A pair of counterpropagating laser beams produces an optical standing wave which acts as a periodic potential for a cloud of atoms. In the presence of such a periodic potential, the atoms behave in some ways like electrons in the periodic potential of a crystal lattice in a metal of semiconductor, in particular they exhibit band-structure effects. If the atoms are bosons and the ir temperature is sufficiently low, they can Bose condense and the entire condensate can be described in terms of a Bloch wave vector. If the inter-atomic interactions are moderately strong then the states of the condensate with large Bloch wave vectors can become dynamically unstable and will decay by the emission of quasiparticles. We have extended earlier work on such instabilities to examine two-dimensional optical lattices, such as would be produced by two orthogonal pairs of lasers and two-component condensates. In the latter case we have shown that two normally imiscible species can be held in intimate contact by an appropriately chosen optical lattice. Finally we have examined the dynamic structure factor of moving condensates in such optical lattices and shown that this contains signatures of the modes that are close to becoming unstable.
Talk given at IOP Low Temperature Group meeting, Cambridge, July 2005.