Quasi-thermal depletion of a polariton condensate by phonons near ...

Quasi-thermal depletion of a polariton condensate by phonons near room temperature Sebastian Klembt,1 Thorsten Klein,2 Anna Minguzzi,3 and Maxime Richard1

arXiv:1603.04206v2 [cond-mat.quant-gas] 31 Mar 2016

1

Institut Néel, Université Grenoble Alpes and CNRS, B.P. 166, 38042 Grenoble, France∗ 2 University of Bremen, P.O. Box 330440, 28334 Bremen, Germany† 3 LPMMC, Université Grenoble Alpes and CNRS, B.P. 166, 38042 Grenoble, France (Dated: April 1, 2016)

Thermalization of ultra-cold atoms confined in a magneto-optical trap occurs on a timescale much faster than the trapping lifetime. Thus, quantum degenerate atomic gases behave in close agreement with the laws of equilibrium thermodynamics. Owing to much higher loss rate and more complex energy relaxation mechanisms, this is not the case for quantum fluids of polaritons in solidstate microcavities, which are characterized by a dominant and generally unknown nonequilibrium character. In this work, we exploit the large polariton-phonon interaction near room temperature to achieve and unambiguously determine a significant degree of thermalization within a polariton condensate. We show that the heat thus picked-up from the phonon bath gives rise to a quasithermal depletion mechanism characterized by a condensation threshold increase, a decrease of the coherence length, and a scrambling of the topological excitations. PACS numbers: 71.36.+c,05.70.Ln,67.10.Ba

Unlike ultra-cold atoms kept in a magneto-optical trap, where Bose-Einstein condensation formation and growth has been well described as a thermal equilibration process [1, 2], photons or exciton-polaritons (polaritons) confined in solid-state optical microcavities have a typical lifetime in the picosecond range, usually shorter than their thermalization time. Their steady state thus results from competition between drive and losses, plus some possible partial thermalization within their lifetime. In this regime, that challenges the textbook thermalequilibrium description of quantum fluids, a drivendissipative version of Bose-Einstein condensation has been clearly shown to take place both for photons [3], and polaritons [4, 5]. In the context of steady-state thermodynamics [6, 7] of quantum gases, this phenomenon is highly intriguing. Indeed, most fundamental results of equilibrium thermodynamics do not apply in a driven-dissipative Bose gases and a whole range of exciting new physics is expected. For instance, condensation can take place in non-zero momentum state as a result of broken time reversal symmetry [8, 9], a non-trivial excitation spectrum is expected which includes a diffusive Goldstone mode [10, 11], and phase transitions with new dynamical universality class are predicted [12]. Experimentally, a steady-state population of photons in a cavity constitute a model system of a driven-dissipative ideal Bose gas (i.e. with negligible interparticle interactions). It has been shown recently that their condensation is mostly by faster-than-lifetime equilibration with a rovibronic thermal reservoir provided by dye molecules filling the cavity [13, 14]. Polaritons are elementary excitations of microcavities in the strong coupling regime [15]. They constitute another type of driven-dissipative bosonic quantum fluid, characterized by significant interparticle interactions resulting from their excitonic fraction. This feature is

FIG. 1. (Color online) Schematic representation of a steadystate polariton condensate. The optical pump P and the polariton radiative loss rate γ are shown and sets the timescale of the driven-dissipative regime. At cryogenic temperature (left panel), phonons play no role in fixing the condensate steadystate. At elevated temperature (right panel) the steady-state involves a quasi-thermal depletion mechanism (figured by the bubbles) disturbing the condensate population and phase, driven by the heat picked up from the thermal phonon bath of elevated temperature T (the flame).

at the basis of incredibly rich quantum hydrodynamics phenomena such as superfluidity, and the spontaneous or triggered occurence of vortices, solitons, and spindependent complex phase structures [16]. From the thermodynamical point-of-view, it has been shown that the excitonic reservoir coexisting at higher energy with the polariton condensate plays a key role in driving their redistribution in phase space and Bose-Einstein condensation [17–21]. However, whether this mechanism is of thermal or driven-dissipative nature is not well established yet, as thermal-like Boltzmann tails in the polariton spectrum might be sometimes coincidental [22] or result from quantum noise of purely driven-dissipative origin [11]. In this work, we have explored the nature of a driven-

