Structuring ultracold atoms with light in an optical cavity

We numerically model the propagation of light through a Kerr medium and through a far-red-detuned Bose Einstein condensate (BEC) inside an optical cavity using Lugiato-Lefever and Gross-Pitaevskii equations. We demonstrate the formation of light-atomic ring lattices with rotation speeds and direction that can be controlled by the orbital angular momentum of the light. In the BEC, we show the possibility of moving from a lattice to a ring-shaped atomic circuit by changing the atomic scattering length, and explore the potential generation of rotating BEC cavity solitons. Our results may be of interest as slow light pulses with fully controllable speed and structure for use in optical quantum memories, for particle manipulation and trapping, and for the novel realization of highly controllable, tightly confined, rotating atomic lattices