I recently read about BEC loaded into the optical lattice p.200
Looking at a condensate released from a lattice after a time of flight typically on the order of a few milliseconds amounts to observing its momentum distribution. A harmonically trapped condensate has a Gaussian momentum distribution in the limit of small interactions, whereas in the Thomas-Fermi limit in which the interactions dominate over the kinetic energy contribution it has a parabolic density profile and expands self-similarly after being released. By contrast, a condensate in a periodic potential contains higher momentum contributions in multiples of 2kL, their relative weights depending on the depth of the lattice. In fact, in the tight-binding limit see Sec. IV we can consider the condensate to be split up into an array of local wave functions that expand independently after the lattice has been switched off. Eventually they all overlap and form an interference pattern that in the absence of interactions is the Fourier transform of the initial condensate.
When there is no lattice potential all particles occupy the same state, but when the lattice appears is it still a single mode condensate or multi-mode one due to appearance of additional interference peaks (particle condense in more than one state)?