Ultrafast dynamic stark shift of an exciton-polariton condensate

Domain: neuroscience
Published: 2026-01-28
Editorial outcome: major_revision

Abstract
Time-dependent spatial modulation of a quantum condensate plays a key role in the investigation of the dynamics of collective coherent systems. Cold-atom condensates were already manipulated into forming solitons, vortices and optical lattices via the dynamic Stark effect. In the solid-state framework, semiconductor microcavity exciton-polaritons present an excellent platform for observing nonequilibrium condensate dynamics. Furthermore, the dynamic manipulation of exciton-polariton condensates offers numerous potential implementations in all-optical logic devices. We report the first observation of the energy modulation of an exciton-polariton condensate via the dynamic Stark effect. A Stark pulse is employed to induce a transient, coherence-preserving blueshift in the energy of the condensate of femtosecond-scale duration. A novel approach is presented for discerning the Stark effect in a condensate from the uncondensed case according to distinctive features in differential reflectance spectra, including spectro-temporal oscillations enabling to detect the buildup of coherence. The ultrafast and non-invasive modulation of the exciton-polariton condensate demonstrated here opens new research avenues of nonequilibrium physics of solid-state condensates as well as opportunities for polariton-based elements in both classical and quantum information technologies.

Introduction
The strong coupling between the cavity vacuum mode and quantum well (QW) excitons in a semiconductor microcavity yields the formation of composite bosonic quasiparticles, the exciton-polaritons, combining light and matter properties. Exciton-polaritons present a platform for phenomena of both fundamental and practical interest, one of them being the transition to a macroscopic quantum condensed state at high temperatures up to room temperature, exhibiting low-threshold lasing. The spatial modulation of quantum condensates represents a stepping-stone to exploring physical aspects of quantum hydrodynamics and topological states. In the field of cold atoms, the spatial and dynamical manipulation of the profiles of Bose-Einstein condensates (BEC) led to the confinement of the BEC in optical lattices and to the generation of solitons and vortices. To induce these phenomena, the dynamic Stark effect by an off-resonant beam was employed, generating a coherence-preserving transient shift in the energy of the state. Exciton-polariton condensates provide a solid-state alternative to cold atoms enabling the observation of new states of the matter and gaining insights into nonequilibrium condensation dynamics in a scalable platform operating at accessible temperatures. Phase imprinting and potential shaping of polariton condensates have been shown to induce phenomena such as solitons, polariton superfluidity and quantized vortices. The manipulation of polariton condensates hold promise for applications in classical and quantum technologies including all-optical circuits, quantum simulators and quantum networks. The increasingly high propagation speeds, as well as the strong nonlinearity arising from efficient interactions between polaritons facilitates the achievement of high operational gains and complex operations in logic devices.

Exciton-polariton condensates enable the formation of topologically protected states maintaining coherence over long distances, which is of interest for quantum computational schemes. Existing methods for dynamically shaping the potential of polariton condensates are usually realized through repulsive interactions with carriers injected by various pumping schemes that irreversibly modify the condensate wavefunction and are often constrained to the duration of the carrier decay; while alternative, non-invasive modulation methods nevertheless operate at ns timescales. The resulting switching rates do not suffice for manipulating states within the condensate coherence time.

It has been demonstrated in previous work that the ultrafast and reversible modulation of the polariton energy level structure can be achieved via the dynamic Stark effect. Until now, however, the Stark shift of a polariton condensate has not been demonstrated.

Here, we report the first modulation of a polariton condensate by the dynamic Stark effect. We developed a novel approach based on time-resolved differential reflectance spectroscopy for observing the Stark effect alongside the onset of condensation, ordinarily determined from photoluminescence (PL) measurements. Our results demonstrate a reversible transient shift on the femtosecond timescale in the energy of the lower polariton (LP) condensate, induced by a Stark sub-resonant pulsed beam. We first identify the signature of the Stark shift below condensation threshold as the known short-lived spectral blueshift of the LP and upper polariton (UP) absorption dips. The density of the polaritons is then increased up to LP condensation threshold, at which point the signature of the dynamic Stark effect is markedly altered by the combination of increased photoluminescence, enhanced repulsion-induced energy blueshift of the LP and the buildup of coherence. The latter is expressed in a change in spectro-temporal oscillations of the reflectance which, according to the theory of coherent transients, decay at a rate determined by the coherence of the induced polarization. Analysis of the decay rate of the oscillations reveals a sharp enhancement in the temporal coherence of the polariton system at threshold density. This behaviour, comparable to polariton condensates observed in standard PL measurements, provides evidence that the dynamic Stark effect is induced on polaritons in the condensed state.

Results
Coherent oscillations in differential reflectivity

A pump-probe experimental setup was employed to obtain time-resolved differential reflectance spectra. Unlike the dynamic Stark shift occurring, roughly, when the probe and the Stark pump pulses overlap in time, the coherent oscillations are observed at pump-probe delay Δt < 0, i.e. when the pump reaches the sample after the probe. A simplified picture of the origin of the oscillations can be depicted as follows (Fig. 1): first, the probe triggers the buildup of polarization in the material, initiating reemission. The Stark pump pulse subsequently reaches the sample and modifies the part of the polarization generated in its presence. Interference of the initial part of the emission (Fig. 1a) with the part altered by the Stark beam (Fig. 1b) results in time-dependent spectral oscillations (Fig. 1c). The decay rate of the fringes trends inversely to the temporal coherence of the polarization; upon formation of a polariton condensate, the buildup of temporal coherence and the narrowing of the PL spectral linewidth result in increased duration of the fringes.

