Thermal fluctuations in a system of microcavity exciton‐polariton condensations

Abstract

The exciton‐polariton condensation scenario in a microcavity matter–light system at finite temperature is investigated in the framework of the unrestricted Hartree–Fock approximation applying the two‐dimensional exciton‐polariton model. Treating electron–hole Coulomb interaction and matter–light coupling effects on an equal footing, we analyze the temperature influence on the excitonic and photonic order parameters. In the thermal equilibrium limit, the Kosterlitz–Thouless type phase transition of the exciton‐polariton condensation has been found. Depending on detuning and excitation density one finds that the system either favors the photonic or excitonic condensate. The effect of temperature on a crossover from a BCS‐excitonic to a BEC‐polaritonic condensed state then is discussed.

Phase diagram of microcavity exciton-polariton condensates

“…At small excitation density (n = 0.2, panel (a)), one finds a domination of the excitonic condensate order parameter in comparison to the photonic condensate order parameter in the entire temperature range. In this situation, the minimum of the photonic band is far from the chemical potential [16,26]. The photonic condensate order parameter is therefore small and vice versa the excitonic condensate order parameter is enlarged.…”

“…To address the formation of the exciton-polariton condensates in the electron-hole-photon system, we look for non-vanishing values of excitonic expectation and polarized photonic field indicating a kind of spontaneous symmetry breaking due to the coupling of excitons and photons [16,26]. The task can proceed if we adapt the unrestricted Hartree-Fock (UHF) approximation [27].…”

“…The non-interacting Hamiltonian form in eq. ( 6) can be simply diagonalized, then the expectation values are selfconsistently evaluated [26]. In this way, we can determine both the excitonic and the photonic order parameters separately.…”