Collective atomic recoil lasing with a partially coherent pump

We investigate the effect of pump phase noise on the collective backscattering of light by a cold, collisionless atomic gas. We show that for a partially coherent pump field, the growth rate of the backscattered field is reduced relative to that for a coherent pump, but the backscattered intensity can be increased. Our results demonstrate that fluctuations and noise can play a counterintuitive role in nonlocally coupled many-body systems.