Measurements of the normalized differential reflectivity were performed at varying pump-probe delays Δt. While the probe spectrally overlaps with both the LP and the UP branches, the Stark pump is significantly red detuned to avoid carrier excitation by one-photon absorption. In our pump-probe scheme, the probe beam is also used for injecting polaritons resonantly. Condensation was obtained by scanning the average probe intensity through a range of 13–214 mW cm−2, covering threshold. The differential reflectivity ΔR/R is given by:

ΔR = R p+pr − R p − R pr + R bg / R pr − R bg (1)

with ΔR being the Stark-induced change in reflectivity and the subscripts p+pr, p, pr and bg standing for pump and probe, pump, probe and background only, respectively. The pump-probe time delay is scanned in a range starting at slightly positive delays around Δt ≈ 0 at which the pump precedes the probe, to negative delays of several picoseconds. The dynamic Stark effect of femtosecond duration around Δt = 0 is associated with the spectro-temporal coherent oscillations of the differential reflectivity at Δt < 0 (Fig. 1c). We detect the buildup of coherence accompanying condensation through the enhanced prolongation of the oscillations above threshold density. A simulation of the differential reflectivity was implemented based on the theoretical model (see Supplementary Note 1). The differential reflectivity was calculated according to the absorption in the presence of the Stark pump, given by:

α(ω) = Im Ω p / 2ε 0 c <χ(ω)> (2)

and in the absence of the pump, assumed to be of the form:

α 0 (ω) = Ω p / 2ε 0 c Im iμ 2 / γ + i(E pol / ℏ − ω) (3)

where Ω p is the pump frequency, μ is the polariton dipole moment, χ(ω) is the material susceptibility, E pol is the polariton energy and γ is the polariton decay rate. The linewidth of the polariton branches and the polariton energy as well as the pump-probe delay Δt were extracted by fitting the calculated result for ΔR/R and the measurements.

Stark effect on LP condensate

The differential reflectivity spectra measured at varying pump-probe delay Δt and acquired at high temporal resolution around Δt ≈ 0 are shown in Fig. 2 for a Stark beam peak intensity of 10.2 GW cm−2 and at cavity-exciton detuning δ = +5.1 meV, for which the LP is mainly excitonic. A Stark shift is exhibited in the polariton branches, as depicted by the arrows. Separate measurements conducted at an extended range of probe intensities and analysed in subsequent sections reveal the onset of a LP condensate at an average probe intensity of ~100 mW cm−2. The measurements shown in Fig. 2a, b were conducted at average probe intensities of 65 mW cm−2 and 130 mW cm−2 in order to represent the cases of uncondensed and condensed LP, respectively.

Below condensation threshold (Fig. 2a), the dynamic Stark effect induces a blueshift of the absorption dips of the empty LP and UP polariton levels. Two clear distinctions from the uncondensed case emerge above threshold (Fig. 2b). The first is the blueshift in the energy of the LP branch, caused by polariton-polariton and polariton-exciton repulsive interactions and unrelated to the Stark shift induced by the pump. This blueshift, usually observed in direct PL measurements, is manifested here in the measured differential reflectivity. The second characteristic of condensation featured in Fig. 2b, is the modified signature of the dynamic Stark effect; unlike the uncondensed regime, a low energy dip is now observed alongside a higher energy peak. The explanation for this transition is in the fact that the Stark shift is now induced on highly populated states, therefore the PL becomes significant, and the absorption dip is replaced by a peak. The observed feature hence corresponds to the Stark shift of the PL of the condensate.

The pump-probe delay at which the Stark shift is largest was extracted from the fit to the model yielding, here, ~−190 fs for the uncondensed case and ~−440 fs for a condensate, as marked by dashed lines in Fig. 2b, respectively. Thus, in the condensed case the Stark pulse must be delayed further relative to the injection probe pulse to achieve the maximal effect. This result can be explained as follows. Below condensation threshold, the Stark effect appears as an energy shift of the reflectivity dips, with its timing corresponding to the buildup of the system polarization. Above the threshold, the Stark shift manifested in the condensate PL reaches its maximum once the condensate has formed. The delay of this shift corresponds to the time required for relaxation into the k ≈ 0 states from higher energy states excited by the resonant, but broadband, probe beam. This contrast in delay times between the condensed and uncondensed systems persists across all probe intensities for δ = +5.1 meV and δ ≈ 0 (Supplementary Fig. 3). The delay times for the condensate are slightly shorter for the exciton-like detuning of δ = +5.1 meV compared to δ ≈ 0, consistent with the longer relaxation times expected for an increased excitonic fraction and a shallower dispersion curve.

Notably, the Stark effect is observed not only on the condensed, blueshifted LP but also on the low-energy LP that have not undergone condensation, as indicated in Fig. 2b by the light arrow for the uncondensed LP and by a dark arrow for the condensate. The coexistence of condensed and uncondensed LP spectral features arises from the nonuniform profile of the spot (the area populated by polaritons). The polariton density decreases towards the edges of the spot, leading to sub-threshold LPs at the periphery alongside with a condensate at the centre. Since the spectrometer collects the signal from a region larger than the spot, the reflectivity spectrum above threshold reflects the contributions of the uncondensed LPs at the edges, in addition to the condensate.

Enhancement of coherence time at condensation

Figure 3 presents the normalized differential reflectivity at varying pump-probe delay Δt, sampled over an extended range of negative delays to trace the evolution of the coherent oscillations. The data shown are representative examples from a series of measurements performed at different probe (excitation) intensities. As in the previous section, the cavity–exciton detuning was fixed at δ = +5.1 meV, while the Stark beam was maintained at a peak intensity of 10.2 GW cm−2. The results are displayed from left to right in order of increasing excitation intensity. The dynamic Stark shift of the LP and UP branches, observed at small delay times |Δt|, is accompanied by coherent oscillations at larger delay. The amplitude of the oscillations decays as e−|Δt|/τ where the value of τ = 1/γ, indicated for each measurement, is the polariton decay time. The measurements were also repeated for detuning δ ≈ 0 (shown in Supplementary Fig. 4).

Below a given probe-generated threshold polariton density, the decay time of the oscillations around the LP branch is inversely dependent on density (Fig. 3a, b). The increasing effect of repulsive polariton-polariton and polariton-exciton interactions leads to decoherence and to the broadening of the PL linewidth. Above a threshold intensity, however, the trend is abruptly reversed, and the decay time increases with the density. The visibility of the fringes extends towards more negative time delay Δt (Fig. 3c, d), indicating the spectral linewidth narrowing characterizing condensation. The presence of prolonged oscillations unequivocally shows that the coherence of the condensate was preserved by the Stark beam. The extension of the temporal coherence above condensation threshold is consistent with results reported with a similar excitation scheme comprising a resonant and normally incident beam, demonstrating the prolongation of the first order correlation g(1) of the PL.

An additional feature displayed in the condensed cases (Fig. 3c, d) consists in two adjacent spectral lines in the differential reflectivity of the condensed LP that are mostly present at Δt > 0, corresponding to times at which the Stark pump reaches the sample before the buildup of the probe-excited condensate. Contrarily to the Stark signature, these long lived and spectrally narrow lines indicate a redshift of the PL due to a long-term effect of the pump on the cavity via, e.g., a two-photon absorption (TPA)-induced change of the mirror refractive index. The assumption of TPA is further supported by pump-induced PL measurements revealing an emission peak from the Al0.2Ga0.8As layers of the top distributed Bragg reflector (DBR) and exhibiting a spectral shift attributed to carrier absorption (Supplementary Note 2).

