From exciton to photon condensation via polariton in electron-holephoton systems

We present a unified theoretical description of the quantum condensates in the electron-hole-photon (ehp) systems, which covers all condensates of exciton, polariton, and photon. To build such model, a phenomenological mean-field treatment for the exciton condensation is employed and extended to include the photon degree of freedom. We clarify changes from exciton/polariton condensations in the low-density limit to photon condensation in the high-density limit as a function of the detuning and the density. Clear change in the microscopic quantities are also found; the carrier distribution function shows broadening in the momentum space, and the minimal excitation energy for breaking an electron-hole (eh) pair increases even in the high density limit. Along this change, relative motion of electron and hole is confined within a tiny radius. In other words, the Wannier-type exciton-polariton picture is replaced by the Frenkel-type. This indicates that the smallest length scale of the system (corresponding to some ultraviolet cutoff) plays important roles due to the presence of coupling between carriers and coherent photons. These features show a remarkable contrast from the scenario of BEC-BCS crossover in the eh systems.