Relaxation kinetics of a low-density exciton gas inCu2O

The thermalization of a low-density gas of excitons in ${\mathrm{Cu}}_2\mathrm{O}$ is analyzed within the phonon-assisted Boltzmann kinetics in the presence of a weak interaction with the light field. For optically quadrupole-allowed orthoexcitons, the thermalization kinetics is formulated in terms of the polariton picture. A “bottleneck” relaxation along the lower polariton branch strongly dominates over the accumulation of orthoexcitons in the energy minimum of the upper polariton dispersion branch. For paraexcitons, which are strictly forbidden in resonant optical transitions, a rather slow nonexponential occupation kinetics of the ground-state mode at temperature $T<~T_c$ ${(T}_c$ is the condensation critical temperature) prevents the development of a steady-state Bose-Einstein condensate within the optical-phonon-assisted radiative lifetime of paraexcitons. While at $T<~T_c$ the high-energy orthoexcitons or paraexcitons quasiequilibrate into the Planck distribution (the effective chemical potential is equal to zero), the low-energy excitons in a narrow spectral band $(<\mathrm{}100\mathrm{}$ μeV) are still far from equilibrium. This provides us with an alternative interpretation of the recent reports on the observation of quasi-steady-state Bose-Einstein condensation of excitons in ${\mathrm{Cu}}_2\mathrm{O}$.