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

TL;DR

This paper proposes a novel optical method to detect exciton Bose condensation by observing stimulated two-photon emission and Raman scattering, which occur only in the presence of a condensate, providing a new experimental signature.

Contribution

It introduces a new detection technique for exciton Bose condensation based on stimulated two-photon emission and Raman scattering involving coherent two-exciton recombination.

Findings

Spectral lines at specific frequencies indicate Bose condensation.

Formulas for cross sections at finite temperatures are derived.

Estimates suggest the method is feasible in Cu₂O experiments.

Abstract

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 excitonic states with nonzero momenta, is investigated. Raman light scattering accompanied by a similar two-exciton recombination (or generation of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, therefore, 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 $\omega_0^s$, the stimulated two-photon emission with the coherent two-exciton recombination leads to the appearance of a line at $2\Omega'-\omega$, where $\Omega'=\Omega-\omega_0^s$ and $\Omega$ is the light frequency corresponding to the recombination of an exciton with zero momentum. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line, corresponding to the stimulated two-photon emission accompanied by the coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu$_2$O.