Radio frequency spectra of interacting bosons in an optical lattice trap

We study the inhomogeneous system of interacting bosons in an optical lattice trap. We focus on the weak tunneling region wherein a condensate is predicted to exist between two Mott insulating phases and we consider the effect of applying a radio- frequency (RF) magnetic field in this region. We find that the RF spectrum for driving transitions from one hyperfine species of bosons to another is markedly different between the Mott insulating phase and the condensed phase. In particular, the former has one resonant peak, while the latter has two peaks which show shifts of the order of the tunneling strength between lattice sites. Our results and analyses provide a means of verifying the existence of the condensate.