2 dissipative polariton condensate interacting with a reservoir of perfectly known thermal state: lattice phonons. While at cryogenic temperatures (T < 50K, Fig.1.a) the polariton-phonon scattering rate γpp is far too weak as compared to the polariton loss rate γ to drive any thermal equilibration with thermal phonons [23], the situation is very different near room temperature. Owing to the much larger phonon population, γpp reaches a point where it matches γ. This criterion characterizes an intermediate steady-state situation, where thermal equilibration and the driven-dissipative kinetics both contribute significantly in setting the polariton condensate equilibrium state. In our specific experimental situations, phonons give rise to a thermal depletion mechanism of the condensate for which, by picking up heat from the phonon bath, polaritons from the condensate are excited into the non-condensed fraction and perturb the condensate phase (T = 243 K, Fig.1.b). This mechanism does not fully determine the new condensate steady state, but modifies it significantly; it can thus be qualified as “quasi-thermal” as opposed to the purely drivendissipative or the thermodynamic limit. We evidence this quasi-thermal mechanism by a specific decrease of the condensate correlation length, and by the modification and disappearance of the topological excitations such as vortices and solitons, as temperature is increased. Our interpretation is backed up by a stochastic drivendissipative model that we have developed.

FIG. 2. (Color online) Circle symbols: measured kk = 0 polariton emission spectrum full width at half maximum (FWHM) below threshold versus polariton energy Elp minus the bare exciton energy Ehh at T = 6 K (a), on a fixed microcavity position labeled ’area 1’ versus temperature (b), and at a fixed temperature T = 243 K versus polariton energy (c). The square symbols in (b) show the measured ground-state polariton energy in area 1 versus temperature. The green (black) dashed lines show the calculated polariton radiative losses ~γ, (quantum well disorder ~γinh ) contribution to the linewidth in (a) and (c). The solid blue (red) line is the calculated polariton FWHM excluding (including) the polaritonphonon scattering contribution γpp . The hatched area shows the parameters region where γpp contributes significantly to the FWHM.

EXPERIMENT

For this set of experiments, we used two high quality Zinc selenide microcavities [24] in which, like in nitride [21], Zinc oxide [25, 26] or organic material-based microcavities [27], a polariton condensate can be driven up to room temperature. Both microcavities are of equal design but tuned differently to achieve polaritonic resonance within two different temperature ranges (cryogenic and close to room temperature). A Rabi splitting of Ωhh = (32 ± 2) meV between the cavity mode and the heavy-hole exciton at T = 5 K is found and kept up to room temperature. The exciton energy varies from Ehh = 2817 meV at T = 10 K, to Ehh = 2730 meV at T = 243 K. Polaritons are excited by non-resonant (∼ 100 meV above Ehh ) picosecond pulses of average power density P generated by a doubled Ti-Sapphire laser.

Quantitative estimate of the crossover between the driven-dissipative and the thermalized regime

As a preliminary requirement to this experiment, we need to characterize the polaritons’ thermodynamical state depending on the experimental parameters, and

in particular the phonon temperature T and the polaritons energy Elp . To do so, we compare the polaritonphonon interaction rate γpp (Elp , T ) with the polariton radiative loss rate γ(Elp ).Thus, when γpp  γ, polaritons are at full thermodynamic equilibrium with the phonons at a temperature T , while when γpp  γ polaritons are in the purely driven-dissipative limit. As mentioned above, the criterion γpp ∼ γ characterizes an intermediate steady-state situation, where thermal equilibration and the driven-dissipative kinetics both contributes significantly in setting the polaritons equilibrium state. To carry out this measurement, we excite polaritons far below the condensation threshold Pth and measure their photoluminescence spectral linewidth ~γp at kk = 0. The latter quantity is directly proportional to γpp , plus to two other contributions: (i) the polariton radiative rate γ which depends on the photonic fraction and (ii), the quantum well disorder which causes elastic scattering of polaritons at a rate γinh towards localized dark exciton states (a review on the latter effect can be found in [28]). In a first stage, we thus perform a linewidth measurement at cryogenic temperature T = 6 K, where γpp can be safely neglected as compared to γ and γinh . The measurement is shown in Fig.2.a versus the polariton energy

3

FIG. 3. (Color online) Polariton condensate correlation amplitude |g (1) (x, −x, y, −y)| (top row), relative phase φ(x, y) − φ(−x, −y) (middle row), and relative velocity |v(x, y) − v(−x, −y)| (bottom row) in color scale, versus position (x, y) for different temperatures: T = 172 K (a,e,i); 196 K(b,f,j); 218 K (c,g,k); 243 K (d,h,l). The diamond,round, and x symbols show the position of a soliton, a +1 and a −1 charge vortex, respectively. Their nature is derived from their specific phase pattern (middle row) and their position matches local velocity maxima (bottom row). The flat areas surrounding the condensate in every panels results from the suppression, during the numerical data analysis, of the raw data with too low signal-to-noise ratio.

