Many-photon coherence of Bose-condensed excitons: Luminescence and related nonlinear optical phenomena

We consider many-photon coherent emission governed by coherent recombination of many excitons from Bose condensate. Momentum conservation makes photons simultaneously created in the coherent recombination of several excitons from the condensate have zero sum momentum. Many-photon correlations in the processes of simultaneous many-photon production (photons squeezing) could be detected by photon counting experiments with several detectors spatially arranged in an appropriate way, i.e., by Hanbury-Brown-Twiss-like experiments. We analyze the stimulated processes of N-exciton coherent recombination from the condensate resonantly induced by $N-1$ external laser beams with momenta ${\mathbf{k}}_1,{\mathbf{k}}_2,\dots ,{\mathbf{k}}_{N-1}.$ Such stimulated processes must reveal themselves through a unidirectional beam with recoil momentum ${\mathbf{k}}_N=-{\sum }_{i=1\mathrm{}}^{N-1}{\mathbf{k}}_i.$ In particular, two-exciton coherent recombination from the condensate stimulated by a laser beam effectively acts in a three-dimensional (3D) exciton system as a laser beam backscattering from exciton Bose condensate. For 2D coherent exciton systems besides the backscattering stimulated two-exciton coherent recombination has an additional manifestation—anomalous beam transmission with the only change in the sign of in-plane momentum component of inducing laser beam. We estimate the rates of many-photon coherent emission from a 3D system of ${\mathrm{Cu}}_2\mathrm{O}$ excitons and from a 2D exciton system in GaAs/AlGaAs coupled quantum wells. The estimations show that these nonlinear optical effects are experimentally observable.