Oscillatory dynamics of nonequilibrium dissipative exciton-polariton condensates in weak-contrast lattices

Abstract

We study the nonlinear dynamics of exciton polaritons in an incoherently pumped semiconductor microcavity with an embedded weak-contrast lattice and coupled to an exciton reservoir. We elucidate fundamental features of nonequilibrium exciton-polariton condensates trapped in one-dimensional periodic potentials both in the vicinity of zero momentum (so-called ``zero-momentum state'') and at the boundaries of Brillouin zone (``$\ensuremath{\pi}$ states''). Within the framework of the mean-field theory, we identify different regimes of both relaxation and oscillatory dynamics governed by superpositions of Bloch eigenstates of coherent exciton polaritons within the periodic lattice. In particular, we theoretically demonstrate stable macroscopic oscillations, akin to nonlinear Josephson oscillations, between different spectral components of the polariton condensate in the momenta space. We discuss a strong influence of dissipative effects and the feedback induced by the inhomogeneity of the incoherent reservoir on the dynamics of coherent polaritons.