Characterization of LP linewidth and blueshift in differential reflectivity

The linewidth and the energy of the LP at varying injection intensity extracted from the fit to the coherent transient model, displaying good agreement with the experimental results, are shown in Fig. 4a–d for cavity-exciton detuning of δ = +5.1 meV and δ = 0. An example for the calculated results compared to experimental data at δ = +5.1 meV is shown in Fig. 4e, f for varying pump-probe delay below and above condensation threshold, respectively.

The threshold-like character of condensation is manifested both in the linewidth and in the energy of the LP at positive cavity-exciton detuning (δ = +5.1 meV). A pronounced narrowing of the extracted linewidth associated with the prolongation of the fringes is observed at threshold polariton density (Fig. 4a), accompanied by a sharp increase in the interaction-induced blueshift (Fig. 4b). At δ ≈ 0 the narrowing is observed as well, in which case, though, the blueshift is much smoother (Fig. 4c, d). A similar trend is observed in the angle resolved spectroscopy results reported by Panna et al. for off-resonantly excited PL from the same sample at varying cavity-exciton detuning. As demonstrated in Fig. 4a, c, when the linewidth is not dominated by interaction-induced decoherence-namely at low probe intensities-it is narrower at δ ≈ 0 than at δ = +5.1 meV, consistent with the larger photonic fraction of the LP at δ ≈ 0. Equivalently, the coherent oscillations decay more slowly. As the probe intensity is increased, resulting in higher polariton densities, the blueshift of the energy of the LP branch induced by the repulsive interactions grows. The high values of the blueshifted LP energy at cavity–exciton detuning δ = +5.1 meV, compared to the energy values obtained at δ ≈ 0, characterize polariton condensates formed at positive detuning, where the excitonic fraction of the LP is enhanced. Measurements of the LP energy versus excitation intensity at δ ≈ 0 obtained using a PL setup, are provided for reference in Supplementary Note 3. To confirm that the blueshift originates from condensed polaritons and to rule out attributing it to photon lasing, we point out both to the short-lived signature of the Stark shift around Δt ≈ 0, well above the bare exciton energy (Figs. 2b and 3c, d), and to the relaxation-induced prolongation above condensation threshold of the pump-probe delay at which the short-lived signature is largest, attributed to the buildup time of the condensate PL (Supplementary Fig. 3).

Around threshold, the Stark effect acts both on the uncondensed edges of the spot populated by polaritons and on the condensate being formed at the centre. The former is observed in the shift of the reflectivity dip of the LP, whereas the condensate, manifested in the Stark shift of PL, remains undetected until higher probe intensities, above condensation threshold, yield a strong enough emission. The energy of the undetected condensate grows with probe power, such that the condensate will have acquired a sizable blueshift when detected, giving rise to the apparent step-like increase of the energy around threshold. For δ ≈ 0, the rate of the interactions inducing the blueshift decreases with the reduced excitonic component of the LP, resulting in a smoother and smaller blueshift.

Notably, the linewidth values presented in Fig. 4 for δ ≈ 0 and δ = +5.1 meV are larger than those extracted from angle-resolved PL at δ = –2.9 meV (Supplementary Fig. 5 and Panna et al.). Likewise, spectra extracted from the detuning map of our sample (Supplementary Fig. 6), acquired through reflectivity from a broadband source, also display broader linewidths compared to angle-resolved PL at similar cavity-exciton detuning. These differences arise from the measurement scheme. Since reflectivity measurements capture the full optical response of the system, contributions from all accessible in-plane momenta within the probed range are included in the measured linewidth. In contrast, angle-resolved photoluminescence captures emission from populated states and is further weighted toward efficiently collected, relaxed polaritons near k ≈ 0. As a result, PL measurements typically exhibit a narrower spectral width near k ≈ 0.

Stark shift at varying pump intensity

Finally, to examine the dependence of the condensate energy shift on the Stark pump power, the differential reflectivity was measured at varying Stark pump peak intensity in the range 2.5–14.7 GW cm−2 and for a detuning of δ = +5.1 meV. The shift of the LP and UP energy, depicted by the dark arrows in Fig. 2, is extracted from the measurement of ΔR/R at small pump-probe time delay Δt ≈ 0 and is shown for a fixed probe (injection) intensity of 13 mW cm−2 yielding sub-threshold LP population (Fig. 5a), and for an average probe intensity of 155 mW cm−2 yielding condensation (Fig. 5b). The results are compared to the calculated Stark shift as function of pump intensity. The ratio between the extracted Stark shifts of the LP and the UP is consistent with their excitonic fraction (LP is 65% excitonic at δ = +5.1 meV). Further details concerning the calculation of the Stark shift are provided in Supplementary Note 4.

The Stark shift of the UP is observed below condensation threshold only (Fig. 5a). Its visibility around Δt = 0 decreases with increasing probe intensity (Fig. 3), likely due to the reflection dip becoming shallower as the branch is more populated. A similar mechanism may also reduce the LP visibility, in combination with linewidth broadening. Above threshold, however, the LP visibility is enhanced by the coherent PL buildup at k ≈ 0, while spectral overlap with the blueshifted LP further contributes to masking the UP feature, which eventually becomes undetectable.

Discussion

We have demonstrated the reversible and coherent modulation of a nonequilibrium polariton condensate on a femtosecond timescale via the dynamic Stark effect. The Stark-induced shift alongside the formation of the condensate are demonstrated in a time resolved differential reflectance spectroscopy framework. The dynamic Stark effect is featured in an ultrafast energy shift of the polariton branches both below and above the excitation threshold corresponding to condensation of the LP; below threshold, the Stark effect is manifested in the blueshift of the absorption dip of the LP, while above threshold a PL peak is shifted instead.

Further confirmation that the Stark-shifted polaritons are indeed condensed is found in the sharp prolongation of spectro-temporal oscillations at threshold density, signalling the buildup of temporal coherence. Additional evidence is found in the enhanced interaction-induced blueshift of the LP energy typical of condensation. These important characteristics of condensation, reported in extensive PL studies, are here detected for the first time through reflectance spectroscopy.

The Stark time-dependent modulation of polariton condensates opens avenues for exploring phenomena of fundamental interest in nonequilibrium solid-state condensates in analogy to existing studies in cold atoms. Our work also paves the way for implementations of polariton-based elements in classical and quantum logics and communication.

