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2015 Jpn. J. Appl. Phys. 54 092801(http://iopscience.iop.org/1347-4065/54/9/092801)
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REGULAR PAPER

Japanese Journal of Applied Physics 54, 092801 (2015)
http://dx.doi.org/10.7567/JJAP.54.092801

Spatial and temporal dynamics of the crossover from exciton–polariton condensation
to photon lasing
Yasuhiro Matsuo1,2,3*, Michael D. Fraser2,3, Kenichiro Kusudo2, Andreas Löfﬂer4,
Sven Höﬂing4, Alfred Forchel4, and Yoshihisa Yamamoto2,3,5
1

Graduate School of Information Science and Technology, The University of Tokyo, Bunkyo, Tokyo 113-8656, Japan
National Institute of Informatics, Chiyoda, Tokyo 101-8403, Japan
3
Quantum Functional System Research Group, RIKEN Center for Emergent Matter Science, Wako, Saitama 351-0198, Japan
4
Technische Physik, Physikalisches Institut, Wilhelm Conrad Röntgen Research Center for Complex Material Systems,
Universität Würzburg, 97074 Würzburg, Germany
5
E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, U.S.A.
E-mail: yasuhiro_matsuo@nii.ac.jp
2

Received March 16, 2015; accepted June 16, 2015; published online August 21, 2015
At a sufﬁciently high density, the bosonic exciton–polariton system breaks down and the constituent electron, hole, and photon nature is revealed.
Although conventional photon lasing is expected in this regime, the nature of the crossover from polariton condensation to photon lasing is not yet
well understood. Through detailed mapping, we deconvolute the spatial, temporal, momentum, and energy dependences of the photoluminescence from this system at the crossover point. Photon lasing is distinctly observed far above this crossover.
© 2015 The Japan Society of Applied Physics

1.

Introduction

Microcavity exciton polaritons are half-light=half-matterbosonic quasi-particles and can form a Bose–Einstein condensate (BEC) at a suﬃciently high phase space density.1,2)
In 1995, the ﬁrst observation of a BEC phase was conﬁrmed
in a dilute gas of atoms. Experiments with atomic BEC
are generally performed in equilibrium, and atomic BEC
has been immensely successful as a test bed of fundamental
quantum mechanics3–7) and condensed matter physics.8,9)
In contrast, the BEC of exciton–polariton, created in asemiconductor microcavity, is inherently in nonequilibriumowing to the ﬁnite polariton lifetime as a result of cavity
photon loss. The improving sample quality and emerging
techniques for manipulating the polariton condensate render
it as an ideal platform for the study of a two-dimensional
nonequilibrium quantum degenerate gas.10,11)
Unlike the atomic system, polaritons are weakly boundcomposite particles, and at very high density, they dissociate
into predominantly fermionic plasma of electrons and holes
coupled to the photon ﬁeld. It is generally believed that conventional photon lasing, owing to free-carrier population
inversion, predominates at high densities, but the nature of
the crossover to the high-density phase is presently not wellunderstood. In the experimental literature, this crossover isoften referred to as the “2nd threshold” to contrast with the
BEC threshold. In this article, through a detailed study of thespatial and temporal dynamics of photoluminescence (PL)from low to high densities, we will investigate the nature ofthis crossover.
In several theoretical studies, the nature of the microcavity electron–hole high-density regime has been considered. Initially, it was predicted that a standard BEC–BCS crossover would occur in thermal equilibrium,12)
although with substantially diﬀerent characteristics owing
to the interaction of the electron–hole pairs with the photonﬁeld.13) Subsequent works revealed the origin of the binding force of electron–hole pairs changing from Coulomb
to photon-mediated interactions in the high-density regime.14,15)

