Spontaneous formation of a polariton condensate in a ...

APPLIED PHYSICS LETTERS 95, 051108 共2009兲

Spontaneous formation of a polariton condensate in a planar GaAs microcavity Esther Wertz,1 Lydie Ferrier,1 Dmitry D. Solnyshkov,2 Pascale Senellart,1 Daniele Bajoni,1,a兲 Audrey Miard,1 Aristide Lemaître,1 Guillaume Malpuech,2 and Jacqueline Bloch1,b兲 1

Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France LASMEA, CNRS, University Blaise Pascal, 24 avenue des Landais, 63177 Aubière Cedex, France

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共Received 26 June 2009; accepted 8 July 2009; published online 7 August 2009兲 We report on polariton condensation in a planar GaAs microcavity under nonresonant optical excitation. Angularly resolved photoluminescence measurements demonstrate polariton condensation for temperature up to 40 K. Numerical simulations using Boltzmann equations give an overall description of the observed condensation for various detunings and temperatures. This model highlights the importance of the polariton relaxation rate as compared to the polariton decay for condensation to occur on the lowest energy polariton states. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3192408兴 Cavity polaritons are quasiparticles arising from the strong coupling regime between an optical cavity mode and quantum well 共QW兲 excitons in semiconductor microcavities.1 Because of their bosonic nature, polaritons offer a good system for final state stimulated scattering or, in other words, massive occupation of a single quantum state analogous to the Bose–Einstein condensation in a solid state system.2 Fascinating properties are expected from such solidstate condensates such as superfluidity3,4 or vortices.5 Moreover, polariton condensates acquire spatial and temporal coherence reflected in their light emission. They behave as low threshold sources of coherent light, operating without inversion.6 Phase diagrams of polariton condensates have been calculated as a function of polariton density and temperature,7 predicting that the greater the exciton binding energy in the considered materials, the higher the maximum operating temperature. Important efforts have been devoted these past years to the development of high finesse optical cavities containing strong oscillator strength excitons. Room temperature polariton lasing has recently been obtained in GaN systems.8,9 The strong coupling regime at room temperature with large Rabi splitting has also been achieved using ZnO.10 At cryogenic temperatures, polariton condensation has been obtained in two-dimensional 共2D兲 CdTe cavities with experimental evidence of spatial coherence11 and vortices.5 All of these semiconductor materials suffer from important crystallographic disorder which localizes polariton condensates.11 Moreover, implementation of electrical injection in a polariton device is difficult in these materials from a technological point of view. In that respect the GaAs system appears as an interesting alternative despite its limitation to low temperature operation: it is less disordered and its growth and technology are well controlled. Up to now, polariton condensation in GaAs cavities has only been observed by resonantly injecting cold excitons in a 2D geometry,12 or, in the case of highly nonresonant pumping, in laterally confined systems a兲

Present address: CNISM and Dipartimento di Elettronica, Universita degli Studi di Pavia, via Ferrata 1, 27100 Pavia, Italy. b兲 Electronic mail: [email protected]. 0003-6951/2009/95共5兲/051108/3/$25.00

