Probing microcavity polariton superfluidity through resonant Rayleigh scattering

We investigate the two-dimensional motion of polaritons injected into a planar microcavity by a continuous wave optical pump in presence of a static perturbation, e.g. a point defect. By finding the stationary solutions of the nonlinear mean-field equations (away from any parametric instability), we show how the spectrum of the polariton Bogoliubov-like excitations reflects onto the shape and intensity of the resonant Rayleigh scattering emission pattern in both momentum and real space. We find a superfluid regime in the sense of the Landau criterion, in which the Rayleigh scattering ring in momentum space collapses as well as its normalized intensity. More generally, we show how collective excitation spectra having no analog in equilibrium systems can be observed by tuning the excitation angle and frequency. Predictions with realistic semiconductor microcavity parameters are given.