Using a nonequilibrium Greens function approach, recent
theoretical works have predicted two diﬀerent types of 2nd
threshold in the high-density regime,16,17) one occurringowing to photon lasing under highly nonequilibrium conditions, and the other being a crossover transition into
photonic polariton BEC under quasiequilibrium conditions.
A notable feature of both scenarios is the existence of anenergy gap above that of the free electron–hole pair, implying
the existence of bound electron–hole pairs.
In contrast, despite the fact that in experimental studies
the 2nd threshold has been widely observed and reported
to indicate the onset of photon lasing in a high-excitation
regime,18–23) there is no clear evidence of either the photonic
polariton BEC phase or simple electron–hole bound pairs in
the high-density regime.
The standard, simple picture regarding the transition fromexciton–polariton condensation to photon lasing is due to thedissociation of Coulomb-bound electron–hole pairs owing to
the screening of their binding energy. In the isolated exciton
system,24) this transition from insulating exciton gas toelectron hole plasma is generally understood to be a gradualtransition rather than an abrupt one.25,26) Indication of asimilarly natured transition in the polariton microcavity
system has also recently been indicated by THz spectroscopy.27) The inﬂuence of photon interaction via the microcavity
is less well understood, but the clear observation of the
2nd threshold and crossover from exciton polariton condensation to photon lasing presents an opportunity tounderstand the insulator–plasma transition in the microcavity-embedded electron–hole system.
After describing the experimental setup and deﬁning
the pump and polarization axes in Sect. 2, we discuss three
aspects of the relaxation dynamics of the highly excited
microcavity polariton system in Sect. 3. In Sect. 3.1, we
consider the time-resolved relaxation dynamics with particular focus on deﬁning the 2nd threshold and characteristic of
the crossover from exciton–polariton condensation to photonlasing. In Sect. 3.2, we describe the eﬀect of inhomogeneousand ﬁnite-k pumping on the spatial dynamics of the condensate and lasing states. Lastly, in Sect. 3.3 we discuss the092801-1© 2015 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 54, 092801 (2015)

Y. Matsuo et al.

Fig. 1. (Color) Coordinate system of the experimental setup, sample, andpumping geometry. The z-axis is deﬁned to be perpendicular to the sample
plane. The pump direction is parallel to the xz-plane and inclined by an angle
θ of ∼60° from the z-axis. The linear polarization angle is characterized by
the angle α, where a positive angle indicates a clockwise rotation of the linear
polarization vector in the travelling direction of the emitted light. The angle
α = 0° is parallel to the y-axis.

temporal polarization dependence and show a linear polarization rotation indicating the cooperative phenomenon ofelectrons, holes, and photons.
2.

Experimental methods

We ﬁrst deﬁne the coordinate system of the experimental
setup, sample, and pumping geometry. Figure 1 shows theexperimental geometry and deﬁnitions of our coordinate
nomenclature for the pumping and polarization axes.
Eﬃcient oﬀ-resonant photon injection into the microcavity is achieved using a pulsed pump laser at a ﬁnite angle(θ of ∼60°) relative to normal incidence, at an energy Epumpof ∼1.668 eV, which couples to the photonic part of theupper polariton branch. The pump source is a mode-locked
Ti:sapphire laser with a pulse width of 3 ps and a repetition
rate of 76 MHz. At this angled incidence, the pumping spot
is focused to an elongated Gaussian with the dimensions
Δx ∼ 30 and Δy ∼ 20 µm. The pump polarization is horizontal linear polarization (TM mode).
In order to make the 2nd threshold appear at reasonable
laser powers, a sample with a red-detuned cavity mode
(ΔE = Ecav − Eexc ; ∼−3 meV) is used. The sample structure
consists of a λ=2 cavity with three sets of four 7-nm-wide
GaAs=AlAs quantum wells at the antinodes of the cavity
mode in a 20- and 16-layer mirror-pair cavity on the bottom
and top sides of the microcavity, respectively. A cavity
photonic quality factor Q of 2000 is measured. The experiment is conducted at a nominal sample temperature of 10 K.
3.
3.1

Results and discussion

BEC–photon lasing crossover
A number of previous works report the observation of
the 2nd threshold when increasing the pump power well
above the BEC threshold, which is generally described as the
crossover from exciton polariton condensation to photonlasing, which is commonly shown in order to substantiate theclaim that the 1st threshold characterizes the Bose–Einsteincondensation of exciton–polaritons. The 1st and 2nd thresholds are typically deﬁned at the point of a discontinuouschange typically in both luminescence intensity and energy atk∥ of ∼0, and in such measurements they are distinguishedonly by their ordering with increasing pump power.1,2,18–20,28)

Fig. 2. (Color) (a)–(d) Time-resolved measurement of the emission
spectra at k∥ of ∼0. P=Pth = (a) 0.7, (b) 5.4, (c) 160, (d) 589. (e)–(h) Pumppower dependence of the emission spectrum at time delays Δt = (e) 0, (f) 50,(g) 99, and (h) 300 ps after pumping. Vertical red dotted lines indicate the 1st
and 2nd thresholds. 0 ps is deﬁned as the moment the pump emission
appears. The exact time delay between pumping and the beginning ofphotoluminescence at the highest excitation power is a 2–3 ps.

