  We propose and analyse a Raman spectroscopy technique for probing the
properties of quantum degenerate bosons in the ground band of an optical
lattice. Our formalism describes excitations to higher vibrational bands and is
valid for deep lattices where a tight-binding approach can be applied to the
describe the initial state of the system. In sufficiently deep lattices,
localized states in higher vibrational bands play an important role in the
system response, and shifts in resonant frequency of excitation are sensitive
to the number of particles per site. We present numerical results of this
formalism applied to the case of a uniform lattice deep in the Mott insulator
regime.
