Condensation kinetics of cavity polaritons interacting with a thermal phonon bath

The kinetics of the boson condensation for micro-cavity (MC) polaritons interacting with thermal acoustic phonons is studied within rate equations, taking into account the finite MC cross-section. For a smoothly switched on cw excitation and finite polariton lifetimes we find a build-up of a large population in the lowest state of the polariton spectrum for sufficiently large deformation potential coupling at sufficiently high densities, which are still below the saturation density. The critical influence of the value of the heavy-hole deformation potential is illustrated, as well as the favorable influence of positive values of the detuning. This spontaneous polariton condensation would result in a perpendicular emission out of the micro-cavity.