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Exact Analytical Solution for the Density Matrix of a Nonequilibrium Polariton Bose-Einstein Condensate
Vladislav Yu Shishkov1, Evgeny S Andrianov1, Anton V Zasedatelev2
1Dukhov Research Institute of Automatics (VNIIA), 22 Sushchevskaya, Moscow 127055, Russia; Moscow Institute of Physics and Technology, 9 Institutskiy pereulok, Dolgoprudny 141700, Moscow region, Russia; and Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, Bolshoy Boulevard 30, building 1, 121205 Moscow, Russia.
Abstract:
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.
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