Relaxation and condensation kinetics of trapped excitons at ultra-low temperatures: numerical simulation

Abstract

This work is a theoretical study of the excitons relaxation dynamics in cuprous oxide at ultra-low temperatures and within a potential trap. Exciton–phonon collisions and exciton–exciton collisions have been included as relaxation processes. Special attention is given to the thermal distribution, cooling process and the condensation of the exciton gas with high number of excitons. It has been done by solving the Boltzmann equation numerically, using MATLAB. In this work, the relaxation behaviour has been analysed for the temperatures between 0.1 and 3 K. It has been found that for the temperatures above 0.1 K the local effective temperatures are coming down to the bath temperatures, i.e. the excitons reach the local equilibrium with the lattice, but for 0.1 K it does not happen. For 3 K, the global distributions do not change at all with time, but for 0.1 K this change is significant. Maybe this thermal loss of excitons for 0.1 K is related to the Bose–Einstein condensation of excitons. Interestingly, for the temperature of 0.1 K the condensate has been formed with sufficiently high number of excitons, for the times larger than 300 ns. Also, the results have been compared with the other theoretical results.