Methods
Sample details

Our sample, grown by molecular beam epitaxy, features a λ/2 cavity embedded between two distributed Bragg reflectors (DBR) stacks of 23 and 27 pairs of Al0.2Ga0.8As/AlAs layers at the top and bottom DBRs, respectively, resulting in a Q-factor of ~5000. It comprises 3 stacks of 4 GaAs QWs of 7 nm widths sandwiched between 4 nm AlAs barriers and placed at the antinodes of the resonant field. A wedged cavity structure enables variation of the cavity-exciton detuning by scanning different regions in the sample. The sample incorporates a unique asymmetric design in which the bottom DBR layers are approximately 4% thicker than those of the top DBR, yielding an entrance dip for the 1550 meV Stark pump beam at an angle of 45°, optically compatible with the cryogenic environment. This design supports the use of high-intensity pump beams, as the bottom DBR–substrate interface exhibits high reflectance, effectively limiting substrate heating. A normal mode splitting of 13.6 meV is associated with the strong coupling between the 1s QW HH1 exciton and the cavity mode in the sample. The sample was kept at a temperature of 4 K in a liquid-He closed cycle cryostat. The energy of the reflectivity dips of the LP and UP were found to be 1607.4 meV, 1621.5 meV at cavity-exciton detuning δ = +5.1 meV, respectively, and 1605.3 meV, 1618.9 meV, respectively, at δ ≈ 0. The approximate respective spectral widths of the LP and UP are 1.1 meV and 2.1 meV around small cavity-exciton detuning values.

Differential spectrometry measurement

The output of a Ti:Sapphire amplifier delivering 1550 meV, 35 fs pulses at a repetition rate of 1 kHz was split into two beams. The first beam pumps an optical parametric amplifier (OPA) tuned to an energy range of 1604 ± 24 meV delivering the probe beam. The direct 1550 ± 31 meV output beam of the amplifier serves as the sub-resonant pump beam inducing the Stark shift. The probe beam was normally incident on the sample and reflected towards a spectrometer while the pump was directed towards the sample at an incidence angle of 45⁰. One-photon absorption-induced excitation of polaritons by the 1550 meV pump is strongly suppressed as the power of the pump at ~1650 meV, corresponding to the cavity mode within the 45⁰ stop band, is reduced by three orders of magnitude relative to its peak. The pump pulse length is stretched to 250 fs by the dip in reflectivity upon entering the sample. The delay between pump and probe is controlled by a translation stage. The experimental setup is depicted in Supplementary Fig. 7.

It should be noted that the choice of pump-probe ultrafast spectroscopy rather than direct PL measurements stems from the need to capture the femtosecond-scale modifications induced by Stark effect. Since PL signals last several orders of magnitude longer, the impact of the Stark shift on time-integrated PL is negligible. The option of time-resolved measurement of PL with a streak camera would not overcome this limitation, as the temporal resolution of the camera is still limited to the picosecond scale.

The pump and probe beams were linearly polarized along the horizontal direction, and the sample was mounted vertically. Unlike transition metal dichalcogenide monolayers, where valley-selective polariton control using a circularly polarized Stark beam has been reported, in our system the rotation direction only distinguishes between spin-degenerate states. It is the orientation of the linear polarization of the oblique pump that has a possible impact as the exciton–light coupling strength may vary between transverse electric (TE) and transverse magnetic (TM) modes. This allows optimization of the Stark effect efficiency by selecting the appropriate polarization. In our case, however, the available laser power exceeded the required power for the Stark effect. Therefore, the pump polarization was not varied, and the magnitude of the Stark shift was determined by the summed contribution of the TE and TM components of the pump.

Data availability

All data required to evaluate the conclusions are presented in the manuscript and in the Supplementary Materials. The raw data used to generate the figures is available on Zenodo at: https://zenodo.org/records/17877726.

