Relaxation kinetics of excitons in cuprous oxide

Due to a simple band structure, the excitons in cuprous oxide (Cu2O) are a model system for kinetic studies. Cuprous oxide appeared to be a host for a Bose-Einstein condensate of excitons, as the excitons showed transient kin etic energy distributions which matched those expected for a Bose gas near the critical density for Bose-Einstein condensation. However, recent absolu te measurements of the exciton density made it clear that two-exciton annih ilation is limiting the exciton density to far below the quantum density. T his paper reconciles the measured exciton density with the observed exciton energy distributions by using a Boltzmann equation approach. We include ex perimentally determined rates for acoustic- and optical-phonon emission, co nversion between exciton spin states, and two-exciton annihiliation, and us e recent diffusion-Monte-Carlo estimates of the exciton-exciton elastic sca ttering cross section. Many experiments intending to produce a dense excito n gas in Cu2O used surface photoexcitation, and we found it important to in clude the resulting spatial inhomogeneities in the model by following the e xciton occupation numbers as functions of space as well as momentum and tim e. A derailed but straightforward numerical integration of the resulting Bo ltzmann equation does in fact match the experimental results, without the a ssumption of quantum statistics for the excitons.