Manifestation of exciton Bose condensation in induced two-phonon emission and Raman scattering

The unusual two-photon emission by Bose-condensed excitons caused by simultaneous recombination of two excitons with opposite momenta leaving the occupation numbers of excitonic states with momenta p not equal 0 unchanged: (below coherent two-exciton recombination) is investigated. Raman scattering accompanied by the analogous two-exciton recombination (or creation) is also analyzed. The excess momentum equal to the change of the electromagnetic field momentum in these processes can be transferred to phonons or impurities. The processes under consideration take place if there is Bose condensation in the interacting exciton system, and, therefore, can be used as a method to reveal exciton Bose condensation. If the frequency of the incident light omega<2 Omega (Omega is the frequency corresponding to the recombination of an exciton with p=0), the coherent two-exciton recombination with the excess momentum elastically transferred to impurities leads to the appearance of the spectral line 2 Omega - omega corresponding to the induced two-photon emission. In this case the anti-Stokes line on frequency omega+2 Omega also appears in the Raman spectrum. If omega>2 Omega, there are both Stokes and anti-Stokes lines on frequencies omega+/-2 Omega in the Raman spectrum. The induced two-photon emission is impossible in this case. The spectral Lines mentioned above have phonon replicas on frequencies \omega +/-(2 Omega-n omega(0)(s))\ corresponding to the transmission of the excess momentum (partially or as a whole) to optical phonons of frequency omega(0)(s) (n is an integer number). The quantitative estimation shows that the light corresponding to the coherent two-exciton recombination can be experimentally observed in Cu2O.