Modulational instability of a resonantly polariton condensate in discrete lattices

We study modulational instability of a resonantly polariton condensate in a discrete lattice. Employing a discrete gain-saturation model, we derive the dispersion relation for the modulational instability by means of the linear-stability analysis. Effects of the pumping strength, the nonlinearity, the strength of the detuning, and the coupling strength on the modulation instability are investigated. It is found that the interplay between these parameters will dramatically change the modulational instability condition. We believe that the predicted results in this work can be useful for future possible experiment of exciton-polariton condensate in lattices.