton condensate and its
supersolid nature. We believe that such coherent parametric emission with intensity comparable to source
condensate enables direct observation of an anomalous supersolid phase with periodic stripes in real space,
which would otherwise be obscured by strong source condensate emission. In strongly confined
microcavities, such phenomenon with correlated momentum space position and real space fringe spacing
was also observed (Supplementary Fig. 21), except with presence of limited number of fringes due to the
finite dimensionality. Circumventing the extreme cooling requirements of traditional quantum fluids
establishes the optical parametric oscillator in our microcavity as an ideal testbed for emergent macroscopic
quantum effects.

In summary, this work establishes quantum confined semiconductor microcavities as a robust platform for
strong coherent parametric polariton generation through the synergistic interplay of geometric confinement
and surface disorder. Highly efficient parametric emission is achieved in presence of disorder in the strongly
confined regime, with parametric emission intensity rivaling those of the source condensate, while
preserving high spectra-purity with sub-1-meV linewidth. The ultra-narrowband emission enables the
observation of phase coherence between signal and idler polaritons. Statistical analysis from experiments
and theory reveals the role of quantum size effect in mediating parametric emission intensity in the quantum
confined microcavity. In addition, the efficient emission enables direct observation of emerging supersolid
phase at room temperature. These results demonstrate that non-trivial potential landscape act as key
enablers of unconventional parametric phenomena—which could be readily extended to other material
platforms, providing transformation strategies to harness polariton nonlinearities and accelerate the
development of quantum photonic devices.

Methods
Perovskite Synthesis
The CsPbBr microplatelets were synthesized using an anti-solvent method31. CsBr and PbBr powders of
3 2
analytical grade were mixed in a 1:1 molar ratio and dissolved in dimethylformamide to prepare a 20 mM
precursor solution. Glass substrates were placed in a placed in dichloromethane anti-solvent filled beaker,
and the precursor solution was dropped onto the substrates, as shown in Supplementary Fig. 2a. Beaker was
covered with perforated Parafilm to and placed in an oven with temperature of 30 ℃ for 48 h, enabling
evaporation and CsPbBr single crystal growth. The synthesis procedure yields microplatelets of various
3
lateral dimensions, shown in Supplementary Fig. 2b.

Microcavity Fabrication
The CsPbBr microcavity consists of top and bottom distributed Bragg reflector (DBR) mirrors and the
3
central CsPbBr microplatelets. Bottom DBR consists of 20 pairs of electron-beam evaporated titanium
3
oxide (TiO ) and silicon dioxide (SiO ) with quarter-wavelength thickness, and top DBR consists of 8 pairs
2 2
of such oxide layers. CsPbBr microplatelets were dry transferred to bottom DBR with
3
polydimethylsiloxane (PDMS) stamps, followed by ~60 nm PMMA layer encapsulation before top mirror
evaporation, acting as protection layer for perovskites.

Optical Characterization
Optical characterization was conducted using a custom-built system based on Fourier imaging, allowing
for both real-space and momentum-space resolved spectroscopy and imaging. For real space imaging and
spectroscopy on the micron-scale sized sample, a short-focal length lens was used to magnify the image, to
resolve emission from the microplatelet microcavity. A Michelson interferometer with mirror symmetric
configuration was utilized to investigate first-order spatial and temporal coherence in both real space and
k-space. Pump laser spot size was enlarged by a long focal distance lens in the excitation path, as shown in
Supplementary Fig. 6. Emission from the sample was captured with a 100× objective (NA = 0.9) and
spatially filtered with an adjustable rectangular aperture at the focal plane and directed to a liquid nitrogen-
cooled charge-coupled device (CCD) spectrometer (Princeton Instruments, SP-2500i). For pulsed
excitation, the 800 nm fundamental pulses (100 fs, 1 kHz) from a Coherent Astrella regenerative amplifier
were directed to a beta barium borate (BBO) crystal to generate non-resonant pump pulses at 400 nm, or
directed to an optical parametric amplifier (Coherent OperA Solo) to generate resonant pump pulses at 540
nm. Continuous-wave excitation was performed using a 405 nm laser.

Other characterizations
Atomic force microscopy (AFM) imaging was carried out in tapping mode with a BRUKER Dimension
ICON system, while laser confocal microscopy was performed using a Zeiss LSM800 Airyscan confocal
microscope. X-Ray diffraction (XRD) measurement was performed with Rigaku XtaLAB PRO. Annular
dark-field scanning transmission electron microscopy (STEM) characterization was performed with Titan
Cubed Themis G2 at 300 kV voltage. SEM images were obtained from Thermo Fisher Helios G4 UX
DualBeam system.

Theoretical model
Our theoretical description of parametric interaction in a microcavity is based on two lower polariton
branches (labeled by the index 𝑛 = 1,2), which originates from the strong coupling of excitons with two
different cavity modes. Each polariton branch in the two-dimensional microcavity planes follows the two-
component driven-dissipative Gross-Pitaevskii equation:

𝝏𝝍 (𝐫,𝒕) 𝒊
𝒊ℏ 𝒏 =[𝑬̂𝐋𝐏+𝑽 (𝐫)− (𝜸−𝑷 (𝐫,𝒕))−𝒊𝚪E|𝝍 (𝐫,𝒕)|𝟐]𝝍 (𝐫,𝒕)
𝝏𝒕 𝒏 𝐝𝐢𝐬 𝟐 𝒏 𝒏 𝒏
+𝟐𝜶𝝍 (𝐫,𝒕)𝟐𝝍∗(𝐫,𝒕)+𝟐𝜶𝝍 (𝐫,𝒕)𝟐𝝍 (𝐫,𝒕)
𝒎 𝒏 P𝒎 𝒏
where 𝐸LP(𝑘) is the kinetic energy operator of the 𝑛-th lower polariton branch, 𝑉 (𝐫) represents the
𝑛 dis
disorder potential in the microcavity, 𝛾 represents decay, and 𝑃 (𝐫,𝑡) represents the net gain to the lower
𝑛
polariton branches. The kinetic energy operator is given by,

𝑬𝐋𝐏(𝒌)= [𝑬 𝒏 𝐜𝐚𝐯 (𝒌)+𝑬 𝐞𝐱 −√(𝑬 𝐜𝐚𝐯 (𝒌)−𝑬 𝐞𝐱 )𝟐+𝙂𝟐] (2)
𝒏 𝟐
where 𝐸cav(𝑘) represents the n-th cavity mode energy, 𝐸 represents the exciton energy and Ω is the
n ex
Rabi-splitting energy. The parametric scattering effects are induced by the nonlinear interaction between
polaritons that are represented by the parameter 𝛼. The nonlinear decay term 𝛤 represent the saturation of
the polariton density due to the effective reduction of the exciton-reservoir induced gain upon the significant
polariton density. Detailed parameter values for the theoretical model are provided in Supplementary
Information.

Polariton de Broglie wavelength
In our microplatelet microcavities, polariton effective mass is 1.1×10-5 m –1.5×10-5 m for most LPBs of
e e
interest for parametric emission. Therefore, polariton thermal de Broglie wavelength32 ( 𝜆 = 
dB
√2πℏ2(𝑚 𝑘 𝑇)−1) is 1.1–1.3 μm.
eff B

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Deng et al. reports efficient parametric emission from CsPbBr3 microcavities while preserving a sub 1meV linewidth. The authors claim that the mechanism enabling the highly efficient generation of parametric emission is modulated by quantum confinement. Furthermore, the authors observe spontaneous ‘crystallization’ at room temperature forming a supersolid phase with real space periodicity. The work is relevant to the community, the efficient generation of narrow linewidth parametric emission is a remarkable outcome. However, a deeper analysis of the mechanism enabling this process is essential to make this a scalable process.\nMain Comments:\n1) The manuscript attributes the discretization of the polariton dispersion to a combination of geometric confinement and disordered surface potentials, with a reported 7.5 meV mode spacing. However, the discussion does not clearly distinguish the contributions from in-plane confinement and disorder. A systematic study isolating the effects of in-plane confinement, and surface roughness, such as comparing dispersions for different lateral sizes and controlled disorder amplitudes, would strengthen the mechanistic interpretation and clarify the origin of the observed discretization. From Fig. 1b, the roughness reaches ~10 nm, an analysis showing that this amplitude can localize lower polaritons and yield a level spacing on the order of the observed, would be beneficial. To separate the two contributions, k-space reflectance for similar cavities with reduced surface roughness would explain how the spacing and the appearance of discrete lines evolve relative to surface roughness.\n2) The term “non-confined cavity” needs an explicit definition. A more detailed explanation of what this means would benefit the paper. Does this denote a planar microcavity with a larger crystal? The authors should report the fabrication process for this larger device. Providing these details will allow for a fair comparison with the confined structures.\n3) The authors claim that the disordered surface potentials that are formed as a result of the fabrication process are instrumental in generating fine modes and efficient parametric emission. However, the role of the disorder in enhancing parametric emission if not quantitively measured. A study of how the different levels of surface roughness effect the signal /ideler ratio would be beneficial.\n4) The authors chose CsPbBr₃ as the active material, but the manuscript does not justify why this particular halide perovskite is uniquely suited for sustaining parametric scattering and supersolid behavior. Could other halide compositions (e.g., CsPbI₃, mixed halides, or hybrid organic-inorganics) offer advantages in terms of exciton binding energy, linewidth, or tunability of the cavity modes? A few sentences in the introduction would help here.\n5) The manuscript would benefit from structural characterization of the CsPbBr₃ microplatelets. While the microcavities are strongly characterized, no direct evidence is provided for the crystallographic quality or phase purity of the material. Techniques such as X-ray diffraction could confirm the absence of secondary phases, strain, or structural defects that might influence the dispersion and parametric scattering behavior. Including such data would strengthen the link between the observed effects in the strongly coupled system and the intrinsic properties of the active material, and ensure that the reported effects are not influenced by variations in material quality.\n6) Given that perovskites are prone to point defects and surface traps, how do the authors ensure that these do not dominate the coherence and linewidth of the parametric emission? Is there any passivation strategy or post-treatment applied or can you comments on how that might affect properties?", "reviewer_2": "The manuscript “Harnessing highly efficient coherent polariton parametric emission in quantum confined perovskite microcavities” by Xinyi Deng et al. reports the first-time observation of resonantly enhanced parametric scattering of exciton- polaritons in a halide perovskite microcavity. The authors emphasize the key result of their work: the strong influence of in- plane polariton quantization, accompanied by potential disorder, on the nonlinear optical response of the studied system. They experimentally observe coherent polariton emission involving parametric scattering and also claim the “first observation of strong phase coherence between the two parametric species in momentum space.”\nThe importance of the observations is not in doubt: the suggested arrangement is suitable for generating phase-correlated photon pairs, with potential for operation down to the single-photon regime. The halide perovskite platform is favorable in this sense, as it is known for its ultimate quantum efficiency of exciton-enabled light emission.\nThe manuscript is generally well-written. However, some further clarifications and polishing of the text would be beneficial, as noted below. The team employs well-established experimental methods; therefore, the data quality is suitable. The analytical model is clear; some parameters used need to be specified in the updated version of the manuscript.\nAlthough I am generally positive about this work, I must point out that some of the authors’ claims require further justification. The authors have to address several questions before I can recommend this work for publication in Nature Communications.\nMajor issue:\nMy primary concern is related to the mechanisms of population of signal and idler states. I can suggest at least three of those:\n(1) Conventional relaxation from the reservoir to a resonant state (gain).\n(2) Linear scattering of polaritons from the source to signal and idler states.\n(3) Nonlinear parametric scattering of source polaritons towards signal/idler state, claimed as the primary mechanism.\nFirstly, the right panel in Figure 2a clearly shows the strong asymmetry in signal (1.36)/idler (0.43) relative intensities. In case of mechanism (3), exclusively responsible signal/idler population, this picture must be purely symmetric. The largest of these two values is compared to other works in Figure 2b and is referred to as “parametric emission efficiency”, which might mislead the reader. This efficiency is fundamentally limited by the minimum of the two values mentioned for each particular measurement.\nThe authors state in the text: ”Below the first threshold, incoherent relaxation from the exciton reservoir is responsible for the population at signal and idler states.” It is unclear why authors neglect this mechanism when discussing the system behavior above the first thresholds.\nLet me suggest an explanation of the observed effects involving only mechanisms (1) and (2). Above the first threshold, the condensate appears at the source state. The polaritons there undergo elastic scattering into signal/idler modes, with efficiency enhanced by surface disorder. These scattered polaritons seed the condensates in signal/idler states, which appear at a larger threshold and remain coherent with the source, as they are seeded by polaritons coming from it. Another reason for the signal, source, and idler states to be mutually coherent is the complete overlap of these modes in real space.\nThe condensation threshold for the signal/idler states can be larger than that of the source state for several reasons, including differences in polariton lifetimes. The nearest polaritonic state below the source is more than 50 meV apart, while for signal/idler states, this distance is below 10 meV.\nI firmly believe that with this massive amount of experimental data in hand, authors can distinguish between mechanisms (1- 3) more accurately.\nAnother way to completely exclude the mechanism (1) from the list is to perform additional measurements with the resonant pumping of the source state by appropriately tuning the excitation photon energy and adjusting the spot size to avoid direct excitation of signal/indler modes. To distinguish pump photons from those in a condensate (and estimate the condensate emission rate), one can pump at an angle, staying within the positive/negative in-plane wavevectors, yet remaining resonant with the source mode.\nAdditional related question: What are the values of net gains P_n for signal, source, and idler used for the modelling in Figure S11?\nMinor remarks:\n1. In the manuscript, only the elastic scattering process is discussed. Meanwhile, Figure 2c reveals an apparent spectral mismatch between signal, source, and indler emission peaks. Owing to the inversion symmetry of the system, is there any explanation for this effect? Could it be a measurement artifact, such as a slight misalignment of the CCD camera, which needs to be corrected during data post-processing?\n2. In the text, the authors compare confined and unconfined microcavities. Unfortunately, I was unable to find the two respective definitions. It is worth clarifying this for the reader.\n3. I suggest adding a discussion on the role of the second dimension of the rectangular microcavities. Why can the confinement in the second dimension be neglected?\n4. I was also unable to find an explicit discussion of the role of potential disorder. How does surface roughness improve the system's performance?\nOne aspect could be as follows. Polariton, scattering on surface roughness, may acquire an additional portion of momentum, inversely proportional to the lateral size of the surface feature. This process, therefore, enhances scattering from the source to signal/idler states.\n5. Authors state: “Meanwhile, downscaling the confinement dimension leads to energy eigenstates with larger spacing that induces the randomness in matching of source and signal/idler energy position, leading to a larger fluctuation amplitude in parametric interaction strength and acquisition of highly efficient parametric emission in confined microcavities.”