Elp − Ehh . Both contributions, γ and γinh to the polariton linewidth ~γp , are well understood within a simple model [29]. This analysis yields a pure cavity photon linewidth ~γc = 1.2 meV, a disordered excitonic density of states linewidth ~Γinh = 11 meV and a characteristic rate of polariton scattering over the quantum well disorder γ0 = 2 meV. Note that these three parameters are temperature independent, and that the last two are structural characteristics of the quantum wells and can thus be used for both microcavities. In order to find a working regime where γpp approaches γ, i.e. contributes significantly to the linewidth, we use the second microcavity and carry out the same linewidth measurement at higher temperature. The results are shown in Fig.2.b where the polariton linewidth on a fixed point of the microcavity, labeled ’area 1’ further on, is shown for temperatures increasing from 150 K to 243 K. In Fig.2.c, the polariton linewidth is also shown at a fixed temperature of T = 243 K and for various points of the microcavity (i.e. various polariton energies Elp [30]). We fit these measurements using the previous analysis(solid blue line) where only γ and γinh are accounted for. The difference, shown as a cross-hatched region in Fig.2.b and Fig.2.c, can thus be attributed to the contribution of

polariton-phonon scattering rate γpp alone. To further verify this interpretation, we have calculated numerically the inelastic scattering rate of kk = 0 polaritons by thermal phonons. We find that the main contribution to the scattering rate is given by longitudinal optical phonons, within the Fröhlich interaction. The contribution of acoustic phonons, via deformation potential interaction, is three orders of magnitude smaller than the optical-phonon one, as previously reported [23, 31], and will be henceforth neglected. Note that for this calculation we used the known material constants as input parameters and left no parameters free [29]. The sum of the calculated γpp to the previously derived γ and γinh yields a quite good agreement with the measurement as shown by the solid red line in Fig.2.c, thus confirming that we have a reliable measurement of γpp at hand. As shown in Fig.2.b, the regime where γpp ∼ γ is achieved on area 1 (a 15 × 10 µm2 surface), for a temperature T ∼ 240 K (i.e. for which the hatched area is about one half of the total polariton linewidth). We choose to work on this specific sample area for two important reasons: (i) ~γ is a bit lower than its average value on the microcavity (3 meV against ∼ 4 meV); and (ii) the photonic disorder landscape is kept identical

4 throughout the experiment. Thus when we change the temperature, the disordered potential Ur (x, y; T ) experienced by polaritons only changes in global magnitude Ur (x, y; T 0 ) = Ur (x, y; T ) × C02 (T 0 )/C02 (T ), where C02 is the polariton photonic fraction, an effect easy to account for. As a result, when a temperature-dependent change is observed on the condensate properties, it cannot be attributed to a change of the disordered potential landscape.

Measurement of the coherence properties throughout the crossover

After this preparatory work, we increase the pulsed optical excitation on area 1 to reach the polariton condensate regime. The pump power is chosen 1.02 times the polariton stimulation power threshold Pth . We checked that the condensate remains in the single mode regime [32] for each investigated temperatures. Interestingly, upon increasing the temperature from T = 150 K to T = 243 K, the condensation threshold increases by 60%, or at fixed excitation power, the condensate vanishes. It means that the net effect of the condensate interaction with thermal phonons is a depletion mechanism, that kicks polaritons out of the condensate much more than it brings some in. Within our experimental parameters, this trend suggests that a hypothetical polariton fluid at full thermal equilibrium with phonons would be further away from condensation than the driven-dissipative case. This is actually in agreement with the fact that the critical polariton density ρeq,c = 2mkB T /h2 = 1014 cm−2 , that would be required to achieve the quantum degenerate regime at thermal equilibrium, is four orders of magnitude larger than in our experiment. From a practical point of view, we compensate for this threshold increase by adjusting the excitation power throughout the experiment, such that P (T ) = 1.02Pth (T ) regardless of the temperature. This strategy maintains an approximately constant condensate fraction. To further characterize the properties of the quasithermal polariton gas, we address its coherence properties. Using an imaging Michelson arrangement in cross-correlation configuration [4], we measure the spatial correlation function g (1) (x, y, −x, −y) of the polariton condensate for various temperatures. In order to remain accurately on area 1 we have used a position tracking optical setup on the backside of the sample holder providing a 0.5 µm repositioning accuracy. The amplitude of the correlation function |g (1) (x, y, −x, −y)|, the phase  condensate relative φ(x, y) − φ(−x, −y) = Arg g (1) (x, y, −x, −y) , and relative velocity field |v(x, y) − v(−x, −y)| = |∇[φ(x, y) − φ(−x, −y)]| are shown in Figs.3.a-d, Figs.3.e-h and Figs.3.j-l respectively, for four different temperatures. We use the relative velocity field (Fig.3 bottom row) to

