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Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
Superflow of Bose-Einstein condensate in an optical lattice is represented by
a Bloch wave, a plane wave with periodic modulation of the amplitude. We review
the theoretical results on the interaction effects in the energy dispersion of
the Bloch waves and in the linear stability of such waves. For sufficiently
strong repulsion between the atoms, the lowest Bloch band develops a loop at
the edge of the Brillouin zone, with the dramatic consequence of a finite
probability of Landau-Zener tunneling even in the limit of a vanishing external
force. Superfluidity can exist in the central region of the Brillouin zone in
the presence of a repulsive interaction, beyond which Landau instability takes
place where the system can lower its energy by making transition into states
with smaller Bloch wavenumbers. In the outer part of the region of Landau
instability, the Bloch waves are also dynamically unstable in the sense that a
small initial deviation grows exponentially in time. In the inner region of
Landau instability, a Bloch wave is dynamically stable in the absence of
persistent external perturbations. Experimental implications of our findings
will be discussed.Comment: A new section on tight-binding approximation is added with a new
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