Collective exchange of orbital angular momentum between cold atoms and light

An analysis of light scattering by ultracold atoms is presented in which the pump and scattered light consists of hollow counter-rotating Laguerre-Gaussian beams possessing orbital angular momentum. It is shown that the interaction between the Laguerre-Gaussian beams and the atoms can give rise to a collective instability in which orbital angular momentum is transferred to the atoms and the scattered/probe field is amplified. The instability involves the development of an azimuthal density modulation in the atomic distribution with angular frequency, 2l, where l is the magnitude of the azimuthal index of the Laguerre-Gaussian modes.