spot the possible presence of a topological excitation and we identify its nature by looking at the phase pattern at this position ((Fig.3 middle row)). At T = 172 K (left panels), γpp is negligible versus γ as determined by our above analysis (cf. Fig.2.b). We thus are in the quasi-pure driven-dissipative regime for which we observe long range correlations, with a shape strongly influenced by local disorder (Fig.3.a), plus several permanent topological excitations, namely a vortex anti-vortex pair and two solitonic structures. Upon increasing temperature, i.e. increasing the ratio γpp /γ, we observe two different features: (i) the correlation length shrinks by ∼ 20% upon reaching T = 243 K (Figs.3.ad), and (ii) the topological excitations are perturbed and their number decreases and eventually vanishes. Regarding point (ii) we observe more specifically that at T = 196 K (Figs.3.b,f,j), a solitonic structure disappears as well as a vortex-anti-vortex pair, and a soliton is observed instead. At T = 218 K one of the two remaining solitonic structures is suppressed, followed by the last one at T = 243 K (Figs.3.d,h,l).

THEORY

In order to provide some insight into these observations, we have simulated the behaviour of the condensed part of the polariton fluid using a time-dependent drivendissipative mean field calculation [10, 16], including a thermal space- and time-dependent noise source accounting for polariton - LO phonon interactions, in a similar fashion as in [33]. The model is presented in detail in [34]. We used the same temperature-dependent phonon amplitude as that derived above to calculate γpp (T, Elp ). The equations are explicitly solved in time and the obtained correlation function is time-integrated, thus simulating the same quantity which is measured in the experiment. The polariton disordered potential Ur (x, y) has been measured in a photoluminescence spectroscopy mapping experiment [35] and accounted for in the simulation. The calculated |g (1) (x, y, −x, −y)|, relative phase φ(x, y) − φ(−x, −y), and relative velocity |v(x, y) − v(−x, −y)| are shown in Figs.4.a-b, Figs.4.cd, and Figs.4.e-f, respectively, for two different temperatures: T = 172 K and T = 243 K. In agreement with the experiment, the calculation shows that the correlations range decrease upon increasing the phonon temperature. However, as shown by the quantitative experimenttheory comparison shown in Fig.4.g-h, the correlations are overestimated at all temperatures. This discrepancy results from the adopted mean-field model, which neglects the noncondensed fraction, while in the experiment a significant non-condensed polariton population is present and increases with temperature. Regarding the topological excitations of the condensate, the theory agrees with the experimental observation

5 the reduction of the correlation length, a topological excitation can still exist but it is not coherent enough with the remote area of the condensate it is overlapped with, and thus does not show up in the measurement. A second possibility is that the condensate vanishes locally, taking with it a topological excitation if present, as it requires a phase degree of freedom to exist.

FIG. 4. (Color online) Calculated Polariton condensate correlation amplitude |g (1) (x, −x, y, −y)| (upper row), relative phase φ(x, y) − φ(−x, −y) (middle row), and relative velocity |v(x, y) − v(−x, −y)| (bottom row) in color scale, versus position (x, y) for two different temperatures: T = 172 K (a,c,e) and T = 243 K (b,d,f). Symbols are defined as in Fig.3.(a-d), with the addition of the triangle corresponding to a charge 2 vortex. Measured (g) and calculated (h) profiles |g (1) (r, −r)| taken across the condensate, along a chosen direction, for temperatures T = 172 K (blue); 196 K (cyan); 218 K (orange); 243 K (red). The dashed arrows are a guide to the eye showing the decrease in correlation length for increasing temperature.

