Effective attractive polariton-polariton interaction mediated by an exciton reservoir

We present a mechanism to endow the polariton gas with attractive interactions. The scheme relies on an exciton reservoir, which can be formed even if the excitons lie outside of the light cone. Such an attractive interaction should open different routes in the physics of quantum fluids, which we illustrate with a simple but nontrivial application whereby the polariton condensate enters the self-oscillation regime powered by the attraction from the reservoir. This results in pulsed emission in the GHz regime.