Collective two-boson decay of excitons in a Bose-Einstein condensate and generation of coherent photon-phonon radiation

The collective decay of excitons from initial Bose-Einstein condensate state is investigated theoretically. As a practically more interesting case we consider excitons of the yellow series in the semiconductor cuprous oxide where we have collective photon and phonon-assisted decay of excitons. It is shown that because of intrinsic instability of recoilless two-boson decay of Bose-Einstein condensate, the spontaneously emitted bosonic pairs are amplified, leading to an exponential buildup of a macroscopic population into the certain modes. The collective decay rate has a nonlinear dependence on the excitonic density being comparable or larger than the Auger recombination loss rate up to the high densities, which makes obtainable its observation. The phenomenon considered can also be applied for the realization of a phonon laser.