\nIndeed, the LA1 and LA2 branches have generally different sets of quantized levels. The detuning (and overlap) between the fundamental level of LA1 (the source state) and the nearest LA2 state is expected to significantly affect both linear and nonlinear elastic scattering processes in the system.\nIn this context, would the data presented in red symbols in Figure 3a, showing nearly random behavior, become better structured when used to correlate signal&idler/source with the LA1-LA2 nearest-level detuning? Of course, the randomness induced by surface roughness will stand.\n6. Within the text, one can find many terms, probably referring to the exact property of the system under study: surface potential landscape, disorder potential landscape, disordered surface potential landscape, transfer-induced potential landscape, disorder potential, etc. I recommend leaving a single term.\n7. The authors should proofread the Supplementary Material:\nFigure S2 ( “microscope” misspelled),\nFigure S5 (d-f) - is it a single frequency or summation over a range?\nFigure S6 (b) and (a) should be exchanged.\nFigure S7 (g) instead of (b). It is unclear why the source and idler energy- and wavevector-dependent spectra are plotted on different axes. I suggest using the exact representation and adding the signal plots as well.\nI would be glad to review the revised manuscript if the authors address the concerns and questions that have been raised.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "The work by Deng et al. reports on the efficient generation of parametric emission in a polaritonic microcavity. The authors claim that the presence of random in-plane potentials is responsible for the observed anomalous enhancement of parametric scattering. To support their claims, they first present a comparison among three configurations: a non-confined microcavity (showing low-efficiency scattering), a laterally confined cavity without random potential (showing no parametric scattering), and a laterally confined cavity with random potential (exhibiting highly efficient scattering). They then perform statistical analysis to justify the observed high efficiency and develop a theoretical model. Finally, they also present evidence of supersolidity at room temperature.\nThe topic is certainly interesting, and the overall idea of investigating the role of disorder and lateral confinement in the regime of nonlinear polariton scattering is nice. However, I found some aspects of the work problematic and the final claims somewhat unclear. The authors attempt to highlight the role of disorder, suggesting that scattering is not observed in a similar laterally confined structure without disorder. This implies that disorder is a fundamental requirement. However, a close examination of Fig. S9 clearly shows that phase matching cannot be satisfied in that case. Therefore, the comparison is not accurate, and the authors’ claim appears incorrect, especially considering that parametric scattering has been previously observed in laterally confined systems (e.g., 10.1103/PhysRevB.87.155302). Indeed, they later acknowledge that downscaling the lateral confinement introduces randomness in the phase-matching conditions, leading to larger fluctuations in the occurrence of highly efficient parametric emission. However, it is unclear what the authors are precisely claiming here. If they intend to argue that strong and coherent parametric emission is uniquely associated with laterally confined disordered microcavities, then they should present a reference sample—free from disorder but with well-matched phase-matching conditions—for a meaningful comparison. Otherwise, the role of disorder appears to be limited to mode broadening which facilitate phase matching, which is less significant.\nEven the comparison with the non-confined system is problematic. The sample shown in Fig. S8 exhibits a more positive detuning (with visible lasing around 2323 meV), while the confined-disordered cavity is more negatively detuned (~2300 meV). This results in a higher excitonic fraction for the non-confined sample, which strongly influences both the visibility of the parametric emission and, in fact, the condensate itself. The condensate at k=0 in the non-confined sample appears to have lower visibility compared to that of the confined-disordered cavity. Therefore, this comparison does not convincingly support the claims regarding coherence. Moreover, the reported efficiency value—while I appreciate the large statistical analysis and the effort put into developing a suitable model—also appears problematic. The claimed efficiency seems to exceed the theoretical limit for a parametric process, in which the combined intensity of the signal and idler cannot surpass that of the pump. This suggests that there may be an issue in how the overall intensity of the condensate is being evaluated.\nOverall, although the work has potential, I cannot recommend publication of the manuscript in its current form. A clear and convincing demonstration of the key claims—particularly regarding the role of disorder and the reported efficiency—is necessary before the work can be considered for publication.\nBelow is a list of my comments.\n-In the introduction, the authors cite the work from J. Wu et al. (10.1021/acs.nanolett.1c00283), stating that the reported case exhibits suboptimal parametric emission efficiency and that pump powers \"several times\" above the condensation threshold are required to observe parametric scattering. However, upon reviewing the referenced paper, it is clear that parametric scattering is already visible at pump powers 2–3 times above the condensation threshold. This would more accurately be described as \"a few times,\" rather than \"several,\" and does not support the implication of particularly poor efficiency.\n-The authors used the same sample in one of their recent publications to observe polariton condensation under CW excitation. Why a pulsed excitation scheme was chosen for the present experiments?. Could the authors show how the excitation regime (CW vs. pulsed) influences the key observed properties—such as parametric efficiency, linewidth, and coherence? Are these parameters intrinsic to the system or strongly dependent on the excitation conditions?\n-Still regarding the excitation scheme, polariton parametric scattering has been extensively studied in GaAs-based 1D microcavities, where, under resonant excitation, compelling evidence for phase matching and its critical role in the scattering process has been demonstrated (10.1103/PhysRevB.87.155302, 10.1002/pssb.201100115). Have the authors attempted similar measurements under resonant excitation? Would the reported effects—particularly the claimed high efficiency and coherence—still hold under pulser or CW resonant excitation? These experiments would help to establish the generality and robustness of the observed phenomena.\n-Regarding the surface-smooth sample shown in Fig. S9, it is unclear why the discretization of the TE₁ and TM₁ modes is not visible. Given that this sample is used as a key comparison point, the absence of clear mode discretization raises questions about the confinement quality. As mentioned earlier, to convincingly support their claims about the role of disorder, the authors should identify a surface-smooth sample with good phase matching, similar lateral dimensions, and comparable detuning.\n-How are the overall intensities of the signal, idler, and source evaluated? Part of the condensate signal may propagate outside the excitation region and thus be excluded from the intensity measurement. If so, this could lead to an underestimation of the total condensate power and therefore to high efficiency. Additionally, the authors should provide an estimate of the experimental uncertainty associated with the efficiency ratio evaluation.\n-The authors emphasize that the presented configuration enables the generation of balanced signal and idler beams. However, in Fig. 2a, the idler appears to be approximately three times weaker than the signal. The authors should clarify the origin of the imbalance.\n-For the non-confined microcavities below threshold dispersion should be shown."}, "author_response": "Response to Reviews (NCOMMS-25-52756-A)\nResponse to Reviewer 1\nThe manuscript by Deng et al. reports efficient parametric emission from CsPbBr\n3\nmicrocavities while preserving a sub-1-meV linewidth. The authors claim that the\nmechanism enabling the highly efficient generation of parametric emission is\nmodulated by quantum confinement. Furthermore, the authors observe spontaneous\n‘crystallization’ at room temperature, forming a supersolid phase with real space\nperiodicity. The work is relevant to the community, the efficient generation of narrow\nlinewidth parametric emission is a remarkable outcome. However, a deeper analysis of\nthe mechanism enabling this process is essential to make this a scalable process.\nResponse:\nWe thank the reviewer for the careful evaluation of our manuscript. We are grateful for\nthe positive comments on the novelty of our work and the on the significance of\nefficient parametric emission with coherent features. We also appreciate the\nconstructive suggestions on clearer identification of energy levels, and illustration of\ndisorder in enhancing parametric emission, which have helped us in a clearer\ndemonstration of the effect of the geometric features. Following these\nrecommendations, we have added additional experimental results together with\nextended analysis and discussions, which we believe could address the reviewer’s\nconcerns. The point-by-point responses are highlighted in blue color, and the\ncorresponding modifications in the main text are marked in blue color.\nComment 1:\nThe manuscript attributes the discretization of the polariton dispersion to a combination\nof geometric confinement and disordered surface potentials, with a reported 7.5 meV\nmode spacing. However, the discussion does not clearly distinguish the contributions\nfrom lateral confinement and disorder. A systematic study isolating the effects of lateral\nconfinement, and surface roughness, such as comparing dispersions for different lateral\nsizes and controlled disorder amplitudes, would strengthen the mechanistic\ninterpretation and clarify the origin of the observed discretization. From Fig. 1b, the\nroughness reaches ~10 nm, an analysis showing that this amplitude can localize lower\npolaritons and yield a level spacing on the order of the observed, would be beneficial.\nTo separate the two contributions, k-space reflectance for similar cavities with reduced\nsurface roughness would explain how the spacing and the appearance of discrete lines\nevolve relative to surface roughness.\nResponse 1:\nWe thank the reviewers for the valuable suggestion on assigning energy levels in Fig.\n1 more clearly to confinement and disorder, which helps us illustrate the role of\n‘confinement’ and ‘disorder’ in the dispersion more explicitly. And we thank the\nreviewer for the helpful suggestions on possible methods to identify the energy levels.\nHere in the revised manuscript, we employed two approaches to isolate the respective\nenergy levels and revised the respective Fig. 1 dispersion.\nAs the reviewer suggested, precisely controlling the disorder amplitude would be very\nvaluable; however, this remains extremely challenging at present. Given the constraints\nof typical top-down fabrication methods (Nat. Commun. 15, 3345 (2024), Science 367,\n1018–1021 (2020)), it is difficult to reliably achieve the required dimensional profile\nshowing an lateral size ranging from several tens to several hundred nanometers,\ncombined with a thickness of 5–15 nm. Thus, herein we employed spatial selection of\nthe PL from different sites showing different degrees of disorder in a microcavity\nsample (L = 3.7 μm, L = 12.6 μm, Fig. R1a). As shown in Fig. R1b, the TM polarized\ny x\nangle-resolved PL spectrum at location-1 (left panel, weak or nearly without disorder)\nreveals the confinement induced energy level quantization on the two lower polariton\nbranches (LPBs), with regularly spaced energy levels (highlighted with gray dashed\nlines) due to geometric confinement (Phys. Rev. B 74, 155311 (2006)), Phys. Rev. B 91,\n075305 (2015)). While in the angle-resolved PL spectrum for the location-2 (disordered\narea, right panel), more quantized energy levels appear in addition to the confinement\ninduced energy levels, suggesting the role of disorder. Moreover, in presence of\ndisorder, the overall linewidth for the LPB modes becomes narrower, indicating the\neffect of moderate level of disorders in generation of extra fine modes as we studied\nbefore (Sci. Adv. 11, eadr1652 (2025)).\nFig. R1. (a) Schematic for collection sites from a confined microcavity, with weak\nsurface disorder (1) and moderate surface disorder (2). (b) Angle-resolved PL spectra\n(TM polarized) from the sites in (a), where region (1) emission is mainly from\nconfinement, and region (2) emission stems from both confinement and disorder. Gray\ndashed lines highlight the energy levels on this LPB associated with confinement in y\ndirection.\nIn a confined microcavity with micron-scale size, the energy of the polariton could be\nwritten as (Phys. Rev. B 74, 155311 (2006), Phys. Rev. B 91, 075305 (2015))\n22 n2 n2 \nE   x  y V\nn x ,n y 2m*  L2 L2  0\n x y \nwhere E is the energy of LPB, m* as the effective polariton mass, n as the\nx,y\nquantum number for quantized lower polariton branches, L as the confinement size\nx,y\nfor x and y directions, V is the potential depth. In our CsPbBr MPs, L >> L , as we\n0 3 x y\nlater discuss in Response 2, the x-direction behavior could be treated as a free particle\nwith continuous momentum k while the y-direction experiences confinement and\nx\nenergy level quantization. The energy difference between adjacent states becomes\n22\n \nE  2n 1\n2m*L2 y\ny\nFor the lowest two energy levels (n = 0 and n = 1), the relationship becomes\n322\nE\n2m*L2\ny\nIn the microcavity as shown in Fig. R1b, the polaritons for LPB2 and LPB3 have\neffective mass (in the limit of small wave vectors, Rev. Mod. Phys. 82, 1489–1537\n(2010)) of 1.404×10-5 m and 1.160×10-5 m , respectively, and the calculated lowest\ne e\nenergy spacing for the two branches are 5.75 meV and 6.96 meV, close to the measured\nmode spacing of 6.0 meV and 7.2 meV, as shown in Fig. S7 and discussions. Therefore,\nsuch derivation could resolve quantized energy levels arising from geometric\nconfinement.\nFor a one-to-one correspondent characterization of AFM profile and polariton\ndispersion, we have demonstrated previously in Sci. Adv. 11, eadr1652 (2025). To\nillustrate the effect of 10 nm variation as raised by the reviewer, we conducted the\ntransfer matrix simulation (Optical Waves in Layered Media. Wiley, 1990, Phys. Rev.\nB 74, 155311 (2006)) of the cavity transmission with 10 nm perturbation in a thick\nperovskite cavity. As an example, the calculation shows that for a cavity with perovskite\nthickness of 2.0 µm, one of the resonant modes appear at 2305.10 meV. When the\nsurface 10 nm of the perovskite layer is replaced with PMMA (refractive index: 1.45),\nthe mode positions shift to 2311.30 meV, giving an energy shift of 6.20 meV in LPB\nbottom. The newly emerged lowest energy level as shown in Fig. R1b right panel lies\n5.46 meV above the original LPB bottom energy level, reflecting a disorder with ~8\nnm thickness, comparable with the disorder profile we depicted in Fig. 1. In addition,\nwhen multiple disorders coexist, their corresponding energy levels undergo further\nhybridization, giving rise to more intricate dispersion profiles. This phenomenon has\nbeen established in our prior work and will not be revisited here.\nRevision 1:\nMain text, page 4, Fig. 1b and Fig. 1d revised.\nMain text, page 3, added: ‘To illustrate the respective roles of confinement and disorder\non polariton dispersion, TM polarized PL spectra was collected from this microcavity\non sites (Fig. S8) with weak disorder (Fig. 1d, left panel) and moderate disorder (Fig.\n1d, right panel). The spacing for lowest two energy levels are 6.0 meV and 7.2 meV\nrespectively for the two LPBs depicted on left panel, consistent with the model\nconsidering L dimension and polariton effective mass in the small wavevector limit\ny\n(Fig. S7)1. For the moderate disorder regime, additional energy levels arise with an\noverall narrowed linewidth, making the dispersion further enriched to fulfill phase\nmatching condition and to enhance polariton parametric interactions through lifted\ndegeneracy2-6. Here the lowest energy associated with disorder lies 5.75 meV above the\nlowest energy level, reflecting an effective disorder height of ~ 8 nm (Fig. S8)7.’\nMain text, page 4, Fig 1d, caption, addd: ‘(d) Transverse magnetic (TM) polarized\nangle-resolved photoluminescence (PL) spectra from a microcavity with L = 3.7 μm\ny\n(excitation laser: CW, 405 nm). Left panel: weak disorder, predominated by L\ny\nconfinement; right panel: moderate disorder, affected by both L confinement and\ny\ndisorder potential (Fig. S8).’