Abstract
In this paper the extended Bose–Hubbard model describing ultracold atoms confined in a shallow, one-dimensional optical lattice is introduced and studied by the exact diagonalization approach. All parameters of the model are related to the only relevant parameter controlled experimentally—the depth of the optical potential. Changes in the shape of the insulating lobe in the phase diagram of the system are explored and the value of the critical tunneling for which the system undergoes the phase transition (from the insulating to the superfluid phase) is predicted. It is shown that the value of the critical tunneling is substantially affected by the presence of the tunnelings to distant sites of the optical lattice. The results may have some importance in upcoming experiments on quantum quench through phase transition points.
© 2015 Optical Society of America
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