BCS-BEC crossovers of microcavity exciton-polariton condensates

Highlights: • 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. -- Abstract: 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.