\nSI, page 7-9, added: Fig. S7 and Fig. S8, and discussion on the evaluation of energy\nlevels associated with confinement and disorder.\nComment 2:\nThe term “non-confined cavity” needs an explicit definition. A more detailed\nexplanation of what this means would benefit the paper. Does this denote a planar\nmicrocavity with a larger crystal? The authors should report the fabrication process for\nthis larger device. Providing these details will allow for a fair comparison with the\nconfined structures.\nResponse 2:\nWe thank the reviewers for pointing out the issue for a clear definition of confinement\nand the fabrication process. We fabricated the single-crystalline CsPbBr MPs using\n3\nthe anti-solvent synthesis route, as shown in Fig. R2, as we reported in previous studies\n(Nano Lett. 20, 6636–6643 (2020)). A glass substrate was placed in a petri-dish in an\nanti-solvent atmosphere. The beaker was filled with diluted anti-solvent and sealed with\nperforated Parafilm which enabled gradual evaporation and crystallization in the\nprecursor solution. Such process yields CsPbBr MPs with various lateral dimensions\n3\nfor the study in this work (Fig. 2b). Notably, neither external spatial confinement nor\npressure was applied during growth, which ensures uniform surface roughness and\ncrystallinity quality for the larger and smaller MPs. The as-grown MPs were then\ntransferred to bottom DBR and spin coated with PMMA and finally encapsulated with\ntop evaporated DBR mirrors. Fig. R2c and R2d show the AFM images and the time-\nresolved photoluminescence (TRPL) spectra on the MPs (before transfer process) with\nvarying lateral dimensions, respectively. The surface roughness is almost the same.\nMeanwhile, TRPL suggests identical bi-exponential decay curves with comparable fast\nand slow decay lifetimes, indicating similar defect densities and carrier recombination\nbehavior (Nat. Photonics 10, 295–302 (2016)).\nFig. R2. Fabrication and characterization for the CsPbBr MPs. (a) Schematic of anti-\n3\nsolvent synthesis procedure. (b) SEM images for tilted view of CsPbBr MPs before\ndifferent lateral dimensions. (d) The time-resolved photoluminescence for the MPs at\npump fluence of 1 μJ·cm-2. Excitation laser: 515 nm, 50 kHz, 250 fs.\nNext, we would like to explain the ‘confinement’ regime according to your suggestion.\nThe MPs typically exhibit an anisotropic lateral dimension with L (length of x-axis) >\nx\nL (length of y-axis). The L is generally no less than 10 μm, while L can be as short as\ny x y\naround 2 μm (Fig. S2). While polariton thermal de Broglie wavelength\n(   22(m k T)1 , Phys. Rev. Lett. 121, 067401 (2018)) is 1.1-1.3 μm.\ndB eff B\nTherefore, the confinement effect is considered according to L dimension. According\ny\nto the model of quantum size effect as displayed in Fig. 3, an evident increase in\nparametric emission ratio emerges at L ~4 μm, which we use as the ‘boundary’ for\ny\ndifferent levels of confinement. To make the statement clear, according to your\nsuggestion, we revise the ‘confined’ and ‘non-confined’ terminology to ‘strongly\nconfined’ and ‘weakly confined’, referring respectively to samples with L smaller than\ny\nor larger than 4 μm.\nRevision 2:\nMain text, page 3, added: ‘The MPs were fabricated by an anti-solvent route (Fig. 1b)8,\nwhich exhibit an anisotropic lateral dimension with L (length of x-axis) > L (length of\nx y\ny-axis). The L is generally no less than 10 μm, while L can be as short as around2 μm\nx y\n(Fig. S2). Nevertheless, the MPs feature smooth facets and exhibit consistent optical\nproperties across the relevant range of lateral dimensions (Fig. S2, S3). Considering the\npolariton thermal de Broglie wavelength (1.1-1.3 μm, Methods)9, the influence of L\nx\ncould be neglected, and we therefore consider the spatial confinement and energy\nquantization according to L dimension7. Since the high-efficiency parametric emission\ny\nemerges when L decreases to 4 μm as shown in later discussions, we define the regime\ny\nwhere L is ‘smaller than’ 4 μm as ‘strongly confined’ and L is ‘larger than’ 4 μm as\ny y\n‘weakly confined’, respectively.’\nMain text, page 4, the caption of Fig.1, added: ‘Inset shows cross-sectional view of the\nMP typical anisotropic dimension with y direction dimension (L ) approximately 2-4\ny\nμm, and the thickness typically ranging from 1 to 3 μm.Surface disorders are formed\nby a stamp transfer process. (b) Scanning electron microscope (SEM) image of an anti-\nsolvent grown CsPbBr MP with clear and smooth facets, and strong L confinement.’\n3 y\nMain text, page 12, Methods, added: ‘The CsPbBr microplatelets were synthesized\n3\nusing an anti-solvent method8. Glass substrates were placed in a placed in\ndichloromethane anti-solvent filled beaker, and the precursor solution was dropped\nonto the substrates, as shown in Fig. S2a. Beaker was covered with perforated Parafilm\nto and placed in an oven with temperature of 30 ℃ for 48 h, enabling evaporation and\nCsPbBr single crystal growth. The synthesis procedure yields microplatelets of various\n3\nlateral dimensions, shown in Fig. S2b.’\nMain text, page 13, Methods, added: ‘In our MP microcavities, polariton effective mass\nis 1.1×10-5 m -1.5×10-5 m for most LPBs of interest for parametric emission. Therefore,\ne e\npolariton thermal de Broglie wavelength9 (  22(m k T)1 ) is 1.1-1.3 μm.’\ndB eff B\nSI, page 2-3, added: Fig. S2 and Fig. S3 for material synthesis description and\ncharacterization.\nComment 3:\nThe authors claim that the disordered surface potentials that are formed as a result of\nthe fabrication process are instrumental in generating fine modes and efficient\nparametric emission. However, the role of the disorder in enhancing parametric\nemission is not quantitively measured. A study of how the different levels of surface\nroughness effect the signal /idler ratio would be beneficial.\nResponse 3:\nWe thank the reviewers for pointing out the need for a clearer comparison to\ndemonstrate role of disorder in enhancing parametric interactions. According to your\nsuggestion, in the revised manuscript we have presented parametric scattering data for\nthe MPs with comparable dimensions but different degrees of disorder. As shown in\nFig. R3, we locate three samples with close parameters including L , detuning energy,\ny\ncoupling strength, and satisfied phase matching condition, ensuring that the variation\nin parametric ratio is mostly affected by levels of surface disorder, respectively. CW\nexcitation (405 nm) was utilized to enhance clarity for the quantized energy levels in\nthe linear regime (a-c), while pulsed excitation (400 nm) was applied to resolve\nnonlinear parametric emission above threshold (d-f).\nIn the weak disorder or surface-smooth case (a), regularly spaced modes with\nsymmetric angular dispersion are resolved in the linear regime, indicating the only\npresence of geometric confinement. In the moderate-disorder case (b), two mode\nmanifolds mainly dominate: the larger spacing for the sets of modes is related to\ngeometric confinement, and the two sets of fine modes indicate the presence of disorder.\nIn the case of strong disorder (c), multiple disorder energy levels are superposed with\nthe geometric confinement induced energy levels and become highly quantized and\nhybridized.\nFig. R3. (a-c) Angle-resolved PL spectra (TM polarized) of phase matched\nmicrocavities at low excitation density. a: weak disorder; b: moderate disorder; c: strong\ndisorder. Dashed lines are guidance for LPB1 and LPB2 dispersion. (d-f) Respective\nangle-resolved PL spectra of phase matched microcavities above nonlinear parametric\nscattering threshold. d: weak disorder; e: moderate disorder; f: strong disorder. (g-i)\nSpectra extracted (as discussed in Fig. S9) for respective signal, idler and source\nemission. g: weak disorder; h: moderate disorder; f: strong disorder.\nFor the parametric emission (nonlinear regime), we observe the weak parametric\nemission in the weak disorder case (d and g), and the linewidth is relatively broad. In\nthe moderate disorder case (e and h), strong parametric emission is observed. A further\nincrease in disorder density (f and i) leads to a decrease in parametric emission intensity.\nIt qualitatively suggests the presence of moderate disorder largely enhances parametric\nemission. The presence of disorder breaks the generalized wavevector selection rule for\npolariton parametric interactions and makes the process happen with less-stringent\nwave vector selection rules (Phys. Rev. B 79, 045319 (2009), Phys. Rev. Lett. 106,\n126401 (2011), Phys. Rev. Lett. 129, 147402 (2022)), enhancing the parametric\nemission efficiency. While further increasing the disorder density decreases the\nemission again, probably due to more randomly distributed scattering pathways (Sci.\nAdv. 11, eadr1652 (2025)), and reduced density of states at the phase-matched energy\nlevels.\nRevision 3:\nMain text, page 7, added: ‘The role of confinement in enhancing polariton–polariton\ninteractions can be anticipated from the increased wavefunction overlap and thus\nstronger nonlinear coupling, as has been reported in a variety of microcavity\nconfigurations2,3,5,10. However, in previously reported confined schemes11,12, the\nparametric emission intensity is often not substantially improved compared to planar\nmicrocavities. In our case, the disorder potential acts as the key enabler for the\nobservation of strong coherent parametric emission. To qualitatively illustrate its role,\nwe investigated variation of parametric emission with different levels of disorder (Fig.\nS17). The markedly enhanced parametric emission in the presence of a moderate\namount of disorder highlights its crucial importance for triggering efficient parametric\nemission. The disorder potential breaks overall inversion symmetry and thereby lifts\nthe degeneracy for wavevector selection rules2,5,13, allowing the parametric process to\noccur under less stringent conditions.’\nSI, page 17, added Fig. S17 and respective discussions.\nComment 4:\nThe authors chose CsPbBr as the active material, but the manuscript does not justify\n3\nwhy this particular halide perovskite is uniquely suited for sustaining parametric\nscattering and supersolid behavior. Could other halide compositions (e.g., CsPbI ,\n3\nmixed halides, or hybrid organic-inorganics) offer advantages in terms of exciton\nbinding energy, linewidth, or tunability of the cavity modes? A few sentences in the\nintroduction would help here.\nResponse 4:\nWe thank the reviewers for raising the suggestion for discussion on choice of CsPbBr\n3\nas active gain material in our study. We chose CsPbBr because of its relatively large\n3\nexciton binding energy (~35–45 meV), which preserves robust exciton–photon\ncoupling at room temperature, and its high PL quantum yield, which ensures efficient\nprobing of light–matter interaction. The Rabi splitting could readily exceed 100 meV\nin DBR microcavities with quality factor ~1000 (Nat. Mater. 20, 1315–1324 (2021)).\nSecondly, compared to other perovskites such as CsPbI and 2D perovskites, CsPbBr\n3 3\nexhibits high stability under photo-excitation and resistance to moisture and oxygen.\nThese advantages make it ideal for creating deterministic cavity geometries with high\nquality confinement without the need for complex top-down fabrication. Further\nconsidering our previous experience (Sci. Adv. 11, eadr1652 (2025), Nano Lett. 20,\n6636–6643 (2020)) in light-matter interactions and low threshold lasing for this\nmaterial, we selected it for the current work.\nWe agree with the reviewer’s point of view that CsPbI 2D perovskites, and many\n3,\nhybrid organic-inorganic materials can also be used for study of polariton physics,\nextending the wavelength range and enhancing nonlinearity, etc. However, CsPbI has\n3\na relatively low exciton binding energy and poorer stability against moisture and\noxygen. 2D perovskites have a high nonlinear coefficient, but based on our laboratory\nresults, their stability under strong photoexcitation is not as good as that of CsPbBr .\nenergies, and if room-temperature condensation can be readily achieved with promising\nstability, they could also be suitable. The focus of the work lies in the mechanism and\ncan be extended to these materials.\nRevision 4:\nMain text, page 3, added: ‘The CsPbBr was selected due to its large exciton binding\n3\nenergy, high photoluminescence quantum yield and good structure stability, enabling\nrobust room-temperature polaritonics14-17.’\nMain text, page 11, added: ‘These results demonstrate that non-trivial potential\nlandscape acts as key enablers of unconventional parametric phenomena—which could\nbe readily extended to other material platforms’.\nComment 5:\nThe manuscript would benefit from structural characterization of the CsPbBr\n3\nmicroplatelets. While the microcavities are strongly characterized, no direct evidence\nis provided for the crystallographic quality or phase purity of the material. Techniques\nsuch as X-ray diffraction could confirm the absence of secondary phases, strain, or\nstructural defects that might influence the dispersion and parametric scattering behavior.\nIncluding such data would strengthen the link between the observed effects in the\nstrongly coupled system and the intrinsic properties of the active material, and ensure\nthat the reported effects are not influenced by variations in material quality.\nResponse 5:\nWe thank the reviewer for this constructive suggestion on structure characterization of\nthe CsPbBr MPs. As the reviewer pointed out, a high density of defects would strongly\n3\nsuppress exciton-photon coupling and hinder the realization of polariton condensation.\nIn this study, we have optimized the precursor solution preparation, and the anti-solvent\ngrowth process by enabling slow evaporation to enhance the crystallinity quality. Using\nthe grown MPs, we have realized very low-threshold condensation and lasing, reported\nin previous work (Sci. Adv. 11, eadr1652 (2025), Nano Lett. 20, 6636–6643 (2020)).\nFig. R4. Crystal structural characterization. (a) XRD characterizations of the\nCsPbBr microplatelets. Diffraction peaks are labelled with crystallographic planes,\n3\ncorresponding to orthorhombic phase CsPbBr (ICSD 97851) shown in lower panel.\nelectron microscopy image of CsPbBr MPs with different lateral dimensions, viewing\n3\nfrom the [010] zone axis, showing an identical crystalline structure orthorhombic\nCsPbBr . Atomic-resolution images reveal an inter-plane spacing of 0.58 nm between\n3\nthe [010] planes and 0.59 nm between the [001] planes, respectively.\nHerein, to emphasize this issue, we include XRD pattern (Fig. R4a) and angular dark\nfield scanning transmission electron microscopy (ADF-STEM) images (Fig. R4b) to\nconfirm the high crystallinity of the MPs. The XRD pattern shows dominant peaks at\n15.04, 15.20, 30.36, and 30.68 degrees, corresponding well to the (002), (110), (004),\n(220), planes of orthorhombic phase CsPbBr (lower panel, ICSD 97851). The narrow\n3\nlinewidth of ~0.04 degree indicates a high degree of crystallinity (Nat Commun 6, 7586\n(2015)). The scanning transmission electron microscopy images for a larger (Fig. R5,\nS1) and smaller MPs (Fig. R5, S2) show identical crystalline structure characteristic of\northorhombic phase CsPbBr (Nat Commun 13, 2587 (2022)). We have also compared\n3\nthe TRPL spectra (Fig. R2 in response to comment 2), and find that the PL decay curve\nis almost identical for different samples, suggesting the consistent optical quality across\nscales.\nRevision 5:\nSI, page 2, added Fig. S3 on structural characterizations.\nComment 6:\nGiven that perovskites are prone to point defects and surface traps, how do the authors\nensure that these do not dominate the coherence and linewidth of the parametric\nemission? Is there any passivation strategy or post-treatment applied or can you\ncomments on how that might affect properties?\nResponse 6:\nWe thank the reviewer for raising the issue of point defects and surface traps and their\npotential impact. The high quality of single crystal has been demonstrated in response\nto comment 5. Meanwhile, as used in our previous studies (Sci. Adv. 11, eadr1652\n(2025), Nat. Commun. 15, 3345 (2024), Nat. Commun. 15, 1893 (2024)) about 60 nm\nof PMMA layer were spin coated after transferring to bottom DBR. The PMMA acts\nas a physical barrier against moisture/oxygen and passivates surface defects, enhancing\nstability and optical properties. Such layer also protects the perovskite crystal during e-\nbeam evaporation of top DBR.