Code availability

Codes supporting this study are available from the authors upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the manuscript, the authors demonstrate the ultrafast, reversible control of polariton condensate via the dynamic Stark effect. The effect is observed through time-resolved differential reflectance spectroscopy. Authors study the dependence of the Stark shift on both pump and probe powers, and observe the shift below and above the condensation threshold, with signatures of condensation confirmed by prolonged coherence and blueshift. Even though the Stark shift was already observed in polariton systems, authors are the first to show it for the polariton condensate. These findings offer a great tool for the manipulation of the polariton condensate on a short time scale that is very useful for the future applications. The manuscript is well-written and structured and presents a concise and interesting study. I will be happy to recommend the manuscript for publication in Nature Communications as long as the Authors address a few comments and concerns arose while I was reading manuscript.\n1. Authors claim that the pump is sufficiently red-detuned and does not induce polaritons in the system (line 96); however, later, they refer to the modification of the cavity due to two-photon absorption (line 165). Could this process result in some polariton populating LP and UP and affecting the dynamics at a positive time delay? To clarify, the authors should provide PL spectra with pump-only excitation. Additionally, please include the spectral linewidths of the pump and probe in the experimental setup description.\n2. The decay time of oscillations is not characterized quantitatively. The decay time seems to be very close for Figures 2 a and b; knowing the value of the time decay would allow to compare the two probe powers better. Also, Authors claim that the decay time of the oscillations around the LP branch is inversely dependent on density (line 138) due to the increased linewidth of PL. However, the dependence of the linewidth on pump power depicted in Figure 3 a on the opposite demonstrates a decrease of the linewidth for probe intensities of 45 mW/ cm2, 92 mW/ cm2 depicted in Figure 2 (a,b), respectively. In this regard, the claim of the inversed dependence of the decay time is now not sufficiently supported by the experimental data.\n3. The explanation of the presence of the condensed and uncondensed LP features is not clear. Could the authors elaborate on how the overlap between the collection and excitation paths influences this? Also, could they plot the schematic of the experimental setup in the supplementary materials so this overlap would be clear for the reader?\n4. Can the Stark shift be observed in direct PL measurements? What are the advantages of utilizing reflectance spectroscopy here?\n5. The manuscript does not clearly explain the physical mechanisms responsible for the smooth versus step-like blueshifts observed at different detunings. A more detailed discussion would be helpful.\n6. Why is the decay of the oscillation so long for zero detuning before the threshold ( Fig. S1(a))? Authors should comment on how detuning affects the results of the measurements.\n7. What was the polarization of the pump and probe? Would the outcome depend on their polarizations?\n8. The authors claim the cavity has a unique design; could they add a description of this design to the main text or methods for clarity?\nSmall remarks:\n1. The notion of bright and opaque purple arrows in Figure 2 (c,d) is mixed throughout the text (lines 136,157).\n2. Could authors add a line marking the zero time delay in Figure 2 to improve the comprehensiveness.\n3. The (a) and (b) labels are missing from Figure 5\n4. \\mu is not defined for equation (3) in the main text.", "reviewer_2": "Feldmann et al. report on the energy modulation of a polariton condensate at ultrafast timescales upon excitation by a sub resonant pulse (i.e. without creating additional polaritons), thanks to the dynamic Stark effect. By monitoring the time-resolved pump-probe differential reflectance, for different pump powers, the authors observe a drastic change on its behavior upon crossing a certain power threshold. In particular, the decay of the spectro-temporal oscillations slows down when crossing the threshold, consistent with the formation of a polariton condensate and the onset of temporal coherence associated to it.\nThe work is certainly original, meaningful and provides a new perspective on polariton condensation, which has been mostly studied up to now by photoluminescence (and coherence) measurements. Thus, this alternative characterization technique and the possibilities it opens in terms of polariton condensate manipulation deserves publication in Nature Communications. However, before it can be accepted for publication a certain number of critical issues need to be clarified, and further analysis and/or additional experiments need to be presented. These are described in detail below. Besides, curing the figures presentation (and figure captions) as well as the text will aid the reader to follow up better the logic behind the results presentation, which is sometimes obscured by the different mechanism in play. In this sense, adding an additional figure (or an additional panel in Figure 2), focusing just on the dynamic Stark shift of the polariton branches at zero delay would be extremely helpful (i.e. not waiting for figure 4 to analyze it in more detail). Otherwise, the interest of this effect is masked by the remarkable oscillations in the differential reflectivity measurements, which are also an important result but not the only one.\nA crucial aspect of the study, pushing the current results far beyond those published previously by the authors (ACS Photonics 2019), is related to the transition into a condensed polariton phase and its modulation in a fs time scale. Polariton condensation in the same sample has been reported by the authors and studied thanks to standard techniques, as commonly employed by the polariton community. In their previous results on the same sample, the exciton energy was indicated to be around 1610 meV. However, if I understand correctly Figure 2 (and, Figure 3b and Figure 4b), it seems that the LPB energy at condensation is shifted above the bare exciton energy, which should be clearly stated anyhow. This aspect deserves either a finer analysis or some clear explanation. It might be enough to monitor the transition to the condensed phase with a finer series of pumping power or provide angle-resolved measurements under the same pumping conditions but, in any case, a clear and unambiguous characterization of the polariton branches close to threshold (below and above) is required.\nSimilarly, the “disappearance” of the UPB signature upon crossing the condensation threshold needs some explanation (and potentially additional measurements). The reasons why the UPB vanishes in reflectivity measurements is not clarified by the authors, and there are no obvious reasons why this should be so (compared to PL measurements). Furthermore, having access to the UPB would allow the reader to compare the blueshift induced by the probe, due to the increase of polariton density, as well as the dynamic Stark shift induced by the Stark pump. In both cases we expect a shift dependent on the excitonic fraction and that, thus, should be different from the shift of the LPB.\nIf one lets aside the claimed spectral position of the LPB at or above threshold, the LPB linewidth evolution extracted from the time-evolution of the differential reflectance for different probe (i.e. pumping) powers shows clear signatures for the increase of temporal coherence, as expected for the polariton condensation transition. Nonetheless, the linewidth values extracted from the fittings of the differential reflectance spectra seem systematically larger than those extracted previously from angle-resolved PL spectra on the same sample. And this, even if one takes into account the effect of detuning (i.e. of excitonic/photonic fractions), whose values are slightly different in the current and previous works. Again, some clarification is needed to keep consistency between the two measurements and, especially, for the polariton community to understand how to compare (if it is not a direct comparison) between the results obtained by PL measurements and those extracted from the current pump-probe reflectance measurements.