In an inhomogeneously pumped condensate, these characteristics are relatively unambiguous when the pump is
Gaussian, and the polariton distribution becomes similarly
deﬁned, i.e., with a rough axial symmetry and peaked in aﬁxed spatial location. However, in the study of the polariton
system over the wide range of pump powers studied in thiswork, it is necessary to carefully deconvolute the energy,
momentum, and space dependences. As such, we deﬁne the
2nd threshold as in Fig. 2 through the analysis of the timeresolved relaxation spectrum.
Figures 2(a)–2(d) show the time-dependent spectral dynamics of the polariton relaxation following pulsed excitation, for the normalized pump powers P=Pth of (a) 0.7, (b)5.4, (c) 160, and (d) 589. The threshold excitation power
density Pth is ∼1.9 × 1017 photons=m2=pulse. The measurement data are taken by isolating the k∥ ∼ 0 part of thespectrum using a streak camera and spectrometer slits in the
Fourier plane with a time resolution of ∼2 ps. The experimental data clearly diﬀerentiate the diﬀerent behaviors of(a) a thermal polariton gas below the 1st threshold Pth , (b)a polariton BEC above Pth , (c) relaxation to both lower

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Jpn. J. Appl. Phys. 54, 092801 (2015)

Y. Matsuo et al.

polariton (LP) and cavity photon states immediately below
the 2nd threshold, and (d) photon lasing at the cavity photon
energy above the 2nd threshold.
Analysis of the PL characteristic as a function of pumping
power [Figs. 2(e)–2(h)] at ﬁxed times permits the identiﬁcation of relaxation dynamics and the intermediate andﬁnal states of the system, which are obscured in timeintegrated measurements. This measurement results in a cleandeﬁnition of the 1st and 2nd thresholds. The ﬁrst occurs at
slightly blue-shifted energies above the LP ground state,indicating polariton condensation and the onset of condensate
self-interaction. The 2nd threshold is characterized by acoherent emission at the cavity photon energy, indicating
the onset of conventional cavity photon lasing.
The pump-power-dependent spectra at ﬁxed time delays
Δt of ∼0, 50, 99, and 300 ps after the initial pump pulse
are shown in Figs. 2(e)–2(h), respectively. In each of theseﬁgures the two vertical lines indicate the threshold powers
for the 1st and 2nd transitions. The cavity photon andsingle-particle LP energy are also shown as horizontal
lines.
Immediately after the pump pulse excites the photoexcited
carriers, a wide range of excited states above the cavity
photon energy exists [Fig. 2(e)].29–32) No distinct LP occupation can be observed at such short timescales. At later times[(f) Δt of ∼50 ps and (g) Δt of ∼99 ps], a distinct occupationof the LP and cavity photon states is observed at intermediateand high pumping powers, respectively. However, at suchintermediate times, the energy of these states is blue-shiftedby the remaining excitons and free-carriers. At (h) Δt of∼300 ps, the condensed LP and photon lasing states areclearly developed, and the 2nd transition is clearly visible.
As is well established,1,2) the 1st transition from thermal
polaritons to polariton BEC is exempliﬁed by an abrupt
linewidth reduction, a PL intensity increase, and a blue-shift
in energy resulting from enhanced bosonic single-mode
occupation. The transition from polariton condensation tophoton lasing is deﬁned here as the midpoint in the relatively
abrupt transition in energy and further linewidth narrowing,where the new energy coincides with that of the cavity
photon, at a pump power P of ∼213.5Pth. The exact transition
power depends sensitively on factors such as sample quality,
pump conﬁguration and energy, and cavity-exciton detuning.
However, note that it is considerably higher than that of theprevious reports of P of ∼10Pth .18,20,22)This transition, however, is not abrupt, and between thepump powers P=Pth of ∼100–300, there is a simultaneous
occupation in both the LP condensation and photon lasingstates before the crossover is complete. With the understanding that, in the electron–hole system, the insulator–
plasma transition is also not abrupt, this is not entirely
surprising, as it is expected that, over this crossover range ofpump powers, the exciton to free-carrier ratio will gradually
decrease towards zero. A similarly broad crossover may beobserved from the condensate to photon lasing.
Until now, however, we have considered only the lowmomentum emission. As the system is inhomogeneously
pumped, and at a ﬁnite angle corresponding to a ﬁnite inplane angular momentum, we next consider the spatial andmomentum dependences of the relaxation dynamics tounderstand the behavior in the vicinity of P=Pth ∼ 200.

