Laser probing of single-particle energy gap of a Bose gas in an opticallattice in a Mott insulator phase

We consider the Mott insulator phase of a Bose gas in an optical lattice.The characteristic feature of the single-particle spectrum in the Mottinsulator phase is the existence of an energy gap between the particle andhole excitations.We show that this energy gap can be directly probed by an output couplingexperiment with Raman transitions.We apply the general expression for the output current derived by Luxat andGriffin, which is given in terms of the single-particle Green's functions,to the Mott insulator phase using the Bose-Hubbard Hamiltonian in thestrong-coupling regime.The momentum-resolved output current has two characteristic peaks in theenergy spectrum corresponding to the particle and hole excitations, and thusused to detect the transition point from the Mott insulator to superfluidphase where energy gap between the two excitations disappears.　In this talk, I will talk about the detail of derivation of the Landaufree energy by using an inversion method.Next I will discuss the possibility of directly probing single-particleexcitations in the Mott phase in an optical lattice by observing the outputcoupling current from the optical lattice.