in predicting their suppression upon increasing the temperature, as hot thermal phonons cause too much spatial phase noise for a vortex or a soliton to maintain its characteristic phase pattern over time. Thus, in our calculation shown in Fig.4, the low temperature condensate (T = 172 K) exhibits two solitons and a charge 2 vortex, while at T = 243 K, the weakest soliton (in terms of phase difference between both sides of the structure) and the vortex are fully scrambled and the strongest soliton exhibits a markedly decreased average phase contrast. Note that the model used does not capture two other mechanisms possibly also responsible for the disappearance of topological excitations. A first one is related to the experimental method used to measure the phase: owing to

To summarize, we have identified two temperaturedependent signatures of the interactions of polaritons with the thermal phonon bath at elevated temperature: a population transfer from the condensed to the non-condensed fraction, as evidenced by the increase of the excitation threshold with temperature, and a perturbation of the condensate phase by thermal noise, as evidenced experimentally and predicted theoretically by the analysis of the first-order correlation function. This set of results is fully consistent with a quasi-thermal depletion mechanism of the nonequilibrium polariton condensate, induced by heat transfer from the thermal phonon reservoir. More generally, this work shows that the nonequilibrium character of a polariton condensate can be tuned and known in an unambiguous and controlled way, by using close-to-room temperature phonons as a heat bath of perfectly known thermodynamical state. As such, polaritons at elevated temperatures constitute a unique experimental platform to investigate nonequilibrium thermodynamics of quantum fluids and the nature of their phase transitions, with many exciting perspectives. The authors acknowledge financial support by the ERC starting grant "Handy-Q" Nb 258608. We thank D. Hommel and C. Kruse for their support in the fabrication activities. Enlightening discussions with I. Carusotto, M. Wouters, A. Chiocchetta, A. Auffèves and C. Elouard are warmly acknowledged. MR wishes to express his immense gratitude to B. Richard for her constant support.

∗

†

[1]

[2]

[3]

[4]

Present address: Technische Physik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany Present address: BIAS, Institute of Applied Beam Technology, Bremen, Germany H.-J. Miesner, D. M. Stamper-Kurn, M. R. Andrews, D. S. Durfee, S. Inouye, W. Ketterle, “Bosonic Stimulation in the Formation of a Bose-Einstein Condensate”, Science 279 1005 (1998) S. Ritter, A. Öttl, Tobias Donner, Thomas Bourdel, Michael Köhl, and Tilman Esslinger, “Observing the Formation of Long-Range Order during Bose-Einstein Condensation”, Phys. Rev. Lett. 98, 090402 (2007) J. Klaers, J. Schmitt, F. Vewinger and M. Weitz “BoseEinstein condensation of photons in an optical microcavity”, Nature 468, 545 (2010) J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P.

6

[5]

[6] [7] [8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16] [17]

[18]

[19]

[20]

[21]

Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymanka, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud and Le Si Dang, “Bose-Einstein condensation of exciton polaritons”, Nature 443, 409 (2006) R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer and K. West “Bose-Einstein Condensation of Microcavity Polaritons in a Trap” Science 316 1007-1010 (2007) T. Hatano and S. Sasa, “Steady-State Thermodynamics of Langevin Systems” Phys. Rev. Lett. 86, 3463 (2001) Y. Oono and M. Paniconi, “Steady State Thermodynamics” Prog. Theor. Phys. Suppl. 130, 29 (1998). M. Richard, J. Kasprzak, R. Romestain, R. André, and L. S. Dang, “Spontaneous Coherent Phase Transition of Polaritons in CdTe Microcavities” Phys. Rev. Lett. 94, 187401 (2005) M. Wouters, I. Carusotto, and C. Ciuti “Spatial and spectral shape of inhomogeneous nonequilibrium excitonpolariton condensates”, Phys. Rev. B 77, 115340 (2008) M. Wouters and I. Carusotto, “Excitations in a Nonequilibrium BoseEinstein Condensate of Exciton Polaritons” Phys. Rev. Lett. 99, 140402 (2007) A. Chiocchetta and I. Carusotto, “Quantum Langevin model for nonequilibrium condensation” Phys. Rev. A 90, 023633 (2014) L. M. Sieberer, S. D. Huber, E. Altman, and S. Diehl, “Dynamical Critical Phenomena in Driven-Dissipative Systems” Phys. Rev. Lett. 110, 195301 (2013) J. Klaers, F. Vewinger and M. Weitz, “Thermalization of a two-dimensional photonic gas in a ’white wall’ photon box” Nature Phys. 6, 512 (2010) J. Klaers “The thermalization, condensation and flickering of photons” J. Phys. B: Atomic, Molecular and Optical Physics, 47, 243001 (2014) C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity” Phys. Rev. Lett. 69, 3314 (1992) I. Carusotto and C. Ciuti “Quantum fluids of light”, Rev. Mod. Phys. 85, 299 (2013) D. Porras, C. Ciuti, J. J. Baumberg, and C. Tejedor, “Polariton dynamics and Bose-Einstein condensation in semiconductor microcavities” Phys. Rev. B 66, 085304 (2002) T. D. Doan, Huy Thien Cao, D. B. Tran Thoai, and H. Haug, “Condensation kinetics of microcavity polaritons with scattering by phonons and polaritons” Phys. Rev. B 72, 085301 (2005) D. Krizhanovskii, A. Love, D. Sanvitto, D. Whittaker, M. Skolnick, and J. Roberts, “Interaction between a highdensity polariton phase and the exciton environment in semiconductor microcavities” Phys. Rev. B 75 233307 (2007) J. Kasprzak, D. D. Solnyshkov, R. André, Le Si Dang, and G. Malpuech, “Formation of an Exciton Polariton Condensate: Thermodynamic versus Kinetic Regimes”, Phys. Rev. Lett. 101, 146404 (2008) J. Levrat, R. Butté, E. Feltin, J.-F. Carlin, N. Grandjean, D. Solnyshkov, and G. Malpuech, “Condensation phase