Fig. 3. (Color) (a) Theoretical three-dimensional (3D) dispersion, where
the eﬀective mass and ground-state energy are determined by white-lightreﬂection-spectrum measurement. (b)–(f) Time-integrated 3D dispersion of
the photoluminescence at P=Pth (b) <1, (c) = 40, (d) = 160, (e) = 323, and(f) = 589. We combine ky-dispersion images measured at each kx andgenerate 3D dispersion. The resolution is Δky = 0.054 × 104=cm andΔkx = 0.098 × 104=cm. (g, h) Cross sections at kx = 0 in (e) and (f).

3.2

Spatial and momentum properties
As the pump angle in a planar microcavity directly controls
the initial in-plane momentum of the excited carriers, pumping at a ﬁnite angle will induce an asymmetric distributionof momentum and coordinate spatial-resolved relaxation
dynamics. Figure 3 shows measurements of the kx − kyresolved PL emission at various pump powers. For reference,
the theoretical microcavity polariton dispersion for our reddetuned sample (i.e., the LP becomes more photon-like) is
schematically shown in Fig. 3(a). The sample parameters are
established by a white-light-reﬂectance measurement of the
microcavity.
Figures 3(b)–3(f) show the energy-momentum dispersionof the emission for ﬁve pump powers. Figures 3(g) and 3(h)show the cross sections at ky = 0 of Figs. 3(e) and 3(f),respectively. Figure 3(b) shows a clear LP dispersion below
the 1st threshold. Figure 3(c) shows the photoemission shift
to higher energies and a contraction of momentum space
occupation above the threshold for condensation. Figure 3(d)shows the induced carrier emission during the relaxation

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Jpn. J. Appl. Phys. 54, 092801 (2015)

Y. Matsuo et al.

Fig. 4. (Color) Time- and energy-resolved measurement of kx-dispersion,using a streak camera to measure photoluminescence at each wavenumber.
The momentum resolution is Δkx = 0.128 × 104=cm.

Fig. 6. (Color) Polarization dependence of relaxation spectrum.
(a)–(d) Above the 1st threshold. (e)–(h) Above the 2nd threshold.
(a, e) Intensity plots. (b, f) S1, (c, g) S2, and (d, h) S3 components.

Fig. 5. (Color) Time-integrated and energy-integrated real-space images
at P=Pth = (a) 40, (b) 121, (c) 185, (d) 246, (e) 370, and (f) 589.

process in the high-excitation regime, exhibiting an asymmetric emission in the +kx direction as a result of the ﬁniteangled pump.
In Figs. 3(e)–3(h), when pumping above the 2nd threshold, a peak emission appears at ﬁnite momentum. The timedependent relaxation dynamics of the kx-asymmetric dispersion in Fig. 3(h) is given in Fig. 4. Figures 4(a) and 4(b)show the emission developing from a blue-shifted cavity
mode, evolving into a ﬂat momentum distribution. At a later
time, Fig. 4(c) shows that the system shifts to an intermediatestage with the simultaneous occupation of two energy levels,

corresponding to the exciton and LP states. 100 ps after
pumping, Fig. 4(d) shows that the transition to photon lasing
is incomplete.
The eﬀect of ﬁnite momentum pumping can also be madeclear by analysis of the spatial distribution. For a ﬁxed pumpspatial distribution, Fig. 5 shows the time- and energyintegrated spatial distribution as the pumping power isincreased. At a low power, but above the BEC threshold[Fig. 5(a)], the (condensate) emission is observed only within
the excitation spot. At higher pump powers [Figs. 5(b)and 5(c)], the emission spreads to the +x region. In thehigh-excitation regime, the in-plane momentum drives thecarriers to escape to low-density regions predominantly on
the +x side of the pump. It becomes clear that, at the highest
pump powers [Figs. 5(d)–5(f)], above the 2nd threshold, theemission concentrates and photon lasing occurs directly
within the pump spot.
3.3

