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Institute of Physics eBooks

Interacting atoms in optical lattices

Farhan Saif, Shinichi Watanabe

Published Dec 1, 2023• 0 citations
Publisher

Abstract

In chapter 6, we explain modified atomic dynamics due to linear confinement. Bloch waves and Landau–Zener transitions are explained. The inter-atomic interaction is presented as the Bose–Hubbard model, which is helpful in understanding advanced topics such as Mott insulators as superfluidity in ultra-cold atoms.
DOI
10.1088/978-0-7503-2308-6ch6

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The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
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The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of bosons to higher Bloch bands, coupled with contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss the implications for cold-atom experiments where expansion of the Mott lobes by fermions has been conclusively established.