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of each defect are spatially separated a nd do not inter- fere [Fig .5(a)]. The momentum distrib ution in k -space [Fig.5(b) ] shows the condensate peak r ight at the initial moment um state and a much fainter re sonant Rayleigh scatterin g ring [7]. The situation is diffe rent for a higher density o f defects. In this case, the real s pace density per- turbatio ns created by the different defe cts substantially overlap with each other [Fig.5(c)]. As a result, interfer- ence effe cts are more likely to create n odes in the con- densate wavefunction and therefore to tr igger dissipation of the su percurrent. The occurrence of such a process is apparent in Fig.5(d) as a much reduce d late-time value of the co ndensate momentum. 

This f act illustrates another important difference with respect to standard, equilibrium condensates: in that case, the dissipation of a supercurrent leads to a signifi- cant hea ting and reduction of the condensate fraction. In the pres ent case, the condensate turns out to be almost rigidly tr ansferred to a lower momentum state; the (co- herent) momentum broadening that is visible in Fig.5(d) is an effe ct of the defects. Remarkably, the frequency de- pendenc e of pumping in the generalized CGLE (1) has a crucial r ole in concentrating the population in low-energy 

modes and preventing the momentum distribution from spreading all over the k -space. 

In conclusion, we have investigated how the non- equilibrium nature of exciton-polariton condensates af- fects their superfluidity properties. A mean-field model based on a generalized Gross-Pitaevskii equation includ- ing a frequency-dependent pumping is developed. Dif- ferent aspects of superfluidity have been considered. A non-equilibrium version of the Landau critical speed for the onset of drag force is formulated and metastability of supercurrents is shown to persist even at speeds well above the critical speed. 

We are indebted to Vincenzo Savona, Cristiano Ciuti and Davide Sarchi for continuous enlightening exchanges. Stimulating discussions with J. Keeling, C. Menotti, F. Piazza, D. Sanvitto, A. Smerzi are acknowledged. 

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