BCS-BEC crossovers of microcavity exciton-polariton condensates

In the present work, we discuss all possible condensation states of the exciton-polariton system in a microcavity. The matter-light system in the microcavity is described in a two-dimensional many-particle interacting model. In the thermal equilibrium limit, a set of self-consistent equations determining the condensate order parameters is derived by adapting the unrestricted Hartree-Fock approximation. Analyzing the condensate order parameters and momentum distributions of the exciton and photon densities, a detail phase structure of the exciton-polariton system has been released. At zero temperature, above a critical density, depending on the Coulomb interaction, one finds all possible condensate phases of the exciton-polariton systems including excitonic-BEC, excitonic-BCS, polaritonic-BEC, polaritonic-BCS, and photonic BEC states. A whole regime of the condensation states is decreased if increasing the detuning parameter. The complex BCS-BEC crossovers of the condensation states are also addressed in the influence of thermal fluctuations and excitation deturning. •Complex excitonic, polaritonic and photonic condensate phase transitions in a microcavity has been investigated.•At zero temperature, the competition is interpreted depending on Coulomb interaction, excitation density at zero temperature.•BCS-BEC crossovers of the excitonic and polaritonic condensates are established simultaneously in the ground state.•An important role of the thermal fluctuations affecting the condensation states and also the crossovers has been indicated.•A compact phase structure of the excitonic-polaritonic-photonic condensates in a microcavity has been addressed.