Finite momentum condensation in a pumped microcavity

We calculate the absorption spectra of a semiconductor microcavity into which a non-equilibrium exciton population has been pumped. We predict strong peaks in the spectrum corresponding to collective modes analogous to the Cooper modes in superconductors and fermionic atomic gases. These modes can become unstable, leading to the formation of off-equilibrium quantum condensates. We calculate a phase diagram for condensation, and show that the dominant instabilities can be at a finite momentum. Thus we predict the formation of inhomogeneous condensates, similar to Fulde-Ferrel-Larkin-Ovchinnikov states.