Polarization
Our ﬁnal discussion explores the polarization properties of
the PL emission above and below the photon lasing thresholdto further clarify the microscopic nature of these states.
In Fig. 6, we show the time-dependent polarization dynamics

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Y. Matsuo et al.

of the PL emission immediately above the 1st threshold P=Pthof ∼2 [Figs. 6(a)–6(d)] and above the 2nd threshold P=Pthof ∼600 [Figs. 6(e)–6(h)]. For these two laser powers, afull set of energy-time-resolved Stokes parameters,33,34)
namely, the total intensity S0 = I [Figs. 6(a) and 6(e)], S1[Figs. 6(b) and 6(f)], S2 [Figs. 6(c) and 6(g)], and S3[Figs. 6(d) and 6(g)], are measured, the last three of which
are deﬁned as
I90  I0
;
I90 þ I0
Iþ45  I45
S2 ¼;
Iþ45 þ I45Iþ  I
S3 ¼
:
ð1Þ
Iþ þ I
The linear polarization angle α is deﬁned as the rotation
angle about the z-axis as shown schematically in Fig. 1.
A positive angle is thus deﬁned as a clockwise rotation in
the travelling direction of the emitted light. I indicates themeasured intensity of the subscripted polarization component. These measurement data are produced by the
cumulative integration of ∼76 × 106 experimental pumppulses, thereby representing the statistical average of polarization of the emitted light.
Above the 1st threshold [Figs. 6(a)–6(d)], each of the
Stokes components are close to zero, indicating that thecondensate polarization varies shot to shot. The system ispumped at an energy of ∼60 meV above the LP branch,which is suﬃciently energetically separated from the groundstate to exhibit strong decay of the polarization informationof the pump through multiple phonon and free-carrier
scattering events in the relaxation dynamics. Furthermore,
the onset of spontaneous coherence via the BEC transition is
generally understood to be accompanied by a spontaneous
symmetry breaking in the choice of condensate phase andpolarization.35–37)
In contrast, above the 2nd threshold [Figs. 6(e)–6(h)], thepolarization of the high-energy peak initially matches thatof the pump pulse. The high pump intensity promotes a more
rapid emission of photons from the system, occurring before
polarization decoherence becomes signiﬁcant. As the highly
excited system relaxes in energy, the initially pump-driven
linear polarization of α = 90° rotates to the linear polarization of 0° over the emission lifetime. The conserved linear
polarization and rotation over 500–600 ps implies that acooperative phenomenon of electrons, holes, and photons ispresent even in the lasing state.
S1 ¼

4.

Conclusions

We have reported here an experimental study of the spatial,
temporal, and polarization dynamics of the crossover fromexciton–polariton condensation to photon lasing. We haverevealed new features of this crossover in a spatially inhomogeneously pumped system, in which the spatial coexistencein the relaxation dynamics of the exciton–polariton condensation and the photon lasing above the 2nd threshold areobserved. The 2nd threshold P=Pth of ∼213.5 is much higher
than the previous P=Pth of ∼10. The crossover from exciton
polariton condensation to photon lasing is clearly identiﬁed
as a gradual transition rather than an abrupt jump and mimics
the typically smooth insulator–plasma transition in an

isolated exciton system. Above the 2nd threshold, the conservation and rotation of linear polarization over 500–600 ps
indicate that a cooperative nature of electrons, holes, andphotons persists in the lasing state. Although it has been
widely accepted that the transition to photon lasing in the
microcavity exciton–polariton system is due to the dissociation of electron–hole pairs, our experiments indicate thatphoton lasing in these structures, particularly near thetransition, results from a more complicated interplay of theelectron, hole, and photon components of this system andwarrants further study.
Acknowledgments

We are grateful to T. Horikiri and M. Yamaguchi for fruitful
discussions. This work was funded by the ImPACT Programof Council for Science, Technology and Innovation (Cabinet
Oﬃce, Government of Japan) and Research for Quantum
Repeater Technology (Subject: Entanglement puriﬁcation
between distant nodes), the Commissioned Research of the
National Institute of Information and Communications
Technology (NICT), Japan.

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