such as micropillars13 or strain induced traps.14 In the present letter, we report on polariton condensation in a 2D GaAs microcavity under cw nonresonant excitation. Thanks to the high finesse of the cavity mode and to the large number of QWs embedded in the cavity, the polariton relaxation rate into the lowest energy states overcomes radiative losses. Angularly resolved photoluminescence measurements give evidence to polariton condensation for temperatures up to 40 K. Depending on the detuning between the exciton and the cavity mode, condensation occurs on the ground state or on a higher energy polariton state. Numerical simulations of polariton relaxation using the semiclassical Boltzmann equation give a good overall description of the two regimes. Our sample was grown by molecular beam epitaxy. It consists of a Ga0.05Al0.95As ␭ / 2 cavity embedded between two Ga0.05Al0.95As/ Ga0.80Al0.20As Bragg mirrors with 26 共30兲 pairs in the top 共bottom兲 mirror. Three sets of four 7 nm GaAs QWs are inserted at the antinodes of the cavity mode, one at the center of the cavity layer and the two others at the first antinode in each mirror. The detuning is defined as ␦ = EC共k = 0兲 − EX共k = 0兲, where EC共k = 0兲 and EX共k = 0兲 are, respectively, the energy of the cavity mode and the exciton at in-plane wavevector k = 0. A wedge in the layer thickness allows the probing of different detunings by moving the excitation spot on the sample. Photoluminescence experiments are performed using a cw Ti:sapphire laser focused onto a 20 ␮m diameter spot. The emission is spectrally dispersed and detected using a nitrogen cooled charge coupled device camera. The sample is kept in a cold finger cryostat with variable temperature. All experiments are performed under highly nonresonant excitation by tuning the laser to a mirror transmission maximum about 100 meV above the lower branch energy. In order to obtain polariton condensation under nonresonant excitation, the polariton relaxation rate into the lowest energy quantum states must overcome the radiative polariton decay 共via the escape of the photon through the mirrors兲. Polariton-polariton scattering provides an increasingly efficient relaxation mechanism as the excitation power is raised. Nevertheless for the system to stay in the strong coupling regime, the overall exciton density per QW must remain be-

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FIG. 1. 共Color online兲共a兲 Photoluminescence spectra measured under normal incidence for different excitation powers at ␦ = 0 , 5 meV. Inset: integrated emission intensity measured under normal incidence as a function of excitation power. Emission intensity as a function of angle and energy measured at ␦ = 0 , 5 meV for 共b兲 P = 0.2 Pth and 共c兲 P = 1.5 Pth 共linear color scale兲. The white lines indicate the uncoupled cavity and exciton modes, T = 10 K.

low the Mott density15 共typically ⬃1010 cm−2兲. By inserting a large number of QWs in the cavity, a high polariton density can be obtained while keeping the exciton density per QW low. Moreover, the polariton radiative decay rate is reduced by increasing the number of pairs in each Bragg mirror. This last point is the key difference with previous samples in which only conventional lasing was observed in 2D geometry.16,17 Indeed these samples exhibited quality factors of a few thousand while it is larger than 12 000 in the present one. Emission spectra measured at normal incidence 共k = 0兲 for a detuning ␦ = 0.5 meV are shown in Fig. 1共a兲 for various excitation powers. Above a marked threshold power Pth, pronounced nonlinear growth of the emission intensity is observed 关see inset of Fig. 1共a兲兴. We have previously reported a cavity with a much lower quality factor that such nonlinearities can be due to regular photon lasing and that such a regime presents strong similarities with a polariton condensate.16 To unambiguously discriminate between the two regimes, angularly resolved measurements have to be performed. To do so, the Fourier plane of the collection lens is directly imaged onto the entrance slit of the spectrometer. Figure 1共b兲 presents the far field emission measured below threshold. Because the experiment is performed at a low temperature, the polariton upper branch is not populated. It could nevertheless be measured by photoluminescence excitation spectroscopy so that the energy of the uncoupled cavity and exciton mode could be precisely determined 关white lines in Figs. 1共b兲 and 1共c兲兴. Above threshold 关P = 1.5 Pth on Fig. 1共c兲兴, the polariton dispersion is still clearly observed, superimposed to a pronounced intensity peak at k = 0. No significant blueshift is observed, as was the case in our previous report on a lower quality factor cavity.16 These measurements indicate that the observed nonlinear behavior occurs in the strong coupling regime and can be attributed to polariton condensation. The real space image of the emission below and above threshold is shown on the inset of Figs. 1共b兲 and 1共c兲. The spot has the same profile as the excitation beam and shows no evidence of localization.11 Temperature

