Dynamics of exciton-polaritons in discrete lattices under incoherent localized pumping

Abstract

The paper deals with the spontaneous coherence building up between exciton-polaritons trapped in an array of deep potential wells in the presence of an incoherent pump. A theoretical approach based on a standard tight-binding mean-field approximation is used to reduce the continuous periodic problem to a discrete model. The typical dynamics of the nonlinear exciton-polariton system for the cases of spatially uniform and for localized pumps are discussed. Special attention is paid to the ``staggered'' coherent steady states with $\ensuremath{\pi}$ jumps in the phases between neighboring sites and to ``uniform'' states with a smooth phase distribution. It is shown that, apart from the states with a single frequency, mixed states with spectra with several harmonics can form in the system. The selection mechanism that controls the type of steady state growing from a weak noise is studied. It is found that in the case of localized pumps the decaying tails of the solutions play a crucial role in the dynamics of the polaritons. The applicability of the obtained theoretical results for a qualitative explanation of the complex phenomena observed in recent experiments is discussed.