What can we learn from the experiment of electrostatic conveyor belt for excitons?

Motivated by the experiment of electrostatic conveyor belt for indirect excitons (Winbow et al 2011 Phys. Rev. Lett.<bold>106</bold> 196806), we studied the exciton patterns for understanding the exciton dynamics. By analyzing the exciton diffusion, we found that the patterns mainly came from the photoluminescence of two kinds of excitons. The patterns near the laser spot came from the hot excitons which can be regarded as the classical particles. However, the patterns far from the laser spot come from the cooled or coherent excitons. Considering the finite lifetime of Bosonic excitons and of the interactions between them, we built a time-dependent nonlinear Schr & ouml;dinger equation including the non-Hermitian dissipation to describe the coherent exciton dynamics. The real-time and imaginary-time evolutions were used alternately to solve the Schr & ouml;dinger equation to simulate the exciton diffusion accompanied by the exciton cooling in the moving lattices. By calculating the escape probability, we obtained the transport distances of the coherent excitons in the conveyor, consistent with the experimental data. The cooling speed of excitons was found to be important in coherent exciton transport. Moreover, the plateau in the average transport distance cannot be explained by the dynamical localization-delocalization transition induced by the disorders.