\nA very interesting aspect of the article is the unequal delay times for the maximum dynamic Stark shift depending on whether the cavity is operated below or above threshold. While the effect is clearly demonstrated from an experimental point of view, its explanation (retarded formation of the condensate) seems somehow contradictory with the fact that the probe beam pumps resonantly the condensate (and the polariton branches below threshold), and thus one would not expect a delay with respect to the formation of the polaritons themselves. It might be due to the fact that, while the probe is resonant, it is still quite broad. Thus, indeed, polaritons contributing to attaining the condensation threshold might need to relax along the LPB from states lying at higher energies. The authors should develop these arguments further, as it is one key observation and deserves some further insight. Furthermore, it would be very useful for the polariton community if the authors provided these unequal delays for a second (or more) detuning, as the effect probably depends on the excitonic/photonic fraction of the state at which polariton condensation occurs.\nOverall, this work provides an insightful view on polariton condensation from an original perspective. The experimental technique can thus provide additional information on the condensation phase transition and, besides, a means for ultrafast polariton condensate control. For all these reasons the referee recommends publication in Nature Communications after the critical issues raised above have been clarified.", "reviewer_3": "In this manuscript, the authors demonstrate ultrafast, non-invasive modulation of an exciton-polariton condensate using the dynamic Stark effect. By employing a sub-resonant Stark pulse in a femtosecond pump-probe setup, they report transient energy shifts of the lower polariton (LP) condensate, distinguishing between uncondensed and condensed regimes through changes in differential reflectivity spectra. The buildup of coherence in the condensate is inferred from the prolongation of spectro-temporal oscillations, interpreted using a coherent transient model.\nWhile the paper somewhat extends the understanding of nonequilibrium condensation dynamics , several key issues remain that the authors should address:\n1. While the authors provide detailed pump–probe data at two cavity-exciton detunings (δ = 0 and δ = +5.1 meV), the manuscript does not present steady-state spectral data(such as reflectivity or PL) under these same detuning conditions. Such a comparison would be useful for identifying how the ultrafast dynamics differ from steady-state behavior, and whether the same trends are observed in the absence of time-resolved perturbation.\n2. In Fig. 2, the Stark-induced coherent oscillations appear to abruptly increase in duration between panels (b) and (c), consistent with a condensation threshold. However, one might expect a more gradual shift in the timing of the Stark signal maxima as a function of increasing probe power, especially if the delay is influenced by scattering dynamics. Could the authors clarify why the response appears threshold-like rather than continuous? Additional explanation, or intermediate power data points, may help resolve this point.\n3. The authors explain the fitting procedure for Fig. 3 in the Supplementary Information, but similar fitting details are missing for Fig. 5. Specifically, the manuscript does not indicate the form of the fitting function used to model the Stark shift vs. pump intensity, nor are any error bars provided. In Fig. 4, the Stark signal from the condensed LP branch appears to overlap with the UP branch signal. How was this spectral overlap handled in the fitting process? Moreover, the dashed line in Fig. 5, labeled as the “calculated Stark shift,” is not clearly explained in terms of how it was derived—what assumptions or theoretical model were used in this calculation?\n4. The title suggests that the condensation process itself is modulated by the dynamic Stark effect, which may be misleading. In the current experiments, the condensate is already formed and is subjected to a transient energy shift induced by the Stark pulse. While this certainly constitutes ultrafast control of the condensate energy, it is not clear that the condensation threshold or coherence properties are themselves being modulated.\n5. A key claim of the paper is that the decay time of the coherent oscillations increases significantly upon condensation, reflecting enhanced temporal coherence. However, the manuscript does not provide quantitative data or extracted time constants to support this statement. A more explicit analysis of the decay rates as a function of probe intensity—and, if possible, comparison with theoretical predictions—would help to substantiate this important point."}, "author_response": "We thank the Reviewer for the positive assessment of our work and appreciate the insightful remarks. We have addressed and clarified each of the points raised below.\n1. Authors claim that the pump is sufficiently red-detuned and does not induce polaritons in the system (line 96); however, later, they refer to the modification of the cavity due to two-photon absorption (line 165). Could this process result in some polariton populating LP and UP and affecting the dynamics at a positive time delay? To clarify, the authors should provide PL spectra with pump-only excitation. Additionally, please include the spectral linewidths of the pump and probe in the experimental setup description.\nResponse: Following the Reviewer’s remark, the statement was corrected on page 5 (previously in line 96) in order to clarify that the pump detuning prevents excitation by one-photon absorption.\nTwo-photon absorption (TPA)-induced population of the LP and UP is expected to be negligible; according to our calculations, experimentally validated by pump-only measurements as suggested by the Reviewer, most pump power undergoes TPA in the top DBR. Further details and the result of pump-only measurement are now included in the supplementary information on page 4, as quoted below.\n“Two-photon absorption -induced spectral feature at positive time delays\nTwo-photon absorption of the pump is expected to be negligible in the QWs. Based on TPA coefficients reported by Nathan et al.[S8] we estimate that while most of the pump power is absorbed in the top distributed Bragg reflector (DBR, only ~0.1% is absorbed by the quantum wells. This estimate is corroborated by photoluminescence (PL) measurements under pump-only excitation in our setup. As shown in Supplementary Figure 1, the PL spectrum exhibits a distinct feature at 1729 meV, close to the bandgap of the Al Ga As 0.2 0.8 DBRs, while no signal is detected at the lower polariton (LP) and upper polariton (UP) LP and UP energies of 1605.3 meV and 1618.9 meV, respectively.\nTPA-induced carriers in the DBR account for the deviation of the measured PL at 1729 meV from the nominal cryogenic band gap of Al Ga As (1768 meV); according to 0.2 0.8 Bennett et al.[S9], a carrier density sufficient to induce a bandgap shrinkage of ~30 meV corresponds to a ~15% modification of the DBR refractive index, leading to an expected red shift of 1–2 meV in the polariton energy. This shift is consistent with the feature observed at positive delays in Fig. 3c,d in the main text and Supplementary Figure 4c,d.”\nFinally, the respective linewidth values of the probe and the pump, of 48 meV and 62 meV, are now mentioned on page 16. The cavity mode at the incidence angle of the pump (45⁰) is ~1650 meV. It is now mentioned in the Methods section on page 16 that since in this spectral region, the pump is reduced by three orders of magnitude relative to its peak at 1550 meV, one-photon absorption–induced excitation of polaritons by the pump is strongly suppressed.\n2. The decay time of oscillations is not characterized quantitatively. The decay time seems to be very close for Figures 2 a and b; knowing the value of the time decay would allow to compare the two probe powers better.\nResponse: Following the Reviewer’s comment, we addressed the subject in the paper on page 9 and added the values of the decay time in Fig. 3 and Supplementary Figure 4 (previously Fig. 2 and Supplementary Figure 1) along with the given corresponding linewidth values: “The amplitude of the oscillations decays as e−|Δt|/τwhere the value of τ=1/γ, indicated for each measurement, is the polariton decay time.”\nAlso, Authors claim that the decay time of the oscillations around the LP branch is inversely dependent on density (line 138) due to the increased linewidth of PL. However, the dependence of the linewidth on pump power depicted in Figure 3 a on the opposite demonstrates a decrease of the linewidth for probe intensities of 45 mW/ cm2, 92 mW/ cm2 depicted in Figure 2 (a,b), respectively. In this regard, the claim of the inversed dependence of the decay time is now not sufficiently supported by the experimental data.