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

摘要

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 non = 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 #omega#_(0~s), whose occupation numbers are negligible, and the incident light frequency satisfies #omega# < 2#OMEGA#_-, where #OMEGA#_- = #OMEGA# - #omega#_0~s is the difference frequency and #OMEGA# 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 2#OMEGA#_- -#omega# and an anti-Stokes component at #omega# + 2#OMEGA#_-, respectively. For #omega# > 2#OMEGA#_- the RLS spectrum contains Stocks and anti-Stokes components at frequencies #omega# +- 2#OMEGA#_-, 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 2#OMEGA#_- - #omega#, corresponding to the stimulated two-photon emission accompanied by coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu_2O.