Coherent and dissipative transport of a Bose-Einstein condensate inside an optical lattice

Bose-Einstein condensates of alkali atoms inside an optical lattice provide a unique opportunity to investigate such issues as coherent transport of matter, Josephson-type phenomena, and dissipation of superfluidity under highly controllable experimental conditions. We give a short review of theoretical progress in evaluating the collective excitations of a periodic condensate and the coherent transport of matter in different configurations, which has been based on an adaptation of the Wannier function representation of quasi-particle states in periodic potentials and on the use of advanced numerical methods for the solution of the Gross-Pitaevskii equation. We present various methods by which the band structure of the elementary excitations may be probed and show that in the superfluid regime the combination of a constant force and a harmonic force in the presence of the optical lattice drives Josephson-type oscillations of the condensate, leading to observable resonances and multimode behaviour. Finally, we discuss decoherence of the condensate and dissipation via sound wave emission above a local velocity threshold.