Probing condensate order in deep optical lattices

We study interacting bosons in optical lattices in the weak-tunneling regime in systems that exhibit the coexistence of Mott-insulating and condensed phases. We discuss the nature of the condensed ground state in this regime and the validity of the mean-field treatment thereof. We suggest two experimental signatures of condensate order in the system. (1) We analyze the hyperfine configuration of the system and propose a set of experimental parameters for observing radio-frequency spectra that would demonstrate the existence of the condensed phase between Mott-insulating phases. We derive the structure of the signal from the condensate in a typical trapped system, taking into account Goldstone excitations, and discuss its evolution as a function of temperature. (2) We study matter-wave interference patterns displayed by the system upon release from all confining potentials. We show that as the density profiles evolve very differently for the Mott-insulating phase and the condensed phase, they can be distinguished from one another when the two phases coexist.