Perspectives in superfluidity in resonantly driven polariton fluids

In this paper we discuss, within the Gross-Pitaevskii framework, superfluidity, soliton-like patterns, and instabilities in a nonequilibrium polariton fluid injected by a spatially localized and continuous-wave coherent pump and flowing against a defect located outside the pump spot. In contrast to equilibrium condensates of ultracold atoms or liquid helium, the steady-state solutions of the driven-dissipative equations in this specific geometry hardly show a clean superfluid flow around the defect and rather feature a crossover from shallow to deep soliton-like perturbation. This is explained in terms of the properties of one-dimensional flows, in particular their weak dependence on the pump parameters and their rapid transition to a supersonic regime under the effect of the quantum pressure. The role of disorder and of an incoherent reservoir in inducing nonstationary behaviors with moving phase singularities is also highlighted. Such complex and highly nonlinear behaviors call for quantitative experimental tests of the underlying Gross-Pitaevskii equation.