\nRevision 6:\nMain text, page 12, Methods section, added ‘followed by ~60 nm PMMA layer\nencapsulation before top mirror evaporation, acting as protection layer for perovskites.\nResponse to Reviewer 2\nThe manuscript “Harnessing highly efficient coherent polariton parametric emission in\nquantum confined perovskite microcavities” by Xinyi Deng et al. reports the first-time\nobservation of resonantly enhanced parametric scattering of exciton-polaritons in a\nhalide perovskite microcavity. The authors emphasize the key result of their work: the\nstrong influence of lateral polariton quantization, accompanied by potential disorder,\non the nonlinear optical response of the studied system. They experimentally observe\ncoherent polariton emission involving parametric scattering and also claim the “first\nobservation of strong phase coherence between the two parametric species in\nmomentum space.”\nThe importance of the observations is not in doubt: the suggested arrangement is\nsuitable for generating phase-correlated photon pairs, with potential for operation down\nto the single-photon regime. The halide perovskite platform is favorable in this sense,\nas it is known for its ultimate quantum efficiency of exciton-enabled light emission.\nThe manuscript is generally well-written. However, some further clarifications and\npolishing of the text would be beneficial, as noted below. The team employs well-\nestablished experimental methods; therefore, the data quality is suitable. The analytical\nmodel is clear; some parameters used need to be specified in the updated version of the\nmanuscript.\nAlthough I am generally positive about this work, I must point out that some of the\nauthors’ claims require further justification. The authors have to address several\nquestions before I can recommend this work for publication in Nature Communications.\nResponse:\nWe sincerely thank the reviewer for reviewing our manuscript. We appreciate the\nfavorable evaluation of the novelty and importance of our study. The constructive\nsuggestions on recognizing population mechanisms on the second branch helps us to\ndevelop a deeper understanding in the scattering process and identify the nonlinear\norigin. In response, we have added respective experimental and theoretical results, with\ndetailed analysis and discussion, which we believe could resolve the reviewer’s\nconcerns. Point‑by‑point replies are shown in light blue in the response letter, and the\ncorresponding changes in the manuscript are indicated in blue in the response letter and\nrevised manuscript.\nComment 1:\nMy primary concern is related to the mechanisms of population of signal and idler states.\nI can suggest at least three of those:\n(1) Conventional relaxation from the reservoir to a resonant state (gain).\n(2) Linear scattering of polaritons from the source to signal and idler states. (power\ndependence transition) not purely linear scattering.\n(3) Nonlinear parametric scattering of source polaritons towards signal/idler state,\nclaimed as the primary mechanism.\nFirstly, the right panel in Fig. 2a clearly shows the strong asymmetry in signal\n(1.36)/idler (0.43) relative intensities. In case of mechanism (3), exclusively responsible\nsignal/idler population, this picture must be purely symmetric. The largest of these two\nvalues is compared to other works in Fig. 2b and is referred to as “parametric emission\nefficiency”, which might mislead the reader. This efficiency is fundamentally limited\nby the minimum of the two values mentioned for each particular measurement.\nThe authors state in the text: ” Below the first threshold, incoherent relaxation from the\nexciton reservoir is responsible for the population at signal and idler states.” It is unclear\nwhy authors neglect this mechanism when discussing the system behavior above the\nfirst thresholds.\nLet me suggest an explanation of the observed effects involving only mechanisms (1)\nand (2). Above the first threshold, the condensate appears at the source state. The\npolaritons there undergo elastic scattering into signal/idler modes, with efficiency\nenhanced by surface disorder. These scattered polaritons seed the condensates in\nsignal/idler states, which appear at a larger threshold and remain coherent with the\nsource, as they are seeded by polaritons coming from it. Another reason for the signal,\nsource, and idler states to be mutually coherent is the complete overlap of these modes\nin real space.\nThe condensation threshold for the signal/idler states can be larger than that of the\nsource state for several reasons, including differences in polariton lifetimes. The nearest\npolaritonic state below the source is more than 50 meV apart, while for signal/idler\nstates, this distance is below 10 meV.\nI firmly believe that with this massive amount of experimental data in hand, authors\ncan distinguish between mechanisms (1-3) more accurately.\nAnother way to completely exclude the mechanism (1) from the list is to perform\nadditional measurements with the resonant pumping of the source state by appropriately\ntuning the excitation photon energy and adjusting the spot size to avoid direct excitation\nof signal/idler modes. To distinguish pump photons from those in a condensate (and\nestimate the condensate emission rate), one can pump at an angle, staying within the\npositive/negative lateral wavevectors, yet remaining resonant with the source mode.\nResponse 1.1: Signal and idler population mechanisms\nWe thank the reviewer for the comprehensive analysis of the possible signal and idler\npopulation mechanisms. We performed respective experimental and theoretical\nanalysis, from which we attribute the nonlinear coherent signal and idler emission to\nthe nonlinear parametric scattering from source condensate.\nAccording to your suggestion, we performed resonant/non-resonant pumping\nexperiments for an identical sample and analyzed the intensity evolution behavior. For\nnon-resonant pumping, a 400 nm (1 kHz, 100 fs) pulsed laser is directed onto the sample.\nFor resonant pumping, a 540 nm (1 kHz, 100 fs) pulsed laser is utilized and filtered to\nhave the laser energy slightly blue-detuned from the source condensate, while also\navoiding excitation of the exciton reservoir. The schematic of resonant pumping can be\nfound in Fig. S10 in the revised version of manuscript.\nAs shown in Fig. R5a, under non-resonant pumping conditions, the population on both\nLPB1 and LPB2 emerges in the linear regime, with discretized energy levels arising\nfrom confinement and disorder. Above the nonlinear parametric emission threshold\n(Fig. R5b, the second threshold), the signal and idler emerge at energy positions\nresonant with the source condensate. Fig. R5d depicts the angle-resolved PL spectra at\nresonant pump condition below the nonlinear parametric scattering threshold (laser\nposition circled out). The emergence of a flat narrow emission, highlighted by white\narrows and just below the excitation energy, is the source emission. While at this stage,\nthe emission on the LPB2 at the respective energy position is missing. As the power\nfurther increased to higher pump fluence (Fig. R5e), parametric emission appears at the\nLPB2 dispersion positions resonant with source condensate. Fig. R5c and f depict the\nrespective growth rate of signal/idler intensity with respect to source emission intensity\nunder non-resonant and resonant pump conditions, respectively. The non-resonantly\npumped case features a two-threshold behavior, while resonantly pumped case exhibits\na single-threshold behavior.\nFig. R5. (a-c) Parametric emission under non-resonant pumping condition. a: angle-\nresolved PL spectra below the condensation threshold; b: angle-resolved PL spectra\nwith parametric emission; c: the respective growth behavior of signal/idler emission\nintensity with respect to source polariton. (d-f) Parametric emission under non-resonant\npumping condition; d: angle-resolved PL spectra below the condensation threshold; e:\nangle-resolved PL spectra with parametric emission; f: the respective growth behavior\nof signal/idler emission intensity with respect to source polariton.\nThe population mechanism (1)(2)(3) as raised by the reviewer stem from different\nmicroscopic origins, therefore exhibit different efficiencies and growth behavior for the\nsignal/idler states with respect to source polariton. Next, we analyze in detail to assign\npredominant mechanism in nonlinear regime to the nonlinear parametric scattering.\n(1) Conventional relaxation from the reservoir to a resonant state:\nSuch possibility could be excluded with observation of nonlinear parametric emission\nin resonant pump condition, where exciton reservoir is absent.\n(1) + (2): Linear scattering of polaritons from the source to signal and idler states, and\nseeded the nonlinear emission\nWe agree with the review that the mechansim (1)+(2) could generate strong signal/idler\nemission. To explore, we have carefully checked experimental data. The seeding effect,\ndescried in this mechanism, would establish the source, signal and idler as independent\nspecies in the nonlinear regime, being continuously replenished by the exciton reservoir.\nHowever, the correlated evolution of the source, signal and idler modes, as reflected in\ntheir comparable blueshift and spectral broadening (Fig. S18), indicates that these\npolaritons are subject to strong mutual nonlinear interactions (Nature 639, 337–341\n(2025)).\nFurthermore, our observations show that forming a macroscopic occupation directly at\na high-k state on a strongly red-detuned LPB (>110 meV) requires a pump fluence of\ntypically 100–200 μJ·cm-2, corresponding to a high photoexcited exciton density (Sci.\nAdv. 7, eabj7667 (2021)). Such high threshold is expected since LPB has its energy\nminimum at k~0, and such minimum is thermo-dynamically favored than a high-k state.\nUnder non‑resonant pumping the polaritons preferentially relax and redistributes\npopulation toward lower‑energy, lower‑k states—so a macroscopic occupation at a\nhigh‑k point is hard to sustain unless the injection rate is very high (Rev. Mod. Phys. 82,\n1489–1537 (2010); Phys. Rev. B 62, R2283–R2286 (2000); Phys. Rev. B 88, 121303\n(2013)) or with band-structure engineered to tailor local energy minimum positions\n(Nat. Commun. 4, 1749 (2013); Nat. Phys. 7, 681–686 (2011)). Consequently, the small\nseparation between our two thresholds (7.1 μJ·cm-2 versus 10.3 μJ·cm-2 in Fig. R5c),\nwould not support the hypothesis of ‘linearly scattered polariton after the first threshold\nseed the nonlinear parametric scattering’, since such seeding would be far too small to\nbridge the carrier density discrepancy required for a direct high-k condensate.\nFinally, we attributed the mechanism that leads to nonlinear signal/idler emission as\nnonlinear scattering from source polariton. As evidenced by the comparable\nparametric emission ratio (Fig. R5b and e), and the respective growth rate (Fig. R5c\nand f), suggesting that identical mechanism dominated such processes. The effective\nslope (k ~ 1.61) in resonant case is slightly larger than that under non-resonant (k ~ 1.32)\nexcitation, due to a relatively stronger nonlinearity when the source condensate is quasi-\ndirectly fed by the fs-laser pulses (Nat Commun 10, 3869 (2019)).\nAccording to your suggestion, we have emphasized the identification of mechanism (3)\nin nonlinear regime and the role of mechanism of (1) and (2) in respective regimes in\nthe revised version of manuscript.\nRevision 1.1:\nMain text, page 5, added ‘Furthermore, to recognize the population mechanism for\nnonlinear parametric emission, resonant and non-resonant pump were performed in an\nidentical microcavity. The comparable parametric ratio and intensity growth behavior\nsuggested the dictating role of nonlinear parametric scattering, rather than direct\ncondensation fed by the exciton reservoir (Fig. S10-12).’\nSI, page 11-13, added part IX on ‘Identification of signal and idler state population\nmechanism’.\nResponse 1.2: Theoretical simulation of resonant excitation\nNext, we show theoretically that the ‘resonant’ excitation on the LPB1 will induce\nparametric emission only when nonlinear coupling term is introduced for LPB1 and\nLPB2.\nOur theoretical model is based on the following two-component driven-dissipative\nGross-Pitaevskii equation:\n߲߰ (ݎ,ݐ) ݅\n݅ℏ ௡ = ൤ܧ෠୐୔ +ܸ (ݎ)− ൫ߛ−ܲ (ݎ,ݐ)൯−݅Γ|߰ (ݎ,ݐ)|ଶ൨߰ (ݎ,ݐ)\n߲ݐ ௡ ௗ௜௦ 2 ௡ ௡ ௡\n+2ߙ߰ (ݎ,ݐ)ଶ߰∗(ݐ,ݐ)+2ߙ߰ (ݎ,ݐ)ଶ߰ (ݎ,ݐ)\n௠ ௡ ௠ ௡\nwhere ݊ = 1,2 represent the index of the different lower polariton branches (here we\nconsidered two such branches, see the Fig. below). In our theoretical model, we have\nexplicitly considered that the gain function of the second branch ܲ (ݎ,ݐ) = 0. We\nଶ\n௥మ ௧\npump only the first mode with a Gaussian profile ܲ (ݎ,ݐ) = ܲ exp[− − ]. This\nଵ ଴ ௅మ ఛ\nchoice of the pump scheme enforces that there is no gain in the second branch except\nthe polariton transfer from the first branch to second one through the nonlinear\nparametric process. We have confirmed this by switching off the nonlinear term in the\ndriven-dissipative Gross-Pitaevskii equation (see the Fig. below). We find that for a\nlinear regime second branch shows no polariton population, which is in good agreement\nwith the experiment. Though the linear scattering regime as we observe in first\nsublinear period (Fig. R5f) in resonant pumping scheme could not be resolved here,\nbecause the coupling in driven-dissipative Gross-Pitaevskii equation could only\ndescribe nonlinear coupling process (Rev. Mod. Phys. 85, 299–407 (2013)), as also\ndescribed in Methods section.\nFig. R6. (a) Gain profile of lower polariton branch 1 (LPB1) ܲ (ݎ,ݐ = 0), while the\nଵ\ngain profile of the second branch (LPB2) is considered zero ܲ (ݎ,ݐ) = 0.\nଶ\n(b) Dispersion obtained without the nonlinear terms (ߙ = 0). As we can see, in the absence\nof the nonlinear term, no effective gain exists in the second branch. (c) Dispersion\nobtained with the nonlinear terms (ߙ ≠ 0) causing the parametric scattering. Here the\nsystem size is 3.6 μm, and OPO ratio ~ 0.82.\nRevision 1.2:\nSI, page 26, added part XVII on Theoretical simulation of resonant pump with, and\nwithout nonlinear LPB1 & LPB2 coupling.\nResponse 1.3: Evaluation of parametric emission ‘ratio’, and efficiency\nWe agree with the reviewer that the parametric emission intensity should not be higher\nthan the pumping intensity which is related to applied laser pump fluence. While herein\nthe “source” intensity is attributed to the source condensate intensity which would be\nmuch lower than the applied non-resonant pump laser, thus an above-unity idler/source\n(remaining source) emission ratio is possible considering the multiple population and\ndepletion mechanisms involved. An above-unity signal-to-source ratio indicates a\nstimulated regime with depletion of the source state and suggests highly efficient\nnonlinear parametric emission, a characteristic that has likewise been reported in pure-\nphotonic OPOs (Opt. Lett. 21, 1336–1338 (1996), Opt. Lett. 26, 620–622 (2001)). And\nthe depletion of pump/source polariton has also been observed in intrabranch polariton\nOPOs (Phys. Rev. Lett. 90, 106401 (2003), Phys. Rev. Lett. 91, 107402 (2003)) in the\nstimulated regime. In addition, exciton reservoir provides small amount of seeding in\nthis nonlinear regime, triggering the stimulated process to reach larger population. In\nour theoretical study, the above-unity ratio has also been observed as shown in data\npoints in Fig. 3a.\nIn our microcavities in an energy-degenerate interbranch parametric scattering process,\ncomponents near k = 0 would serve as the most effective source to create parametric\ny\npolariton pairs at opposite in-plane wavevectors, due to the highly satisfied phase\nmatching condition. Therefore, we extracted the spectra from central regions\n(integrated over 7 pixels in the angular direction) of the respective states (Fig. S9),\nconsidering that the source emission is broadened due to spatial confinement. On the\nother hand, the ‘ratio’ values for some literatures (Nano Lett. 22, 2023–2029 (2022),\nPhys. Rev. B 106, L020301 (2022), Phys. Rev. B 107, L060303 (2023), Nano Lett. 22,\n3026–3032 (2022)) are not directly mentioned, therefore we extract the value\n(maximum) by reading the RGB color in the color bar. For the literature (Nature 639,\n337–341 (2025), Nano Lett. 21, 3120–3126 (2021), Phys. Rev. Lett. 108, 166401 (2012))\nthat directly gave the value, we utilized their given values and checked in respective\nangle-resolved plots that the values are not underestimated.\nAccording to reviewer’s suggestions, we have revised the term in main text from\n‘efficiency’ exclusively into ‘parametric ratio’, and highlighted the feasibility of above\n-unity ratio, the method for extracting parametric ratio in the revised version of\nmanuscript and SI. While we keep the title as ‘highly efficient’, since the general\nparametric emission intensity is still higher than it is normally observed in planar\nmicrocavities.