\nResponse: We appreciate the Reviewer’s helpful remark. Indeed, a correction was necessary in estimating the linewidth at probe intensities near the condensation threshold. In this regime, as the linewidth broadens, the amplitude of the oscillations decreases and the signal competes with noise at advanced time delays. We therefore shifted the range of delay times employed for fitting the measurements to the model within proper SNR limits for a couple of relevant data points. The revised results now align with the observed inverse relationship between decay time and polariton density below threshold, as illustrated in Fig. 3 on page 9. We updated the highest values of the linewidth in Fig. 4a accordingly on page 11.\n3. The explanation of the presence of the condensed and uncondensed LP features is not clear. Could the authors elaborate on how the overlap between the collection and excitation paths influences this? Also, could they plot the schematic of the experimental setup in the supplementary section so this overlap would be clear for the reader?\nResponse: As suggested by the Reviewer, we rephrased and clarified the explanation for the presence of the condensed and uncondensed features on page 8.\n“The coexistence of condensed and uncondensed LP spectral features arises from the nonuniform profile of the spot (the area populated by polaritons) [41]. The polariton density decreases towards the edges of the spot, leading to sub-threshold LPs at the periphery alongside with a condensate at the center. Since the spectrometer collects the signal from a region larger than the spot, the reflectivity spectrum above threshold reflects the contributions of the uncondensed LPs at the edges, in addition to the condensate.”\nA sketch of the experimental setup was added to the supplementary information (Supplementary Figure 7).\n4. Can the Stark shift be observed in direct PL measurements? What are the advantages of utilizing reflectance spectroscopy here?\nResponse: The choice of reflectance spectroscopy was dictated by the need for high temporal resolution, compatible with the ultrafast dynamics of the Stark effect. Following the Reviewer’s insightful question, we now address the subject in detail in the Methods section on page 17:\n“It should be noted that the choice of pump-probe ultrafast spectroscopy rather than direct PL measurements stems from the need to capture the femtosecond-scale modifications induced by Stark effect. Since PL signals last several orders of magnitude longer, the impact of the Stark shift on time-integrated PL is negligible. The option of time-resolved measurement of PL with a streak camera would not overcome this limitation, as the temporal resolution of the camera is still limited to the picosecond scale.”\n5. The manuscript does not clearly explain the physical mechanisms responsible for the smooth versus step-like blueshifts observed at different detunings. A more detailed discussion would be helpful.\nResponse: A step-like blueshift is observed at δ = +5.1 meV, where the LP is mainly excitonic, while for δ ≈ 0 the shift evolves smoothly. The discontinuity at δ = +5.1 meV originates from the contribution of uncondensed lower polaritons (LP) at the edges of the spot (the area populated by polaritons), detected in reflectivity, and condensed LP at the center, detected in PL. For the condensate to become visible in differential reflectivity, strong PL is required. The latter is achieved at intensities above condensation threshold, for which the blueshift has already grown to large values, resulting in apparent step-like behavior although the energy in fact grows smoothly with excitation power [46]. In contrast, weaker interactions at δ≈0 lead to a smooth dependence. We note that although an apparent step-like blueshift in angle-resolved measured PL is also reported in other work [46] and observed in our own sample (Supplementary Figure 2), it is due to temporal integration, rather than to spatial integration as is the case in our differential reflectivity measurements. This topic is now discussed in detail in the revised manuscript on pages 12-13.\n6. Why is the decay of the oscillation so long for zero detuning before the threshold ( Fig. S1(a))? Authors should comment on how detuning affects the results of the measurements.\nResponse: The measurement shown in Supplementary Figure 4(a) on page 8 (previously 1a), presenting differential reflectivity at zero detuning, was performed at low excitation intensity, below the range of substantial spectral broadening. Under these conditions, the lower polariton (LP) linewidth is narrower at δ ≈ 0 compared to the exciton-like detuning (δ = +5.1 meV), due to the smaller excitonic fraction of the LP. This results in longer coherence times, or equivalently, a slower decay of the oscillations. In response to the Reviewer’s remark, a comment discussing the role of detuning has been added to the manuscript on page 12.\n7. What was the polarization of the pump and probe? Would the outcome depend on their polarizations?\nResponse: Following the Reviewer’s comment, the following clarification was added in the Methods section on pages 17:\n“The pump and probe beams were linearly polarized along the horizontal direction, and the sample was mounted vertically. Unlike transition metal dichalcogenide monolayers, where valley-selective polariton control using a circularly polarized Stark beam has been reported [47], in our system the rotation direction of normally incident light only distinguishes between spin-degenerate states. The orientation of the polarization of the oblique pump has a possible impact, as the exciton–light coupling strength may vary between transverse electric (TE) and transverse magnetic (TM) modes [48]. This allows optimization of the Stark effect efficiency by selecting the appropriate polarization . In our case, however, the available laser power exceeded the required power for the Stark effect. Therefore, the pump polarization was not varied, and the magnitude of the Stark shift was determined by the summed contribution of the TE and TM components of the pump.”\n8. The authors claim the cavity has a unique design; could they add a description of this design to the main text or methods for clarity?\nResponse: In response to the Reviewer’s suggestion, we have revised the Methods section on pages 15-16 to provide a more detailed description of the sample design, specifically highlighting the modifications that enable stable operation at high pump intensities and accommodate moderate angles of incidence.\nResponse: We thank the Reviewer for the constructive evaluation of our work. We appreciate the positive assessment of our approach and the recognition of its potential impact as well as the identification of points that require clarification and further analysis. We have carefully considered all the comments and have revised the manuscript accordingly.\nFollowing the Reviewer’s comment above, we have reordered the sections of the manuscript and now begin by presenting the Stark effect on the uncondensed and condensed polaritons at Δt≈0 in the section titled “Stark effect on LP condensate” which comprises Fig. 2 (previously Fig. 4) on pages 6-8, prior to the analysis of the coherent oscillations.\nResponse: Indeed, above the condensation threshold, the LPB energy exceeds the bare exciton energy of approximately 1612 meV. Such a pronounced blueshift has been reported in previous studies of condensates, particularly at positive detuning [45]. Angle-resolved PL measurements under off-resonant excitation performed on our sample also show LP energies reaching the bare exciton energy above threshold at δ ≈ 0, as shown in Supplementary Note 3 (presented below). These results are comparable to the case of δ > 0 observed in our reflectivity setup. In addition, the following comment regarding the trend in the LP energy in the measured differential reflectivity is now presented in the manuscript on page 12.\nResponse: In response to the Reviewer’s comment, we have added further clarification regarding the UP to the manuscript on page 14.\nResponse: We thank the Reviewer for raising this valuable point which we now address in the paper on page 13 as quoted below. Profiles of the sample detuning map displaying reflectivity spectra at varying cavity-exciton detuning values, and the linewidth measured in PL measurements, were added in the supplementary information (Supplementary Figure 6 and Supplementary Figure 5, shown below).