Bosonic atoms trapped in an optical lattice at very low temperatures can be modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson approach for dealing with the Bose-Hubbard model, which enables us to analytically describe the physics of this model at nonzero temperatures. With our approach the phase diagram for this model at nonzero temperatures can be quantified.
We present the theory for ultracold atomic gases in an optical lattice near a
Feshbach resonance. In the single-band approximation the theory describes atoms
and molecules which can both tunnel through the lattice. Moreover, an avoided
crossing between the two-atom and the molecular states occurs at every site. We
determine the microscopic parameters of the generalized Hubbard model that
describes this physics, using the experimentally known parameters of the
Feshbach resonance in the absence of the optical lattice. As an application we
also calculate the zero-temperature phase diagram of an atomic Bose gas in an
optical lattice.Comment: Published version, 4 pages, 3 Figure
We propose to use Bragg spectroscopy to measure the excitation spectrum of the Mott-insulator state of an atomic Bose gas in an optical lattice. We calculate the structure factor of the Mott insulator taking into account both the self-energy corrections of the atoms and the corresponding dressing of the atom-photon interaction. We determine the scattering rate of photons in the stimulated Raman transition and show that by measuring this scattering rate in an experiment, in particular, the excitation gap of the Mott insulator can be determined.
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