\nFig. R7. Angle-resolved PL spectra showing areas used for integration and evaluation\nof parametric ratio. The angle resolved emission collected from the objective (100x,\nNA=0.9) was mapped to 166 pixels (angular direction) on the Fourier plane in the\nspectrometer. The emission centered around (red dashed lines) the respective states\nwith 7 pixels were integrated in the angular direction for evaluation.\nRevision 1.3:\nMain text, page 4, added ‘In the energy-degenerate interbranch parametric scattering\nprocess, components near k = 0 would serve as the most effective source to create\ny\nparametric polariton pairs at opposite in-plane wavevectors, due to the highly satisfied\nphase matching condition18-21. Therefore, we extracted the spectra from central region\nspectra of the respective states (Fig. S9), considering that the source emission is\nbroadened due to spatial confinement7.’\nMain text, page 5, added ‘The above-unity signal-to-source ratio suggests depletion of\nthe source state in the stimulated regime and indicates highly efficient nonlinear\nparametric process, a characteristic that has likewise been reported in pure-photonic22,23\nOPOs. The depletion of source state has also been observed in polariton OPOs in the\nstimulated regime24,25.In our theoretical study, an above-unity ratio has also been\nobserved as presented in the following discussion (Fig. 3a).’\nMain text, page 6, Fig. 2b caption, added: ‘A comparison of parametric emission ratio\nand linewidth of our work with reported literature values (based on given data10,11,23 or\nestimated from color-scale maximum13-16).’\nSI, page 9, added Fig. S9 on Schematic for extraction of spectrum in Fig. 2a, and\nevaluation of parametric ratio.\nResponse 1.4: Mechanism for imbalance behavior.\nThe unbalanced intensity of signal and idler is induced by asymmetry in both population\nand depletion pathways in the driven-dissipative system, which are further magnified\nin presence of surface disorder that breaks inversion symmetry. Such imbalance\nexisting even in the nonlinear regime has been theoretically discussed (Phys. Rev. B 93,\n064203 (2016)) and experimentally observed in polariton nonlinear emission\nmodulated by trap or disorder (Phys. Rev. Lett. 104, 126403 (2010), Nat. Commun. 13,\n3080 (2022)). The emission intensity reflects averaged gain and loss at signal/idler in\nthe driven dissipative unequilibrium system. Exciton relaxation and scattering from the\nsource populate the signal and idler states, whereas radiative recombination and\nrelaxation into LPB2 lower energy states act as loss channels. Due to broken inversion\nsymmetry, the energy levels and scattering pathways become intrinsically asymmetric,\nwhich distort these linear processes and bias the subsequently stimulated scattering and\npopulation in nonlinear regime, resulting in the asymmetric/imbalanced angular\nemission as we observed.\nFig. R8. (a) Evolution of source to signal, and source to idler energy mismatch with\npump fluence from 0.3 to 27.5 μJ·cm-2. The dashed line indicates condensation\nthreshold. (b) Zoom-in view of energy mismatch in dashed circled area from 8.0 to 25.0\nμJ·cm-2. (c) Corresponding linewidth broadening for source, signal, and idler, with\npump fluence from 8.0 to 25.0 μJ·cm-2. The source to signal, and source to idler\nmismatch tend to saturate, accompanied by continuous broadening in linewidth.\nFurthermore, a nonlinear and driven–dissipative behavior of the parametric oscillator\ncould be reflected in the evolution of the energy mismatch in the nonlinear regime.\nAbove the nonlinear parametric emission threshold (Fig. R8), the mismatch tends to\nsaturate, while the linewidth continues to broaden, revealing that nonlinear interactions\ngradually drive the populations towards a dynamic equilibrium and pin the mismatch\nto an almost constant value. In addition, in a theoretically simulated nonlinear\nparametric oscillator as we show in Fig. R6c, the emission intensity is unbalanced as\nwell, supporting that the imbalance is theoretically applicable.\nAccording to your suggestion, we have emphasized the mechanism for the imbalanced\nsignal and idler emission in the revised version of manuscript.\nRevision 1.4:\nMain text, page 5, added: ‘An imbalance in the intensity of signal and idler emission\ncould also be observed, which is expected in these microcavities dressed with disorder\nand confinement3,26,27, considering the asymmetry in both population and depletion\npathways in the driven-dissipative system.’\nComment 2:\nAdditional related question: What are the values of net gains P for signal, source, and\nn\nidler used for the modelling in Fig. S11?\nResponse 2:\nIn the supersolid phase simulation corresponding to Fig. S11 (now as Fig. S22), we\nmodel the net gain for the source by setting the decay rate to ߛ = 0.5 ܸ݉݁ and by\nusing the following pump profile for the LPB1 mode:\nݎଶ ݐ\nܲ (ݎ,ݐ) = ܲ exp[− − ],\nଵ ଴ ܮଶ ߬\nwith ܲ = 11.6 ܸ݉݁, ߬ = 50 ݌ݏ, and a pump spot size ܮ = 11.7 ߤ݉. Although the\n଴\napplied non-resonant pulsed pump is on the femtosecond scale, the effective temporal\nprofile experienced by the system is governed by the exciton reservoir. This reservoir\nacts as an incoherent pump with a phenomenological lifetime much longer than 100 fs,\nthereby setting the relevant time scale for the non-resonant pumping process. In our\ntheoretical model, there is no linear process existing between LPB1 and LPB2.\nFig. R9. (a) The net gain of the LPB1 band, extracted from the imaginary part of the\ncorresponding energy eigenvalues. The mode with the highest positive net gain (6.68\nmeV), indicated by the red arrow, identifies the state in which the source condensate\nforms. (b) The net gain of the LPB2 band, where all values are negative, reflecting the\nshorter lifetime of these modes and the absence of external pumping. (c) The spatial\ndensity profile of the LPB1 mode with the largest net gain, illustrating the real-space\ndistribution of the condensate.\nThe net gain at t = 0 for the modes in LPB1 is shown in Fig. R9a and is obtained from\nthe imaginary part of the energy eigenvalues of the corresponding Hamiltonian. As no\nexternal gain is applied to LPB2 in the model, all LPB2 modes exhibit negative net gain\n(Fig. R9b), reflecting losses arising solely from their finite lifetimes.\nAccording to your suggestion, we have added the respective discussion on the gain for\nthe different polariton modes in the supplementary information.\nRevision 2:\nSI, page 25, added Fig. S23 and discussions on gain profile.\nComment 3:\nIn the manuscript, only the elastic scattering process is discussed. Meanwhile, Fig. 2c\nreveals an apparent spectral mismatch between signal, source, and idler emission peaks.\nOwing to the inversion symmetry of the system, is there any explanation for this effect?\nCould it be a measurement artifact, such as a slight misalignment of the CCD camera,\nwhich needs to be corrected during data post-processing?\nResponse 3:\nWe thank the reviewers for the suggestion on checking the measurement artifact and\nsuggestion of explanation. We included the mechanism explanation on both energy\nmismatch and intensity imbalance in response to comment 1.\nFig. R10. (a) Angle-resolved spectrum of a 532 nm laser. The laser was focused in real\nspace and therefore angularly dispersed in Fourier space. (b) Normalized spectrum\nextracted at position A, B, C indicated by the white arrow in (a). The overlapped\nspectrum indicates identical dispersive feature at different positions on CCD camera,\nexcluding the system error for the imbalanced signal/idler emission.\nHere we present the analysis on exclusion of measurement artifact. We utilized a single-\nwavelength 532 nm CW laser to resolve the spectrum in Fourier space. The laser was\nfocused on the focal plane and thereby dispersed in Fourier space. The corresponding\nangle-resolved spectrum is shown in Fig. R10a. The spectrum at the pixels\ncorresponding to typical positions (source, signal, and idler) in the parametric oscillator\nwere extracted and plotted in Fig. R10b. As illustrated by the normalized spectrum, the\nsharp-peaked emissions all centers around the same pixel in the wavelength axis.\nTherefore, the parametric emission with slightly mismatched energy reflects the\nintrinsic property of the parametric oscillator. In addition, we checked the energy\nmismatch by flipping the sample in y direction and observed identical mismatch\ntowards the respective direction, excluding the system error as well.\nAccording to your suggestion, we have revised the manuscript and added respective\ndiscussion on asymmetry mechanism, and exclusion of system error.\nRevision 3:\nSI, page 11, added Fig. S18(d) (e) for exclusion of system error when estimating energy\nmismatch.\nComment 4:\nIn the text, the authors compare confined and unconfined microcavities. Unfortunately,\nI was unable to find the two respective definitions. It is worth clarifying this for the\nreader. I suggest adding a discussion on the role of the second dimension of the\nrectangular microcavities. Why can the confinement in the second dimension be\nneglected?\nResponse 4:\nWe thank the reviewer for the suggestion of clear definition in confinement size and\nconsideration of second dimension. The MPs typically exhibit an anisotropic lateral\ndimension with L (length of x-axis) > L (length of y-axis). The L is generally no less\nx y x\nthan 10 μm, while L can be as short as around 2 μm (Fig. S2). While polariton thermal\ny\nde Broglie wavelength (  22(m k T)1 , Phys. Rev. Lett. 121, 067401 (2018))\ndB eff B\nis 1.1-1.3 μm. Therefore, the confinement effect is considered according to L\ny\ndimension. According to the model of quantum size effect as displayed in Fig. 3, an\nevident increase in parametric emission ratio emerges at L ~4 μm, which we use as the\ny\n‘boundary’ for different levels of confinement. To make the statement clear, according\nto your suggestion, we revise the ‘confined’ and ‘non-confined’ terminology to\n‘strongly confined’ and ‘weakly confined’, referring respectively to samples with L\ny\nsmaller than or larger than 4 μm.\nIn response to your suggestion, we have revised the manuscript, added descriptions of\nsample geometry in the respective discussion in Fig. 1 and discussed how the geometry\ndefines the ‘confinement’ as we studied in this work. The definition for ‘strongly\nconfined’ and ‘weakly confined’ is added in this part and utilized throughout the\nmanuscript.\nRevision 4:\nMain text, page 3, added: ‘The MPs were fabricated by an anti-solvent route (Fig. 1b)8,\nwhich exhibit an anisotropic lateral dimension with L (length of x-axis) > L (length of\nx y\ny-axis). The L is generally no less than 10 μm, while L can be as short as around2 μm\nx y\n(Fig. S2). Nevertheless, the MPs feature smooth facets and exhibit consistent optical\nproperties across the relevant range of lateral dimensions (Fig. S2, S3). Considering the\npolariton thermal de Broglie wavelength (1.1-1.3 μm, Methods)9, the influence of L\nx\ncould be neglected, and we therefore consider the spatial confinement and energy\nquantization according to L dimension7. Since the high-efficiency parametric emission\ny\nemerges when L decreases to 4 μm as shown in later discussions, we define the regime\ny\nwhere L is ‘smaller than’ 4 μm as ‘strongly confined’ and L is ‘larger than’ 4 μm as\ny y\n‘weakly confined’, respectively.’\nMain text, page 4, the caption of Fig.1, added: ‘Inset shows cross-sectional view of the\nMP typical anisotropic dimension with y direction dimension (L ) approximately 2-4\ny\nμm, and the thickness typically ranging from 1 to 3 μm.Surface disorders are formed\nby a stamp transfer process. (b) Scanning electron microscope (SEM) image of an anti-\nsolvent grown CsPbBr MP with clear and smooth facets, and strong L confinement.’\n3 y\nMain text, page 12, Methods, added: ‘The CsPbBr microplatelets were synthesized\n3\nusing an anti-solvent method8. Glass substrates were placed in a placed in\ndichloromethane anti-solvent filled beaker, and the precursor solution was dropped\nonto the substrates, as shown in Fig. S2a. Beaker was covered with perforated Parafilm\nto and placed in an oven with temperature of 30 ℃ for 48 h, enabling evaporation and\nCsPbBr single crystal growth. The synthesis procedure yields microplatelets of various\n3\nlateral dimensions, shown in Fig. S2b.’\nMain text, page 13, Methods, added: ‘In our MP microcavities, polariton effective mass\nis 1.1×10-5 m -1.5×10-5 m for most LPBs of interest for parametric emission. Therefore,\ne e\npolariton thermal de Broglie wavelength9 (  22(m k T)1 ) is 1.1-1.3 μm.’\ndB eff B\nSI, page 2-3, added: Fig. S2 and Fig. S3 for material synthesis description and\ncharacterization.\nComment 5:\nI was also unable to find an explicit discussion of the role of potential disorder. How\ndoes surface roughness improve the system's performance? One aspect could be as\nfollows. Polariton, scattering on surface roughness, may acquire an additional portion\nof momentum, inversely proportional to the lateral size of the surface feature. This\nprocess, therefore, enhances scattering from the source to signal/idler states.\nResponse 5:\nWe thank the reviewer for suggesting a more explicit discussion on role of disorder.\nWe added in the respective parts of the manuscript to discuss how it assists a more\nefficient parametric process and added respective literature references.\nRevision 5:\nMain text, page 3, added ‘For the moderate disorder regime, additional energy levels\narise with an overall narrowed linewidth, making the dispersion further enriched to\nfulfill phase matching condition and to enhance polariton parametric interactions\nthrough lifted degeneracy2-6.’\nMain text, page 7, added: ‘The role of confinement in enhancing polariton–polariton\ninteractions can be anticipated from the increased wavefunction overlap and thus\nstronger nonlinear coupling, as has been reported in a variety of microcavity\nconfigurations2,3,5,10. However, in previously reported confined schemes11,12, the\nparametric emission intensity is often not substantially improved compared to planar\nmicrocavities. In our case, the disorder potential acts as the key enabler for the\nobservation of strong coherent parametric emission. To qualitatively illustrate its role,\nwe investigated variation of parametric emission with different levels of disorder (Fig.\nS17). The markedly enhanced parametric emission in the presence of a moderate\namount of disorder highlights its crucial importance for triggering efficient parametric\nemission. The disorder potential breaks overall inversion symmetry and thereby lifts\nthe degeneracy for wavevector selection rules2,5,13, allowing the parametric process to\noccur under less stringent conditions.’\nMain text, page 7, added: ‘When the system size (predominated by confinement L in\ny\nCsPbBr microcavity) becomes comparable to de-Broglie wavelength9, disorder\n3\npotential would induces a strong sensitivity of nonlinear processes to system parameters\nlike energy level position, energy level density of states, etc.’\nMain text, page 7, added: ‘Disorder in such quantum confinement configuration induce\nsignificant fluctuations in energy positions and density of states for signal/source/idler on\nrespective LPBs even with small perturbations, strongly affecting the phase matching\nconditions and final state population density to stimulate efficient parametric scattering.’\nSI, page 17, added part XIII and Fig. S17 and discussions.\nComment 6:\nAuthors state: “Meanwhile, downscaling the confinement dimension leads to energy\neigenstates with larger spacing that induces the randomness in matching of source and\nsignal/idler energy position, leading to a larger fluctuation amplitude in parametric\ninteraction strength and acquisition of highly efficient parametric emission in confined\nmicrocavities.” Indeed, the LA1 and LA2 branches have generally different sets of\nquantized levels. The detuning (and overlap) between the fundamental level of LA1\n(the source state) and the nearest LA2 state is expected to significantly affect both linear\nand nonlinear elastic scattering processes in the system. In this context, would the data\npresented in red symbols in Fig. 3a, showing nearly random behavior, become better\nstructured when used to correlate signal&idler/source with the LA1-LA2 nearest-level\ndetuning? Of course, the randomness induced by surface roughness will stand.