dependent experiments show that polariton condensation is observed up to 40 K, in accordance with theoretical predictions18 for GaAs based samples. At higher temperatures, the cavity mode dispersion is measured above threshold and only photon lasing occurs.16 Let us now discuss polariton condensation as a function of the exciton photon detuning. An example of far field emission measured for ␦ = −6 meV is presented in Fig. 2共a兲. A pronounced threshold is also observed, but the accumulation of polaritons does not occur in the lowest energy quantum states but at higher energy in finite k states. This feature is further illustrated in Fig. 2共b兲 where the in-plane wavevector at which stimulated emission occurs is summarized as a function of detuning. As the detuning becomes more negative, polariton relaxation into the lowest energy states becomes less efficient. The trap in k-space is deeper and in addition, polaritons in the trap are more photonlike and thus less sensitive to interactions. As a result, occupation factors larger than unity are primarily reached in excited states then triggering stimulated scattering. This is the clear signature of an out of equilibrium situation, governed by the kinetics of relaxation processes. This situation seems in contradiction

FIG. 2. 共Color online兲共a兲 Emission intensity as a function of angle and energy measured at P = 1.5 Pth for ␦ = −6 meV 共linear color scale兲. The white lines indicate the uncoupled cavity and exciton modes. 共b兲 Measured and 共c兲 calculated in-plane wavevector of the condensate at threshold as a function of detuning.


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FIG. 3. 共Color online兲共a兲 Measured spectral blueshift at the wavevector where stimulation occurs 共black squares兲 compared to ␣2 Pth as discussed in the text 共red circles兲. 共b兲 Threshold power Pth measured as a function of detuning at T = 10 K 共black squares兲 and T = 30 K 共blue circles兲. 共c兲 Corresponding simulations.

with the original proposal of thermodynamical condensation given by Bose and Einstein.19 Nevertheless, in open systems, an extended definition of “out of equilibrium condensation” can be generalized,20 which includes condensation in an excited state. Numerical simulations of polariton relaxation were performed using the semiclassical Boltzmann equations to describe the dynamics of polaritons along the lower polariton branch.21 Exciton-phonon as well as exciton-exciton interactions are considered in this model. The calculated inplane wavevector at which condensation occurs is presented on Fig. 2共c兲 and reproduces qualitatively the experiments, namely, condensation in excited states for negative detuning and on the lowest energy polariton state at k = 0 for positive detunings. Figure 3共a兲 summarizes the spectral blueshift measured at threshold on the emission of the polariton state at which condensation occurs. This blueshift is the signature of polariton interactions with excitons present in the system. It is proportional to the density of excitons 共and thus to the excitation power Pth兲, and to the polariton excitonic part ␣2. As shown on Fig. 3共a兲 the blueshift varies as ␣2 Pth, a further evidence that the nonlinear emission arises in the polaritonic regime. The threshold power Pth has been measured as a function of detuning and is summarized for two temperatures in Fig. 3共b兲, together with the calculated values. Pth presents a minimum close to zero detuning. This feature can be understood as follows: at negative detunings, the relaxation kinetics is slow due to less efficient scattering rates, thus increasing the threshold power needed to reach a polariton occupancy close to unity. On the other hand, for positive detunings, Pth is determined by the critical density to reach a quasiequilibrium on the lower branch. For increasing positive detuning, the critical density increases because of a larger density of states close to k = 0. As temperature is increased, the threshold is reduced for negative detunings because polariton relaxation becomes more efficient. On the opposite, for positive detunings, Pth increases as does the critical density with temperature. Numerical simulations give a good overall description of the Pth evolution. To conclude, spontaneous polariton condensation is demonstrated under nonresonant excitation in a planar high finesse GaAs microcavity. Depending on the exciton-cavity detuning, condensation occurs on an excited state, signature of a strongly out of equilibrium system or on the lowest

energy k = 0 state. Numerical simulations using semiclassical Boltzmann equations provide a good overall description of the detuning and temperature dependence of the polariton condensation. These results obtained in a well controlled and weakly disordered semiconductor system are very promising for further investigation of condensate propagation and superfluidity.22,23 Moreover such GaAs cavities are a model system for the first implementation of electrically driven polariton lasers.24 This work was partly supported by the ANR contract “GEMINI” 共Grant No. ANR-07-NANO-005兲 and by C’nano Ile-de-France. 1

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