Coexistence of superfluid and Mott phases of strongly-interacting lattice bosons

Recent experiments on strongly-interacting bosons in optical lattices [1,2] have revealed the co-existence of spatially-separated Mott-insulating and number-fluctuating phases in the presence of an external trapping potential. Employing a simple theoretical model [3], we obtain an effective description of the superfluid state trapped between the Mott states. We calculate the collective excitation spectrum of such a superfluid and its critical temperature, and discuss the crossover between two- and three-dimensional behavior of its thermal properties as a function of the lattice parameters. \newline [1] S.~F\"olling, A.~Widera, T.~M\"uller, F.~Gerbier, and I.~Bloch, Phys. Rev. Lett. {\bf 97}, 060403 (2006). \newline [2] G.~K.~Campbell, J.~Mun, M.~Boyd, P.~Medley, A.~E.~Leanhardt, L.~Marcassa, D.~E.~Pritchard, and W.~Ketterle, Science {\bf 313}, 649 (2006). \newline [3] R.~A.~Barankov, C.~Lannert, and S.~Vishveshwara, cond-mat/0611126.