\nResponse 6:\nWe thank the reviewer for the constructive suggestion on correlating\ndetuning/mismatch with the size vs. parametric ratio plot. To do this we plot the data\npoints in Fig. 3 in a 3D configuration, where one axis represents confinement dimension\nand another axis represents the energy mismatch/detuning, as shown in Fig. R13. A\ntrend could be observed that when the L scales down and when mismatch is smaller,\ny\nefficiency reaches higher values. In addition, most of the parametric oscillators have an\nenergy mismatch smaller than 0.35 meV. Such value is less than full width half\nmaximum of the source/signal/idler emission, suggesting a quasi-phase matching\ncondition is still needed to enable efficient parametric processes (Nonlinear Optics\n(Academic Press, 2019), Phys. Rev. Lett. 84, 1547–1550 (2000), Nature 414, 731–735\n(2001)). Meanwhile, in our microcavities, the parametric ratio would not only be\ndetermined by such energy conservation but are also influenced by the density of\navailable final states (Phys. Rev. Lett. 84, 1547–1550 (2000), Nat. Nanotechnol. 17,\n396–402 (2022)) within the quantized polariton energy levels, and modified linear\nscattering channels assisted by the surface disorder as well as mentioned by the\nreviewer. The quantum size effect reflects a collective effect of rapid fluctuation in\nthese parameters (energy mismatch, density of states, etc.) that finally gives fluctuating\nmacroscopic order parameters (Science 306, 1915–1917 (2004), Nat. Mater. 9, 550–\n554 (2010), Rep. Prog. Phys. 77, 116503 (2014)) which reflect as parametric ratio in\nthis case and give rise to largely enhanced emission in the strongly confined scenario.\nTherefore, we kept Fig. 3 as originally sketched and added the 3D histogram chart as\nsupporting information to reflect the respective energy mismatch values in the model,\nas suggested by the reviewer. In the revised version of manuscript, we have also\nhighlighted the influence of energy mismatch on the intensity of parametric emission.\nFig. R11. The parametric ratio in relation to both confinement dimension and\nLPB1/LPB2 energy mismatch. When confinement scales down and when mismatch is\nsmaller, efficiency reaches higher values.\nRevision 6:\nMain text, page 8, added ‘The fine-energy-matching mechanism could be reflected in\nthe gradually decreasing energy mismatch of signal/source, idler/source with increasing\npump fluence (Fig. S18) and acquisition of highly efficient parametric emission in\nstrongly confined microcavity with small mismatch (shown in Fig. S19 in a histogram\nmap that correlates energy mismatch into the counted ratio).’\nSI, page 20, added Fig. S19.\nComment 7:\nWithin the text, one can find many terms, probably referring to the exact property of\nthe system under study: surface potential landscape, disorder potential landscape,\ndisordered surface potential landscape, transfer-induced potential landscape, disorder\npotential, etc. I recommend leaving a single term.\nResponse 7:\nWe thank the reviewers for the suggestion on a more consistent terminology across the\nmanuscript. We have revised all the terms as surface disorder and disorder potential\nlandscape.\nRevision 7:\nMain text, and SI, change the respective terms to ‘surface disorder’ or ‘disorder\npotential’.\nComment 8:\nFig. S2 ( “microscope” misspelled)\nResponse 8:\nWe thank the reviewers for pointing out the misspelling, we have corrected it in the\nrevised supplementary information.\nRevision 8:\nSI, page 9, ‘microscopr’ revised as ‘microscope’.\nComment 9:\nFig. S5 (d-f) - is it a single frequency or summation over a range?\nResponse 9:\nFig. S5 (d-f) are k-space resolved emission collected over the complete range of\nwavelength, without spectral filtering, except for 405 nm long pass filter for the pump\nlaser.\nRevision 9:\nSI, page 21: Added Figure S20 (d-f) caption: ‘no additional spectral filtering was\napplied when collecting the momentum space image.’\nSI, page 21, removed Fig. S20 (g-i) power-dependent intensity/linewidth/blueshift\nevolution. Power dependence behavior was added in Fig. S12 for the respective\ncomparison with resonant excitation and discussion on population mechanism.\nComment 10:\nFig. S6 (b) and (a) should be exchanged.\nResponse 10:\nWe thank the reviewers for pointing out the error. In the revised version of manuscript,\nwe made corresponding revisions.\nRevision 10:\nSI, Page 14: replace (b) momentum and (a) coordinate space’ with ‘(a) momentum and\n(b) coordinate space’.\nComment 11:\nFig. S7 (g) instead of (b). It is unclear why the source and idler energy- and wavevector-\ndependent spectra are plotted on different axes. I suggest using the exact representation\nand adding the signal plots as well.\nResponse 11:\nWe thank the reviewers for the suggestion of plotting both signal and idler here. We\nnow plot both ‘signal’ and ‘idler’ emission, as shown in Fig. R12.\nFig. R12. (a) Energy-resolved spectra for the ‘signal’ emission with increasing pump\nfluence. (b) Wavevector-resolved spectra for the ‘signal’ emission extracted at peak\ncenter (maximum) in (a). (c) Energy-resolved spectra for the ‘idler’ emission with\nincreasing pump fluence. (d) Wavevector-resolved ‘spectra’ extracted at energy\npositions in (c). (e-f) Zoomed-in angle-resolved PL emission of (e) signal and (f) idler\nat four different pump densities, with black solid line as reference to highlight relative\nwavevector shift.\nRevision 11:\nSI, page 14, revised as Fig. S13.\nResponse to Reviewer 3\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nResponse:\nWe thank the reviewer for co-reviewing our manuscript. The comments are responded\nwith point-to-point responses and revisions in manuscript.\nResponse to Reviewer 4\nThe work by Deng et al. reports on the efficient generation of parametric emission in a\npolaritonic microcavity. The authors claim that the presence of random lateral\npotentials is responsible for the observed anomalous enhancement of parametric\nscattering. To support their claims, they first present a comparison among three\nconfigurations: a non-confined microcavity (showing low-efficiency scattering), a\nlaterally confined cavity without random potential (showing no parametric scattering),\nand a laterally confined cavity with random potential (exhibiting highly efficient\nscattering). They then perform statistical analysis to justify the observed high efficiency\nand develop a theoretical model. Finally, they also present evidence of supersolidity at\nroom temperature.\nThe topic is certainly interesting, and the overall idea of investigating the role of\ndisorder and lateral confinement in the regime of nonlinear polariton scattering is nice.\nHowever, I found some aspects of the work problematic and the final claims somewhat\nunclear. Overall, although the work has potential, I cannot recommend publication of\nthe manuscript in its current form. A clear and convincing demonstration of the key\nclaims—particularly regarding the role of disorder and the reported efficiency—is\nnecessary before the work can be considered for publication.\nResponse:\nWe thank the reviewer for reviewing our manuscript and appreciate the reviewer’s\nacknowledgment of the novelty and scientific significance of coherent parametric\nemission. We are grateful for the constructive suggestions which largely helped in\nstrengthening the work. Accordingly, we have added further experimental data and\nexpanded the analysis and discussion, and we believe these updates could address the\nquestions raised. For clarity, point‑by‑point responses appear in blue in the response\nletter, and all revisions in the manuscript and supplementary information are shown in\nblue.\nComment 1.1:\nThe authors attempt to highlight the role of disorder, suggesting that scattering is not\nobserved in a similar laterally confined structure without disorder. This implies that\ndisorder is a fundamental requirement. However, a close examination of Fig. S9 clearly\nshows that phase matching cannot be satisfied in that case. Therefore, the comparison\nis not accurate, and the authors’ claim appears incorrect, especially considering that\nparametric scattering has been previously observed in laterally confined systems (e.g.,\n10.1103/PhysRevB.87.155302). Indeed, they later acknowledge that downscaling the\nlateral confinement introduces randomness in the phase-matching conditions, leading\nto larger fluctuations in the occurrence of highly efficient parametric emission.\nHowever, it is unclear what the authors are precisely claiming here. If they intend to\nargue that strong and coherent parametric emission is uniquely associated with laterally\nconfined disordered microcavities, then they should present a reference sample—free\nfrom disorder but with well-matched phase-matching conditions—for a meaningful\ncomparison. Otherwise, the role of disorder appears to be limited to mode broadening\nwhich facilitate phase matching, which is less significant.\nResponse 1.1\nWe thank the reviewers for the constructive suggestions on presenting the role of\ndisorder with more rigid comparison and analysis. According to your suggestion, in the\nrevised manuscript we have presented parametric scattering data for the MPs with\ncomparable dimensions but different degrees of disorder. As shown in Fig. R13, we\nlocate three samples with close parameters including L (3.4 μm, 3.8 μm, 3.8 μm,\ny\nrespectively for a, b, c), detuning energy, coupling strength, and satisfied phase\nmatching condition, ensuring that the variation in parametric ratio is mostly affected by\nlevels of surface disorder, respectively. CW excitation (405 nm) was utilized to enhance\nclarity for the quantized energy levels in the linear regime (a-c), while pulsed excitation\n(400 nm) was applied to resolve nonlinear parametric emission above threshold (d-f).\nIn the weak disorder or surface-smooth case (a), regularly spaced modes with\nsymmetric angular dispersion are resolved in the linear regime, indicating the only\npresence of geometric confinement. In the moderate-disorder case (b), two mode\nmanifolds mainly dominate: the larger spacing for the sets of modes is related to\ngeometric confinement, and the two sets of fine modes indicate the presence of disorder.\nIn the case of strong disorder (c), multiple disorder energy levels are superposed with\nthe geometric confinement induced energy levels and become highly quantized and\nhybridized.\nFig. R13. (a-c) Angle-resolved PL spectra (TM polarized) of phase matched\nmicrocavities at low excitation density. a: weak disorder; b: moderate disorder; c: strong\ndisorder. Dashed lines are guidance for LPB1 and LPB2 dispersion. (d-f) Respective\nangle-resolved PL spectra of phase matched microcavities above nonlinear parametric\nscattering threshold. d: weak disorder; e: moderate disorder; f: strong disorder. (g-i)\nSpectra extracted (as discussed in Fig. S9) for respective signal, idler and source\nemission. g: weak disorder; h: moderate disorder; f: strong disorder.\nFor the parametric emission (nonlinear regime), we observe the weak parametric\nemission in the weak disorder case (d & g), and the linewidth is relatively broad. In the\nmoderate disorder case (e & h), strong parametric emission is observed. A further\nincrease in disorder density (f &i) leads to a decrease in parametric emission intensity.\nThese data suggest enhanced emission in presence of disorder. The presence of disorder\nbreaks the generalized wavevector selection rule for polariton parametric interactions and makes the\nprocess happen with less-stringent wave vector selection rules (Phys. Rev. B 79,\n045319 (2009), Phys. Rev. Lett. 106, 126401 (2011), Phys. Rev. Lett. 129, 147402\n(2022)), enhancing the parametric emission efficiency. While further increasing the\ndisorder density decreases the emission again, probably due to more randomly distributed\nscattering pathways (Sci. Adv. 11, eadr1652 (2025)), and reduced density of states at\nthe phase-matched energy levels.\nRevision 1.1\nMain text, page 7, added: ‘The role of confinement in enhancing polariton–polariton\ninteractions can be anticipated from the increased wavefunction overlap and thus\nstronger nonlinear coupling, as has been reported in a variety of microcavity\nconfigurations2,3,5,10. However, in previously reported confined schemes11,12, the\nparametric emission intensity is often not substantially improved compared to planar\nmicrocavities. In our case, the disorder potential acts as the key enabler for the\nobservation of strong coherent parametric emission. To qualitatively illustrate its role,\nwe investigated variation of parametric emission with different levels of disorder (Fig.\nS17). The markedly enhanced parametric emission in the presence of a moderate\namount of disorder highlights its crucial importance for triggering efficient parametric\nemission. The disorder potential breaks overall inversion symmetry and thereby lifts\nthe degeneracy for wavevector selection rules2,5,13, allowing the parametric process to\noccur under less stringent conditions.’\nSI, page 17, added Fig. S17 and respective discussions.\nComment 1.2\nEven the comparison with the non-confined system is problematic. The sample shown\nin Fig. S8 exhibits a more positive detuning (with visible lasing around 2323 meV),\nwhile the confined-disordered cavity is more negatively detuned (~2300 meV). This\nresults in a higher excitonic fraction for the non-confined sample, which strongly\ninfluences both the visibility of the parametric emission and, in fact, the condensate\nitself. The condensate at k=0 in the non-confined sample appears to have lower\nvisibility compared to that of the confined-disordered cavity. Therefore, this\ncomparison does not convincingly support the claims regarding coherence.\nResponse 1.2\nWe thank the reviewer for the valuable suggestion and pointing out this issue. In the\nprevious version of manuscript, we provided the angle-resolved PL of a typical weakly-\nconfined cavity in supplementary information as an example to demonstrate the weak\nparametric emission intensity. In the revised version of manuscript, as shown in Fig.\nR14 we provide the correspondent angle-resolved PL spectra for the sample in Fig. 2f\nand change to similar colormap for consistency. This sample has comparable detuning\nenergy with the one in Fig. 2a and its parametric emission intensity is significantly\nsmaller than the strongly confined one in Fig. 2a.\nFig. R14. (a) Parametric scattering in a weakly confined microcavity at threshold. (b)\nParametric scattering in a weakly confined microcavity above threshold. (c) k-space\nimage of for (b), showing bright condensate emission and weak parametric emission.\nFor the comparison of coherence, we initially present these two figures here to compare\nthe coherence between a strongly confined microcavity and a weakly confined\nmicrocavity at comparable parametric emission intensity, to demonstrate that the\nstrongly confined sample is a more suitable platform for developing coherent\nparametric light emission. Because the parametric emission in the weakly confined\nmicrocavity is usually weaker, we increased the pump power to 3 times the\ncondensation threshold to obtain a stronger parametric emission from the weakly\nconfined microcavity. This unavoidably led to linewidth broadening and a reduction of\ncoherence as we discussed in the main text. To make the comparison more rigorous and\nillustrate the idea more straightforward, we included the extracted source interference\nprofile for them and added the case of 1.5 P for weakly confined microcavities as\nth\nshown in Fig. R15, into supplementary information. At similar pump fluence, the\nsource visibility is at comparable level. Whereas the parametric emission in a strongly\nconfined cavity preserves a higher level of coherence as demonstrated by a stronger\nvisibility in region of interest. Furthermore, when pump fluence reaches 3P to have\nth\nthe comparable parametric emission intensity with that of the strongly confined sample,\na drop in source visibility could be seen, the accompanied drop in parametric emission\nvisibility is also shown as discussed in main text.\nRevision 1.2:\nMain text, page 6, revised as In contrast, for the weakly confined microcavity, when it\nwas pumped at similar level (1.5 P ), parametric emission is rather weak (Fig. S15).\nth\nSI, page 15, added Fig. S15 showing dispersions for the sample in main text Fig. 2f and\nincluded near threshold image to show the emergence of parametric emission from the\nLPB dispersion.\nFig. R15. (a) Interferometry patterns of parametric polaritons in a strongly confined\nmicrocavity at 1.5 P (condensation threshold). (b) Interferometry patterns of\nth\nparametric polaritons in a weakly confined microcavity at 1.5 P . (c) Interferometry\nth\npatterns of parametric polaritons in a strongly confined microcavity at 3.0 P .\nth\n(d-f)\nRespective intensity profiles extracted from the interferometric images circled by the\nwhite dashed line highlighted ‘source’ condensate area. d: strongly confined, 1.5 P .