Loss of coherence in cavity-polariton condensates: Effect of disorder versus exciton reservoir

Time evolution of long-range spatial coherence in a freely decaying cavity-polariton condensate excited resonantly in a high-$Q$ GaAs microcavity is found to be qualitatively different from that in nonresonantly excited condensates. The first-order spatial correlation function ${g}⁽¹⁾({r}₁,{r}₂)$ in response to resonant 1.5 ps pump pulses at normal incidence leaving the exciton reservoir empty is found to be nearly independent of the excitation density. ${g}⁽¹⁾$ exceeds 0.7 within the excited spot and decreases very slowly in the decaying and expanding condensate. It remains above 0.5 until the polariton blue shift $\ensuremath{\alpha}|{\ensuremath{\psi}}²|$ gets comparable to the characteristic amplitude of the disorder potential $\ensuremath{\delta}{E}_LP$. The disorder is found to reveal itself at $\ensuremath{\alpha}|{\ensuremath{\psi}}²|\ensuremath{\lesssim}\ensuremath{\delta}{E}_LP$ in fast and short-range phase fluctuations as well as vortex formation. They lead to oscillations in ${g}⁽¹⁾(t)$, but have little effect on the overall coherence, which is well reproduced in the framework of the Gross-Pitaevskii equations.