Bosons in a Lattice: Exciton-Phonon Condensate in Cu2O

TL;DR

This paper develops a nonlinear model for exciton-phonon interactions in Cu2O, predicting localized moving condensates, their stability, and explaining recent experimental observations of coherent exciton-phonon phenomena.

Contribution

It introduces a dynamic equations framework for exciton-phonon condensates, including localized solutions and stability analysis, specific to Cu2O's long-living para-excitons.

Findings

Localized exciton-phonon condensate solutions are supported.

The model predicts conditions for moving inhomogeneous condensates.

It explains observed interference and nonlinear interactions in Cu2O.

Abstract

We explore a nonlinear field model to describe the interplay between the ability of excitons to be Bose-condensed and their interaction with other modes of a crystal. We apply our consideration to the long-living para-excitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we derive the dynamic equations for the exciton-phonon condensate. These equations can support localized solutions, and we discuss the conditions for the moving inhomogeneous condensate to appear in the crystal. We calculate the condensate wave function and energy, and a collective excitation spectrum in the semiclassical approximation; the inside-excitations were found to follow the asymptotic behavior of the macroscopic wave function exactly. The stability conditions of the moving condensate are analyzed by use of Landau arguments, and Landau critical parameters appear in the theory. Finally, we apply our model to describe the recently observed interference and strong nonlinear interaction between two coherent exciton-phonon packets in Cu2O.