\ne:\nth\nweakly confined, 1.5 P . f: weakly confined, 3.0 P .\nth th.\n(g-i) Respective intensity profiles\nextracted from left panel interferometric images circled by the white dashed line\nhighlighted ‘signal + idler’ area. g: strongly confined, 1.5 P .\nth\nh: weakly confined, 1.5\nP .\ni: weakly confined, 3.0 P\nth th.\nRevision 1.2:\nMain text, page 5, revised as: ‘To directly visualize the superiority of strong parametric\nemission with preserved coherence in quantum confinement regime, we compare the k-\nspace interferometry in a strongly confined microcavity and a weakly confined cavity\n(both dressed with disorder) at time delay of ~ 0.03 ps.’.\nMain text, page 6, revised as: ‘Fig. 2d shows the momentum space interferogram for a\nstrongly confined microcavity at 9 μJ·cm-2 (1.5 P )’.\nth\nMain text, page 6, revised as: ‘Such visibility demonstrates strong phase-coherence\nbetween signal and idler polaritons in our microcavities. In contrast, for the weakly\nconfined microcavity, when it was pumped at similar level (1.5 P ), parametric\nth\nemission is rather weak (Fig. S15). Therefore, higher pump fluence (20 μJ·cm-2, 3.0 P )\nth\nis needed for the generation of strong parametric emission comparable with the strongly\nconfined microcavities. Such pump fluence inevitably leads to dephasing processes and\nbroadens of the linewidth of signal and idler polaritons (Fig. 2f and 2g, Fig. S16).’\nMain text, Fig. 2 caption, revised as: ‘(d) k-space interferometry patterns of parametric\npolaritons in a strongly confined microcavity (9.0 μJ·cm-2, 1.5 P ), where clear\nth\ninterference fringes appear for superimposed signal and idler polaritons. Line profiles\nin dashed rectangle area are plotted in (e) and a visibility of 0.72 could be extracted. (f-\ng) Respective interferometry and line profiles in a weakly confined microcavity (20.0\nμJ·cm-2, 3.0 P ), when parametric emission is of comparable intensity to that in (d).\nth\nPoor visibility is observed for superimposed signal and idler polaritons.’\nSI, page 16, added Fig. R15 as Fig. S16.\nComment 1.3:\nMoreover, the reported efficiency value—while I appreciate the large statistical\nanalysis and the effort put into developing a suitable model—also appears problematic.\nThe claimed efficiency seems to exceed the theoretical limit for a parametric process,\nin which the combined intensity of the signal and idler cannot surpass that of the pump.\nThis suggests that there may be an issue in how the overall intensity of the condensate\nis being evaluated.\nResponse 1.3:\nWe thank the reviewer for raising concerns on the evaluation of ‘ratio’. We agree with\nthe reviewer that the theoretical limit of parametric emission intensity should not be\nhigher than the pumping intensity which is related to applied laser pump fluence. While\nherein the “source” intensity is attributed to the source condensate intensity which\nwould be much lower than the applied non-resonant pump laser, thus an above-unity\nemission ratio is possible considering the multiple population and depletion\nmechanisms involved. An above-unity parametric ratio indicates a stimulated regime\nwith depletion of the source state and suggests highly efficient nonlinear parametric\nemission, a characteristic that has likewise been reported in pure-photonic OPOs (Opt.\nLett. 21, 1336–1338 (1996), Opt. Lett. 26, 620–622 (2001)). And the depletion of\npump/source polariton has also been observed in intrabranch polariton OPOs (Phys.\nRev. Lett. 90, 106401 (2003), Phys. Rev. Lett. 91, 107402 (2003)) in the stimulated\nregime. In addition, exciton reservoir might provide small amount of seeding in\nthis nonlinear regime, triggering the stimulated process to reach larger population. In\nour theoretical study, the above-unity ratio has also been observed as shown in data\npoints in Fig. 3a.\nIn our microcavities in an energy-degenerate interbranch parametric scattering process,\ncomponents near k = 0 would serve as the most effective source to create parametric\ny\npolariton pairs at opposite in-plane wavevectors, due to the highly satisfied phase\nmatching condition. Therefore, we extracted the spectra from central regions\n(integrated over 7 pixels in the angular direction) of the respective states (Fig. R16),\nconsidering that the source emission is broadened due to spatial confinement. On the\nother hand, the ‘ratio’ values for some literatures (Nano Lett. 22, 2023–2029 (2022),\nPhys. Rev. B 106, L020301 (2022), Phys. Rev. B 107, L060303 (2023), Nano Lett. 22,\n3026–3032 (2022)) are not directly mentioned, therefore we extract the value\n(maximum) by reading the RGB color in the color bar. For the literature (Nature 639,\n337–341 (2025), Nano Lett. 21, 3120–3126 (2021), Phys. Rev. Lett. 108, 166401 (2012))\nthat directly gave the value, we utilized their given values and checked in respective\nangle-resolved plots that the values are not underestimated.\nAccording to reviewer’s suggestions, we have revised the term in main text from\n‘efficiency’ exclusively into ‘parametric ratio’, and highlighted the feasibility of above\n-unity ratio, the method for extracting parametric ratio in the revised version of\nmanuscript and SI. While we keep the title as ‘highly efficient’, since the general\nparametric emission intensity is still higher than it is normally observed in planar\nmicrocavities.\nFig. R16. Angle-resolved PL spectra showing areas used for integration and evaluation\nof parametric ratio. The angle resolved emission collected from the objective (100x,\nNA=0.9) was mapped to 166 pixels (angular direction) on the Fourier plane in the\nspectrometer. The emission centered around (red dashed lines) the respective states\nwith 7 pixels were integrated in the angular direction for evaluation.\nRevision 2:\nMain text, page 4, revised as ‘In the energy-degenerate interbranch parametric\nscattering process, components near k = 0 would serve as the most effective source to\ny\ncreate parametric polariton pairs at opposite in-plane wavevectors, due to the highly\nsatisfied phase matching condition18-21. Therefore, we extracted the spectra from central\nregion spectra of the respective states (Fig. S9), considering that the source emission is\nbroadened due to spatial confinement7.’\nMain text, page 5, added ‘The above-unity signal-to-source ratio suggests depletion of\nthe source state in the stimulated regime and indicates highly efficient nonlinear\nparametric process, a characteristic that has likewise been reported in pure-photonic22,23\nOPOs. The depletion of source state has also been observed in polariton OPOs in the\nstimulated regime24,25.In our theoretical study, an above-unity ratio has also been\nobserved as presented in the following discussion (Fig. 3a).’\nMain text, page 6, Fig. 2b caption, added: ‘A comparison of parametric emission ratio\nand linewidth of our work with reported literature values (based on given data10,11,23 or\nestimated from color-scale maximum13-16).’\nSI, page 9, added Fig. S9 on Schematic for extraction of spectrum in Fig. 2a, and\nevaluation of parametric ratio.\nComment 3:\nIn the introduction, the authors cite the work from J. Wu et al.\n(10.1021/acs.nanolett.1c00283), stating that the reported case exhibits suboptimal\nparametric emission efficiency and that pump powers \"several times\" above the\ncondensation threshold are required to observe parametric scattering. However, upon\nreviewing the referenced paper, it is clear that parametric scattering is already visible\nat pump powers 2–3 times above the condensation threshold. This would more\naccurately be described as \"a few times,\" rather than \"several,\" and does not support the\nimplication of particularly poor efficiency.\nResponse 3:\nWe thank the reviewer for pointing out the relative comparison of second threshold\ncompared to the first threshold at condensation should be more appropriately described\nas ‘few time’. We have revised the description in manuscript.\nRevision 3:\nMain text, page 3 revised from ‘several’ to ‘a few times’.\nComment 4:\nThe authors used the same sample in one of their recent publications to observe\npolariton condensation under CW excitation. Why a pulsed excitation scheme was\nchosen for the present experiments? Could the authors show how the excitation regime\n(CW vs. pulsed) influences the key observed properties—such as parametric efficiency,\nlinewidth, and coherence? Are these parameters intrinsic to the system or strongly\ndependent on the excitation conditions?\nResponse 4:\nWe thank the reviewer for recognizing our recent work on CW pumped polariton\ncondensation. Here in this study, we utilized CsPbBr microplatelets with much larger\n3\nthickness (1-3 μm) to induce multiple LPBs and support the configuration of energy\ndegenerate interbranch parametric scattering. The fine energy modes induced by\nsurface disorder could also be observed, whereas the features of condensation\n(macroscopic population towards ground state, nonlinear intensity growth, linewidth\nnarrowing, etc.) were not observed in CW pumped case. Such difference is because\nthicker samples support multiple LPB modes, and relaxation into multiple branches\ncompetes mutually, thereby making it difficult for relaxation and bosonic final‑state\nstimulation to favor a specific polariton mode. Therefore, to achieve polariton\ncondensation and to initiate the nonlinear interbranch parametric scattering,\nfemtosecond pulsed excitation is required in this case.\nFig. R17. The emission properties of a typical microcavity under CW and pulsed\nexcitation condition. (a) Angle-resolved PL spectra under CW excitation. (b) Angle-\nresolved PL spectra showing condensation and nonlinear parametric emission, under\npulsed excitation. (c, d) Pump density dependent evolution of source, signal and idler\nemission intensity for CW (c) and pulsed (d) excitation, respectively. (e, f) Pump\ndensity dependent evolution of linewidth of source, signal and idler emission for the\nCW (e) and pulsed (f) excitation, respectively. (g, h) Pump density dependent evolution\nof blueshift of source, signal and idler emission peaks for the CW (g) and pulsed (h)\nexcitation, respectively. (g, h) Pump density dependent evolution of blueshift of source,\nsignal and idler emission peaks for the CW (g) and pulsed (h) excitation, respectively.\nAs shown in Fig. R17 for the comparison for an identical microcavity under CW (a, c-\ne) and pulsed excitation (b, f-h). The population under CW excitation (a) distributes\nover a large energy range, while in pulsed pumped case (b) at high pump fluence, the\nemission from source/signal/idler dominates the spectrum. Under CW excitation\ncondition, the intensity of signal/idler emission was sublinear with pump density (c),\nwhich is identical to that of pulsed excitation below condensation threshold (f). While\nfor pulsed excitation, the intensity of signal/idler emission exhibits few transitions,\nrelated to source condensation and nonlinear parametric scattering. Furthermore, the\nlinewidth of signal/idler emission for CW excitation (d) is almost constant throughout\nthe measured pump density ranges. While for pulsed excitation, the linewidth (g) and\nblueshift (h) exhibit evident changes. These results suggest that although the observed\nfeature of coherent parametric emission is endowed by disorder, pulsed excitation is\nrequired to induce the nonlinear process.\nComment 5:\nRegarding the surface-smooth sample shown in Fig. S9, it is unclear why the\ndiscretization of the TE1 and TM1 modes is not visible. Given that this sample is used\nas a key comparison point, the absence of clear mode discretization raises questions\nabout the confinement quality. As mentioned earlier, to convincingly support their\nclaims about the role of disorder, the authors should identify a surface-smooth sample\nwith good phase matching, similar lateral dimensions, and comparable detuning.\nResponse 5:\nWe thank the reviewer for raising the respective concerns related to Fig. S9. The\ncomment on the need of a surface-smooth (weak disorder) sample to do the comparison\nis included in Response 1. In previous Fig. S9, the presentation of the dispersion below\nthreshold is not well presented to show cavity confinement quality, due to the mix of\npolarization, and that the condensation occurs on a LPB close to exciton which\ndiminishes the mode quantization feature. We now present polarization split results for\na thick confined cavity (L =3.7 ߤm; L = 12.6 μm) and fit the LPB dispersion to show\ny x\nstrong coupling and mode quantization features, as shown in Fig. R18. The\nyellow/green/white dashed lines represent the coupled‑oscillator model fits to the three\nLPBs. In Fig. 18c, we list the respective experimental and calculated parameters for the\nTM modes. The as-measured mode spacings are comparable with calculated values\n322\nE  for LPB2 and LPB3. For LPB1, however, the effective mass is large, so\n2m*L2\ny\nthe mode spacing is further reduced to 3.98 meV, close to its linewidth of 3.0 meV\n(broadened when approaching exciton resonance). Therefore, the quantization of the\nLPB1 can no longer be resolved.\nFig. R18. Exciton-photon coupling in a strongly confined microcavity (L =3.7 ߤm; L\ny x\n= 12.6 μm) by a CW 405 nm laser. (a) Angle-resolved PL spectra for TE polarization.\nThe dashed lines: disperison fitting for LPBs based on coupled oscillator model. (b)\nAngle-resolved PL spectra for TM polarization with dashed lines fitting the respective\nLPBs. (c) Fitted Rabi splitting, fitted LPB effective mass, measured energy spacing and\ncalculated energy spacing for LPB1, LPB2 and LPB3 lowest two energy levels shown\nin (b), respectively.\nRevision 5:\nMain text, page 3, added ‘The micron-scale thickness of MPs enables multiple sets of\nlower polariton branches (LPBs) which further split into transverse electric (TE) and\ntransverse magnetic (TM) branches due to material birefringence28. The coupled\noscillator model fitting in both polarizations are depicted in Fig. S7, showing strong\ncoupling characteristics.’\nSI, page 7, added Fig. S18 as Fig. S7 and discussed the respective evaluation of energy\nlevels associated with confinement. Discussed the TM branch quantization features and\nthe reason of missing quantization features for some LPB which are close to exciton.\nComment 6:\nHow are the overall intensities of the signal, idler, and source evaluated? Part of the\ncondensate signal may propagate outside the excitation region and thus be excluded\nfrom the intensity measurement. If so, this could lead to an underestimation of the total\ncondensate power and therefore to high efficiency. Additionally, the authors should\nprovide an estimate of the experimental uncertainty associated with the efficiency ratio\nevaluation.\nResponse 6:\nWe thank the reviewer for the constructive suggestions on a clearer description on\nexperimental measurement and a more accurate analysis of experimentally measured\nand extracted parametric ‘ratio’. We included the approach we estimate the ‘ratio’ in\nresponse to comment 1.3. Next, we would like to explain the experimental setup. The\nmicrocavities were excited by a non-resonant pulsed (400 nm, 1kHz, 100 fs) laser with\na beam spot size of ~ 50 μm (therefore samples are uniformly excited) and collected in\na Fourier setup as sketched in Fig. S8. To enable spatial selection of the desired area,\nan adjustable rectangular spatial aperture was positioned at the confocal plane of the 1st\nand 2nd Fourier lens. When collecting the emission, we spatially selected the whole\nsample area therefore all the respective emissions from the sample were projected onto\nthe Fourier plane, eliminating the possible propagation out of excitation/collection\nregion and underestimation of condensate polariton intensity.\nWe also appreciate the reviewer’s suggestion on estimation of experimental uncertainty\nin ratio evaluation. The uncertainty in experiments could be excluded here as discussed\nabove. For data processing, we obtain the value from accumulated spectrum projected\non 7-pixels in angular direction centering the emission, instead of from a single pixel\nspectrum, as we discussed in Response 2. In addition, such extraction would not affect\nthe relative intensity between signal and idler, thus ensuring negligible impact on the\nmodel in Fig. 3. Therefore, we expect that errors could be excluded here.\nRevision 6：\nMain text, page 4, added ‘In the energy-degenerate interbranch parametric scattering\nprocess, components near k = 0 would serve as the most effective source to create\ny\nparametric polariton pairs at opposite in-plane wavevectors, due to the highly satisfied\nphase matching condition18-21. Therefore, we extracted the spectra from central region\nspectra of the respective states (Fig. S9), considering that the source emission is\nbroadened due to spatial confinement7.’