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Physics

Matter-Light Condensates Reach Thermal Equilibrium

Jonathan Keeling, Francesca Maria Marchetti

Published Jan 5, 2017• 1 citation
Publisher

Abstract

The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects.Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures.However, polariton lifetimes are typically too short to permit thermal equilibration.This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect.Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures.With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram.The measured phase boundary agrees well with the predictions of basic quantum gas theory.

DOI
10.1103/physics.9.154

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The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects.Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures.However, polariton lifetimes are typically too short to permit thermal equilibration.This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect.Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures.With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram.The measured phase boundary agrees well with the predictions of basic quantum gas theory.
Bose-Einstein condensation (BEC) is a thermodynamic phase transition of an interacting Bose gas. Its key signatures are remarkable quantum effects like superfluidity and a phonon-like Bogoliubov excitation spectrum, which have been verified for atomic BECs. In the solid state, BEC of exciton-polaritons has been reported. Polaritons are strongly coupled light-matter quasiparticles in semiconductor microcavities and composite bosons. However, they are subject to dephasing and decay and need external pumping to reach a steady state. Accordingly the polariton BEC is a nonequilibrium process of a degenerate polariton gas in self-equilibrium, but out of equilibrium with the baths it is coupled to and therefore deviates from the thermodynamic phase transition seen in atomic BECs. Here we show that key signatures of BEC can even be observed without fulfilling the self-equilibrium condition in a highly photonic quantum degenerate nonequilibrium system.
We study theoretically superfluidity in a driven-dissipative Bose gas out of thermal equilibrium, and discuss the relation with conventional superfluids. We show how the superfluid behavior is characterized by a dramatic increase in the lifetime of a quantized vortex and point out the influence of the spatial geometry of the condensate. We apply our study to a condensate of polaritons in a semiconductor microcavity, whose properties can be directly inferred from optical spectroscopy. We propose three different experimental schemes to measure the vorticity of the polariton condensate.
Abstract Superfluidity, first discovered in liquid 4He, is closely related to Bose–Einstein condensation (BEC) phenomenon. However, even at zero temperature, a fraction of the quantum liquid is excited out of the condensate into higher momentum states via interaction-induced fluctuations—the phenomenon of quantum depletion. Quantum depletion of atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This measurement is even more challenging in driven-dissipative exciton–polariton condensates, since their non-equilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of a high-density exciton–polariton condensate by detecting the spectral branch of elementary excitations populated by this process. Analysis of this excitation branch shows that quantum depletion of exciton–polariton condensates can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the exciton fraction in an exciton polariton. Our results reveal beyond mean-field effects of exciton–polariton interactions and call for a deeper understanding of the relationship between equilibrium and non-equilibrium BECs.
We report on the experimental observation of stimulated cooling in the non-equilibrium Bose-Einstein condensate (BEC) of weakly interacting exciton-polaritons from approximately room temperature down to 20K. By resolving the condensate in energy-momentum space and performing interferometric measurements, we distinguish the condensate from thermalized particles yet occupying excited states macroscopically. In contrast to the analytical quantum theories of non-equilibrium BEC [Shishkov et al., Phys. Rev. Lett. 128, 065301 (2022)], we observe segmentation of the particle density along the excited states into two fractions both following Bose-Einstein distribution, albeit with different effective temperatures and chemical potentials. Our results indicate that the temperature of the weakly interacting Bose gas is universally set by the density-dependent chemical potential, revealing a defining property of non-equilibrium BECs. Finally, we demonstrate that the stimulated nature of the cooling process directly governs the emergence of quantum coherence of the condensate and shapes the dissipative properties of the excited states.
We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.
In this Letter, we give an analytical quantum description of a nonequilibrium polariton Bose-Einstein condensate (BEC) based on the solution of the master equation for the full polariton density matrix in the limit of fast thermalization. We find the density matrix of a nonequilibrium BEC, that takes into account quantum correlations between all polariton states. We show that the formation of BEC is accompanied by the build-up of cross-correlations between the ground state and the excited states reaching their highest values at the condensation threshold. Despite the nonequilibrium nature of polariton systems, we show the average population of polariton states exhibits the Bose-Einstein distribution with an almost zero effective chemical potential above the condensation threshold similar to an equilibrium BEC. We demonstrate that above threshold the effective temperature of polaritons drops below the reservoir temperature.