Photon-Number-Resolved Measurement of an Exciton-Polariton Condensate
Martin Klaas, Elisabeth Schlottmann, Hugo Flayac, Fabrice P. Laussy, F. Gericke, M. Schmidt, Martin von Helversen, J. Beyer, Sebastian Brodbeck, Holger Suchomel, Sven Höfling, Stephan Reitzenstein, Christian Schneider
We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.
We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.
Second-order time correlation measurements with a temporal resolution better than 3 ps were performed on a CdTe microcavity where spontaneous Bose-Einstein condensation is observed. After the laser pulse, the nonresonantly excited thermal polariton population relaxes into a coherent polariton condensate. Photon statistics of the light emitted by the microcavity evidences a clear phase transition from the thermal state to a coherent state, which occurs within 3.2 ps after the onset of stimulated scattering. Following this very fast transition, we show that the emission possesses a very high coherence that persists for more than 100 ps after the build-up of the condensate.
A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.
A full quantum theory beyond the mean-field regime is developed for an exciton polariton condensate, to gain a complete understanding of quantum fluctuations. We find analytical solution for the polariton density matrix, showing the polariton nonlinearity causing fast relaxation correlated with the pump so as to yield the condensation at threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian and to a nonclassical distribution beyond the understanding at the level of off-diagonal long-range order. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning and temperature.
The advent of controlled experimental accessibility of Bose-Einstein condensates, as realized with e.g. cold atomic gases, exciton-polaritons, and more recently photons in a dye-filled optical microcavity, has paved the way for new studies and tests of a plethora of fundamental concepts in quantum physics. We here describe recent experiments studying a transition between laser-like dynamics and Bose-Einstein condensation of photons in the dye microcavity system. Further, measurements of the second-order coherence of the photon condensate are presented. In the condensed state we observe photon number fluctuations of order of the total particle number, as understood from effective particle exchange with the photo-excitable dye molecules. The observed intensity fluctuation properties give evidence for Bose-Einstein condensation occurring in the grand-canonical statistical ensemble regime.
BEC of exciton-polaritons and related effects such as superfluidity1,2, spontaneous symmetry breaking3,4 and quantised vortices5,6 open way to creation of novel light sources7 and optical logic elements8. Remarkable observations of exciton-polariton BEC in microcavities9-12 have been reported in the recent ten years. Very recently, thermalisation and subsequent condensation of cavity photons in a dye-filled microcavity have been observed13. Here we show that BEC of both exciton-polaritons and photons can be created in the same system under different optical excitation conditions. A dynamic phase transition between a photon and a polariton BEC takes place after a single high-power excitation pulse and we find both condensed states in thermal equilibrium with the excited states. At the crossover, photons and polaritons coexist, which results in a decrease in the long-range spatial coherence. Build-up and successive depinning of polarisation is observed at the threshold of both polariton and photon condensation.
We implement full polarization tomography on photon correlations in a spinor exciton-polariton condensate. Our measurements reveal condensate pseudospin mean-field dynamics spanning from stochastic switching between linear polarization components, limit cycles, and stable fixed points, and their intrinsic relation to the condensate photon statistics. We optically harness the cavity birefringence, polariton interactions, and the optical orientation of an incoherent exciton reservoir to engineer photon statistics with precise control. Our results demonstrate a smooth transition from a highly coherent to a super-thermal state of the condensate polarization components.