\nMain text, page 5, added ‘The above-unity signal-to-source ratio suggests depletion of\nthe source state in the stimulated regime and indicates highly efficient nonlinear\nparametric process, a characteristic that has likewise been reported in pure-photonic22,23\nOPOs. The depletion of source state has also been observed in polariton OPOs in the\nstimulated regime24,25.In our theoretical study, an above-unity ratio has also been\nobserved as presented in the following discussion (Fig. 3a).’\nSI, page 9, added Fig. S9 on Schematic for extraction of spectrum in Fig. 2a, and\nevaluation of parametric ratio.\nComment 7:\nThe authors emphasize that the presented configuration enables the generation of\nbalanced signal and idler beams. However, in Fig. 2a, the idler appears to be\napproximately three times weaker than the signal. The authors should clarify the origin\nof the imbalance.\nResponse 7:\nWe thank the reviewer for suggestion on adding the explanation of intensity imbalance\nin the discussion. The unbalanced intensity of signal and idler is induced by asymmetry\nin both population and depletion pathways in the driven-dissipative system, which are\nfurther magnified in presence of surface disorder that breaks inversion symmetry. Such\nimbalance existing even in the nonlinear regime has been theoretically discussed (Phys.\nRev. B 93, 064203 (2016)) and experimentally observed in polariton nonlinear emission\nmodulated by trap or disorder (Phys. Rev. Lett. 104, 126403 (2010), Nat. Commun. 13,\n3080 (2022)). The emission intensity reflects averaged gain and loss at signal/idler in\nthe driven dissipative non-equilibrium system. Exciton relaxation and scattering from\nthe source populate the signal and idler states, whereas radiative recombination and\nrelaxation into LPB2 lower energy states act as loss channels. Due to broken inversion\nsymmetry, the energy levels and scattering pathways become intrinsically asymmetric,\nwhich distort these linear processes and bias the subsequent stimulated scattering and\npopulation in nonlinear regime, resulting in the imbalanced emission as we observed.\nFurthermore, a nonlinear and driven–dissipative behavior of the parametric oscillator\ncould be reflected in the evolution of the energy mismatch in the nonlinear regime.\nAbove the nonlinear parametric emission threshold (Fig. R19), the mismatch tends to\nsaturate, while the linewidth continues to broaden, revealing that nonlinear interactions\ngradually drive the populations towards a dynamic equilibrium and pin the mismatch\nto an almost constant value. In addition, in a theoretically simulated nonlinear\nparametric oscillator as we show in Fig. S23, the emission intensity is unbalanced as\nwell, supporting that the imbalance is theoretically applicable.\nAccording to your suggestion, we have emphasized the mechanism for the imbalanced\nsignal and idler emission in the revised version of manuscript.\nFig. R19. (a) Evolution of source to signal, and source to idler energy mismatch with\npump fluence from 0.3 to 27.5 μJ·cm-2. The dashed line indicates condensation\nthreshold. (b) Zoom-in view of energy mismatch in dashed circled area from 8.0 to 25.0\nμJ·cm-2. (c) Corresponding linewidth broadening for source, signal, and idler, with\npump fluence from 8.0 to 25.0 μJ·cm-2. The source to signal, and source to idler\nmismatch tend to saturate, accompanied by continuous broadening in linewidth.\nRevision 7:\nMain text, page 5, added: ‘An imbalance in the intensity of signal and idler emission\ncould also be observed, which is expected in these microcavities dressed with disorder\nand confinement3,26,27, considering the asymmetry in both population and depletion\npathways in the driven-dissipative system.’\nComment 8:\nFor the non-confined microcavities below threshold dispersion should be shown.\nResponse 8:\nWe thank the reviewer for the suggestion of adding below threshold dispersion for\nweakly confined microcavities. We made the respective revision as discussed in\nResponse 1.2.\nRevision 8:\nMain text, page 6, revised as In contrast, for the weakly confined microcavity, when it\nwas pumped at similar level (1.5 P ), parametric emission is rather weak (Fig. S15).\nth\nSI, page 15, added Fig. S15 showing dispersions for the sample in main text Fig. 2f and\nincluded near threshold image to show the emergence of parametric emission from the\nLPB dispersion.\nResponse to Reviews (NCOMMS-25-52756-B)\nResponse to Reviewer 1\nOverall comment:\nThe authors have thoroughly addressed all points raised during the first round of\nrevisions. The revised manuscript and improved Supplementary Information will be\nvaluable to the community, and I therefore recommend publication.\nResponse:\nWe sincerely thank the reviewer for their time and careful review of our manuscript,\nand we appreciate the reviewer’s support for the publication of our work.\nComment 1:\nOne minor point remains regarding terminology. The manuscript uses the term\n“disorder” in a way that is ambiguous, since disorder can refer to multiple mechanisms\n(morphological, crystallographic, compositional, or energetic). In the present context,\nthe effect being discussed is specifically due to surface or interface roughness. I\nrecommend replacing “disorder” with something more specific, like roughness. This\nwill make it more clear for the reader that the disorder being discussed here is\nmorphological.\nResponse 1:\nWe thank the reviewer for pointing out the potential ambiguity of the term “disorder”\nfor a general readership.\nWe utilized the terminology to be more consistent with other polariton literatures (Nat.\nCommun. 12, 4839 (2021), Phys. Rev. Lett. 96, 066405 (2006), Phys. Rev. B 73,\n241308(R) (2006)), where ‘disorder’ is often used as a general term to describe the\nvariation of an effective potential energy, i.e., static spatial fluctuations of the\nphotonic/polaritonic energy that break translational symmetry and lead to localization\nand energy level quantization. The terminology ‘roughness’ describes the\nmorphological origin that might not fully convey the potential energy variations\nexperienced by polaritons and potential configurations used in our mathematical\nmodeling framework. Therefore, we consider it more appropriate to retain the term\n“disorder” when referring to the effective photonic energy landscape in our\nmicrocavities.\nTo avoid ambiguity for a general readership, we revised the manuscript to define the\nterminology explicitly at first use, stating that throughout the manuscript “disorder”\nrefers only to morphology-induced surface/interface roughness and the corresponding\nroughness-induced disorder potential energy landscape.\nRevision 1:\nMain text, page 2, revised as ‘Dispersion characteristics enabled by surface disorder\n(refer to morphological roughness, in this context) and geometric confinement allow\nenhanced parametric interactions.’\nResponse to Reviewer 2\nOverall comment:\nFirst, I appreciate the authors’ impressive efforts, including additional experiments,\nwhich enabled them to address the concerns raised by the reviewers in the previous\nstage. In particular, in the refactored text, the authors address previously missing critical\npoints: explicitly define terms, identify the dominant parametric scattering mechanism\nof the observed coherent emission, and distinguish the roles of confinement and\nroughness in achieving high emission efficiency. The authors' claims and conclusions\nare now well supported by the data and analysis presented in the manuscript. In its\ncurrent form, the work constitutes a valuable contribution to nonlinear polaritonics. I\ntherefore strongly support its publication in Nature Communications.\nResponse:\nWe sincerely thank the reviewer for carefully reviewing our manuscript and strongly\nsupport publication of our work.\nComment 1:\nAfter carefully reading the updated text, I have two minor suggestions to further\nimprove the paper's clarity: The authors define a specific threshold value (4 μm) for\nconfinement, which is likely structure-specific. To be more general and material-\nplatform-independent, one could define a strongly confined system as one capable of\nsupporting a parametric ratio greater than 1.\nResponse 1:\nWe thank the reviewer for suggesting a definition of ‘strongly confined’ with more\nphysically related quantities, rather than limited to material-platform related aspects. In\nthe counted parametric ratios in Fig. 3, a parametric ratio greater than 1 appears when\nconfinement reaches down to ~4.5 μm. Following the suggestion, we therefore revise\nthe threshold value for confinement from 4 μm to 4.5 μm and added respective\ndescriptions for the value when first define it in main text.\nRevision 1:\nMain text, page 3, revised as ‘Since the high-efficiency parametric emission (with a\nparametric ratio of larger than 1 as shown in later discussions) emerges when L\ny\ndecreases to 4.5 μm as shown in later discussions, we define the regime where L is\ny\n‘smaller than’ 4.5 μm as ‘strongly confined’ and L is ‘larger than’ 4.5 μm as ‘weakly\ny\nconfined’, respectively’.\nComment 2:\nIt is worth specifying the sizes of the pump spot and the spatially filtered detection\nregion, since both may affect the observations. Accordingly, a long focal distance lens\nmay be missing in the excitation channel in Fig.S6.\nResponse 2:\nWe thank the reviewer for pointing out the need to specify the sizes of the pump spots.\nAs mentioned by the reviewer, a long focal distance lens was placed in the excitation\npath, to enable an enlarged laser spot (~50 μm) for (a) spatially uniform exciton\nreservoir generation in non-resonant excitation and (b) focused spot size in Fourier\nspace.\nWe added the long focal distance lens in Fig. S6 and respective discussions on pump\nspot size and spatially filtered region by the aperture.\nRevision 2:\nSI, page 6, Fig. S6, revised as:\nFig. R1. CsPbBr microplatelet (gray cube in upper left corner) and respective signal\n3\nand idler polariton (green arrows near the sample, and bright high-k spots in Fourier\nspace) are depicted. (Obj: objective, L: lens, P: polarizer, BS: beam splitter) L5 denote\nthe long focal distance lens utilized for enlarging the spot size to ~50 μm. An adjustable\nrectangular aperture was used to spatially select the emission from the entire MP\nmicrocavity except its edges, with cavity dimensions ranging from ~2 μm to ~15 μm,\nas shown in Fig. 3.\nMain text, Methods, revised as ‘Pump laser spot size was enlarged by a long focal\ndistance lens in the excitation path, as shown in Fig. S6. Emission from the sample was\ncaptured with a 100× objective (NA = 0.9) and spatially filtered with an adjustable\nrectangular aperture at the focal plane and directed to a liquid nitrogen-cooled charge-\ncoupled device (CCD) spectrometer’.\nResponse to Reviewer 3\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nResponse:\nWe thank the reviewer for co-reviewing our manuscript. The comments are responded\nwith point-to-point responses and revisions in manuscript.\nResponse to Reviewer 4\nOverall comment:\nThe authors have carefully addressed the concerns raised in my previous report and\nhave substantially strengthened the manuscript through additional experiments and a\nclearer discussion. In particular, the role of disorder is now supported by more\nappropriate reference samples with comparable confinement, detuning, and phase-\nmatching conditions, and the comparison between strongly confined and weakly\nconfined microcavities is significantly improved. The clarification regarding the\ndefinition of the parametric ratio and the distinction from pump efficiency also resolves\nthe main conceptual ambiguity……Apart from this point, the main scientific issues\nraised in the previous review have been addressed, and the manuscript is close to being\nsuitable for publication.\nResponse:\nWe thank the reviewer for carefully reviewing our revised manuscript and appreciate\nthe reviewer’s strong support of the results and discussions in responses to the major\nissues raised in the first round of review.\nComment 1:\nIn addition, I note that further measurements requested by other referees (such as\nresonant excitation experiments) have been successfully implemented and add\nimportant information. At this stage, I believe that only one additional clarification\nwould further consolidate the physical picture. Since the manuscript now explicitly\ndiscusses TE and TM mode quantization and presents their respective dispersions, as\nrequested in the previous review, it would be highly valuable to demonstrate whether\nparametric scattering under resonant excitation can be achieved by pumping a\ndiscretized localized mode rather than the ground state where condensation occurs.\nSpecifically, with reference to Fig. R18, it would be important to clarify whether\nparametric scattering can be realized within the same polariton branch by resonantly\nexciting one of the higher-energy localized states at zero in-plane momentum. As phase\nmatching for these higher-energy states is satisfied in both LPB2 and LPB3, as well as\nin both TE and TM polarizations, demonstrating parametric scattering under these\nconditions would provide a stringent test of the proposed mechanism.\nResponse 1:\nWe thank the reviewer for proposing the experiments to support the mechanism of\nmatched energy levels, making use of the discretized higher energy states in the same\nLPB with intrinsically matched energy positions to satisfy phase matching condition\n(Phys. Rev. B 87, 155302 (2013)), a prerequisite for parametric interactions.\nIn Fig. R2 we show the schematic of resonant pumping on such higher energy levels.\nPulsed laser was filtered to match the energy and tuned to normal incidence to\nresonantly pump central ‘d’ state as indicated by the blue circle in Fig. R2a. Below\nthreshold as shown in Fig. R2b, only reflected laser is observed and polaritonic\nemission was absent. Above threshold, central ‘d’ state was resonantly injected and\nmasked by the strong reflected laser as shown in the central saturated part. Two\nadditional high k emissions were observed, indicating the occurrence of such\nparametric scattering as schematically shown in Fig. R2a.\nFig. R2. Schematic for resonant pump induced parametric scattering on higher\nenergy levels. (a) Angle-resolved PL spectra in the linear regime. Blue circle highlights\nposition for resonant pump laser, while the arrows indicate parametric scattering on the\nenergy degenerate states on the same LPB. (b) Angle-resolved spectra below polariton\nemission threshold, where only reflected laser signal is observed. (c) angle-resolved\nspectra above polariton emission and parametric scattering threshold.\nIn Fig. R3 we summarized the resonant pump results on LPB2 and LPB3 for both TE\nand TM polarizations, as suggested by the reviewer. Fig. R3 (a) and (d) show the linear\nregime PL spectra as discussed in Fig. S7, with ‘d’ orbital states highlighted by dashed\ngreen or white rectangles utilized for resonant pump induced parametric emission .\nAs shown in Fig. R3b, in TE polarization, resonant pump on LPB2 results in emergence of\ntwo high-k states, demonstrating typical parametric scattering. The source emission\nbeing resonantly injected was obscured by strong reflected laser which was co-\npolarized with the TE mode polaritons.\nFig. R3. Resonant pump induced parametric scattering on higher energy levels. (a)\nAngle-resolved PL spectra in the linear regime for TE polarization, as the one shown\nin Fig. S7a. Green and white dashed rectangle highlight the ‘d’ orbital states LPB2 and\nLPB3, respectively, for energy degenerate parametric process. (b) Resonant pump\ninduced parametric scattering in TE polarization on LPB2. (c) Resonant pump induced\nparametric scattering in TE polarization on LPB3. (d) Angle-resolved PL spectra in the\nlinear regime for TM polarization, as the one shown in Fig. S7b. (e) Resonant pump\ninduced parametric scattering in TM polarization on LPB2. (f) Resonant pump induced\nparametric scattering in TM polarization on LPB3.\nThe same occurs for LPB3 in TE polarization and LPB2 and LPB3 in TM polarizations,\nrespectively, indicating that the matched energy levels enable polariton parametric\ninteractions. We have added discussion on parametric emission within the same\npolariton branch according to the reviewer’s suggestion.\nRevision 1:\nSI, page 20, Fig. S19 caption, added ‘Such phase matching condition in confined\nmicrocavities has also been investigated by resonantly induced parametric scattering at\nhigher energy levels within the same LPB, as reported in previous literature15.’"}]

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