Bosons and Fermions in dynamic optical lattices

Collective scattering of light due to atomic recoil, also known as collective atomic recoil lasing (CARL), occurs when a gas of atoms coherently scatters light from a pump laser via a collective instability. The scattering process can become unstable due to the atoms in the gas recoiling under the influence of the dynamic optical forces which arise due to the interference of the pump and scattered fields. The atoms move to form a spatially periodic density grating, which in turn amplifies the scattered field. This paper presents a theoretical analysis of CARL phenomena in degenerate ultracold gases of bosons and fermions. In the case of bosons i.e. in a Bose-Einstein Condensate (BEC),the effect of atom-atom interactions due to collisions on the CARL instability in the case of both attractive and repulsive condensates, is investigated. In the case of fermionic gases, the effect of Fermi pressure, is also presented. The linear and nonlinear evolution of the optical field and the atomic momentum distribution are considered for both cases.