\nResponse: We agree with the Reviewer’s observation that the broad probe pump states which subsequently relax along the lower polariton branch (LPB). This relaxation process accounts for the delay observed in the timing of the maximal Stark shift in the condensed regime. Below condensation threshold, the Stark effect appears as an energy shift of the reflectivity dips, hence its timing corresponds to the buildup of the system polarization. However, above threshold, the condensate PL dominates, and the Stark effect manifests as a shift in the PL. Consequently, the maximal effect is delayed by relaxation into the k ≈0 states associated with the observed PL. This contrast in delay times between the condensed and uncondensed systems persists across all probe intensities for δ = +5.1 meV and δ ≈ 0 (Supplementary Figure 3). The delay times for the condensate are slightly shorter for the exciton-like detuning of δ = +5.1 meV compared to δ ≈ 0, consistent with the longer relaxation times expected for an increased excitonic fraction and a shallower dispersion curve.\nResponse: We thank the Reviewer for his constructive comments and for the insightful review of our manuscript. We have carefully addressed the key issues raised and revised the manuscript accordingly.\nIn accordance to the Reviewer’s suggestion, we have added reflectivity and PL measurements to the supplementary information (Supplementary Figure 6 and Supplementary Figure 5), as detailed below. Supplementary Figure 6 presents normalized reflectivity profiles acquired using a broadband CW light source at various detuning values, including δ~0 and δ~+5 meV. PL measurements, demonstrated in Supplementary Figure 5, were obtained by off-resonant pulsed excitation at the energy corresponding to the first dip above the stop band at varying excitation power below and above condensation threshold for δ=-2.9 meV.\nResponse: The timing of the Stark maxima versus excitation intensity, extracted for all intensity values plotted in Fig. 4a-d (previously Fig. 3), indeed exhibits threshold-like behavior at excitonic LP detuning (δ=+5.1 meV). Following the Reviewer’s suggestion, the results for cavity-exciton detuning δ~0 and δ=+5.1 meV are now presented in Supplementary Figure 3, as shown below.\nThe threshold excitation intensity for the time delay roughly corresponds not just to the linewidth threshold, but also to the transition of the Stark shift signature from a blueshifted reflectivity dip to a blueshifted PL peak. This transition, demonstrated for example in Fig. 2, is responsible for the abrupt rise in the timing of the Stark signal maxima and can be explained as follows: below condensation threshold, the Stark effect appears as an energy shift of the reflectivity dips, hence its timing corresponds to the buildup of the system polarization. However, above threshold, the condensate PL dominates, and the Stark effect manifests as a shift in the PL rather than the reflectivity dips. Consequently, the maximal effect is delayed by relaxation into the k ≈0 states (from states excited at higher k by the broad probe) associated with the observed PL. This point was clarified in the paper on page 8.\nResponse: In response to the Reviewer’s comment, the fitting procedure and theoretical model for the Stark shift are now described in the Supplementary Note 4 on page 7.\nThe theoretical Stark shift, shown as dashed lines in Fig. 5 on page 14, is obtained from a Hamiltonian describing the Stark-induced modification of the polariton energies, as now detailed in the supplementary section.\nThe fitting procedure for the Stark effect in condensed LP does not include the effect of the overlap with the UP branch since its signature is reduced at high probe intensity. The following clarification was added on page 14.\nThe Stark shift dependence on pump intensity of the UP below condensation threshold is now included in Fig. 5 alongside the Stark shift of the LP. Additionally, error bars have been included.\nResponse: In response to the Reviewer’s remark, the title was changed to: “Ultrafast Dynamic Stark Shift of an Exciton-Polariton Condensate”.\nResponse: Following the Reviewer’s comment, we addressed the subject in the paper and added the values of the decay time in Fig. 3 (previously Fig. 2) on page 9 and Supplementary Figure 4 on page 8 along with the given corresponding linewidth values."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have thoroughly addressed all my comments and concerns and have implemented the appropriate changes in the manuscript. I am pleased to recommend it for publication.", "reviewer_2": "The authors have answered most of the questions I raised during the first revision round, as well as those of the other two referees, and have provided substantial additional and interesting information, which now appears mostly in the Supplementary Information. Besides, the authors have reorganized the sections in the main text, whose logic can now be followed more easily than in the first version.\nHowever, there is still one important question, associated to the blue shifted LPB mode above the exciton energy, that I don’t yet understand. The authors refer to two references (Appl. Phys. Lett. 102 (2013) 08115 and Phys. Rev. B 85 (2012) 075318) and claim that polariton condensates blueshifted above the exciton energy were investigated. My understanding of these two references is that, while there is indeed a large blueshift when the polariton condensate is formed (see for example Figure 3 in the Phys. Rev. B article), its energy never surpasses the energy of the bare exciton energy. This only happens when the second threshold is attained, corresponding to the standard photon lasing. I think this aspect needs to be critically analysed and clearly discussed before the current paper can be published. Otherwise, the reader might understand that some of the experiments could have been conducted across the strong-to-week coupling regimes transition.", "reviewer_3": "The authors have well addressed my comments and concerns. The manuscript presents an original and significant demonstration of ultrafast, reversible control of a polariton condensate. I would like to recommend publication of this manuscript."}, "author_response": "Response: We thank the Reviewer for the recommendation and for the contribution of their insightful comments.\nResponse: We thank the Reviewer for his valuable comment. Indeed, at zero cavity-exciton detuning where the exciton bare energy coincides with the cavity energy, the energy of the blueshifted lower polariton shown in [46] and [45], does not surpass the exciton energy in the polariton condensate regime. With increasing positive detuning and enhanced excitonic fraction, larger blueshifted energy values are reported, eventually exceeding the bare exciton beyond a certain positive detuning value (Fig. 3 in [45]). In our measurements, two additional observations confirm that the blueshift corresponds to a polariton condensate. The first is the short-lived signature of the Stark shift feature visible in Fig. 2b (shown below), indicating the presence of an excitonic component interacting with the Stark beam. In addition, a prolongation of the pump-probe delay Δt for which the Stark effect is maximal is manifested above threshold (dashed lines in Fig. 2b versus Fig. 2a). This prolongation is attributed to the fact that above threshold, where the Stark beam induces a shift in a strong PL rather than absorption dips, this delay is determined by the buildup time of the condensate. Following the Reviewer’s comment, the subject has been clarified on page 12:\n“The high values of the blueshifted LP energy at cavity–exciton detuning δ = +5.1 meV, compared to the energy values obtained at δ ≈ 0, characterize polariton condensates formed at positive detuning [45], where the excitonic fraction of the LP is enhanced. Measurements of the LP energy versus excitation intensity at δ≈0 obtained using a PL setup, are provided for reference in Supplementary Note 3. To confirm that the blueshift originates from condensed polaritons and to rule out attributing it to photon lasing, we point out both to the short-lived signature of the Stark shift around Δt≈0, well above the bare exciton energy (Fig. 2b, Fig. 3c,d), and to the relaxation-induced prolongation above condensation threshold of the pump-probe delay at which the short-lived signature is largest, attributed to the buildup time of the condensate PL (Supplementary Figure 3).”\nResponse: We greatly appreciate the Reviewer’s positive evaluation, helpful comments and the recommendation of our manuscript for publication."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have addressed my concern on the spectral position of the LPB and have discussed it appropriately in the manuscript. I am pleased to recommend it for publication"}, "author_response": ""}]

Decision letter