Superfluid-Mott-Insulator Phase Transition and CollectiveFluctuations in both Phases of Bosons in an Optical Lattice

Abstract

The Bose Hubbard model describing interacting bosons in an opticallattice is reduced to a simple spin-1 XY model with single-ionanisotropy in the vicinity of the Mott phase. In the strong couplingMott insulating regime, we propose a mean field theory based on aconstraint SU(3) pseudo-boson representation on the effective modeland discuss the excitation spectra and the phase transition to thesuperfluid state. Further to the superfluid phase, we use thecoherent-state approach to derive the collective excitation modes. It isfound that the Mott phase has two degenerate gapped quadratic excitationspectra which graduate into two degenerate gapless linear ones at thetransition point, and one gapless linear mode with one gapped quadraticmode in the superfluid phase.