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

diagram of cavity polaritons in GaN-based microcavities: Experiment and theory” Phys. Rev. B 81, 125305 (2010) D. Bajoni, P. Senellart, A. Lemaitre, and J. Bloch, “Photon lasing in GaAs microcavity: Similarities with a polariton condensate” Phys. Rev. B 76, 201305(R) (2007) F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, and P. Schwendimann, “Bottleneck effects in the relaxation and photoluminescence of microcavity polaritons” Phys. Rev. B 56, 7554 (1997). S. Klembt, E. Durupt, S. Datta, T. Klein, A. Baas, Y. Léger, C. Kruse, D. Hommel, A. Minguzzi, and M. Richard, “Exciton-Polariton Gas as a Nonequilibrium Coolant” Phys. Rev. Lett. 114, 186403(2015) F. Li, L. Orosz, O. Kamoun, S. Bouchoule, C. Brimont, P. Disseix, T. Guillet, X. Lafosse, M. Leroux, J. Leymarie, M. Mexis, M. Mihailovic, G. Patriarche, F. Réveret, D. Solnyshkov, J. Zuniga-Perez, and G. Malpuech, “From Excitonic to Photonic Polariton Condensate in a ZnOBased Microcavity” Phys. Rev. Lett. 110, 196406 (2013) A. Trichet, E. Durupt, F. Médard, S. Datta, A. Minguzzi, M. Richard, “Long-range correlations in a 97% excitonic one-dimensional polariton condensate” Phys. Rev. B 88, 121407 (2013) J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf,R. F. Mahrt, “Room-temperature Bose-Einstein condensation of cavity exciton-polaritons in a polymer” Nature Materials 13, 247-252 (2014) V. Savona “Effect of interface disorder on quantum well excitons and microcavity polaritons” J. Phys.: Condes. Matter 19 295208 (2007) See Supplemental Material at http://link.aps.org... for details on the model used for the polariton linewidth analysis. As frequently done, the microcavities have been fabricated with a slightly wedged shape, such that the cavity mode energy can be tuned at will by changing the working point on the microcavity. G. Cassabois, A. L. C. Triques, F. Bogani, C. Delalande, Ph. Roussignol, and C. Piermarocchi “Polaritonacoustic-phonon interaction in a semiconductor microcavity” Phys. Rev. B 61, 1696(2000) D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities” Phys. Rev. B 80, 045317 (2009) I. G. Savenko, T. C. H. Liew, and I. A. Shelykh “Stochastic Gross-Pitaevskii Equation for the Dynamical Thermalization of Bose-Einstein Condensates” Phys. Rev. Lett. 110, 127402 (2013) See Supplemental Material at http://link.aps.org... for details on our model describing the polariton condensate mean-field perturbation by thermal phonons. A. Baas, K. G. Lagoudakis, M. Richard, R. André, Le Si Dang, and B. Deveaud, “Synchronized and Desynchronized Phases of Exciton-Polariton Condensates in the Presence of Disorder” Phys. Rev. Lett. 100, 170401 (2008)