Stability and spatial coherence of nonresonantly pumped exciton-polariton condensates

We investigate the stability and coherence properties of one-dimensional exciton-polariton condensates under nonresonant pumping. We model the condensate dynamics using the open-dissipative Gross-Pitaevskii equation. In the case of spatially homogeneous pumping, we find that the instability of the steady state leads to significant eduction of the coherence length. We consider two effects that can lead to the stabilization of the steady state, i.e. the polariton energy relaxation and the influence of an inhomogeneous pumping profile. We find that, while the former has little effect on the stability, the latter is very effective in stabilizing the condensate which results in a large coherence length.