New method for detection of exciton Bose condensation using stimulated two-photon emission

Abstract

An investigation is reported of stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation numbers of exciton states with momenta p≠0. Raman light scattering (RLS) accompanied by a similar two-exciton recombination (or production of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, so their detection can be used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted to optical phonons with frequency ω ^s₀ , whose occupation numbers are negligible, and the incident light frequency satisfies ω<2Ω, where Ω_=Ω−ω ^s₀ is the difference frequency and Ω is the light frequency corresponding to the recombination of an exciton with zero momentum, stimulated two-photon emission and RLS with coherent two-exciton recombination give rise to a line at 2Ω_ −ω and an anti-Stokes component at ω+2Ω_, respectively. For ω2Ω_ the RLS spectrum contains Stokes and anti-Stokes components at frequencies ω±2Ω_, whereas stimulated two-photon emission is impossible. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line at 2Ω_−ω, corresponding to the stimulated two-photon emission accompanied by coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu₂O.