Bose-Hubbard model in a ring-shaped optical lattice with high filling factors

TL;DR

This paper investigates the high-filling regime of a Bose-Einstein condensate in a ring-shaped optical lattice, deriving a generalized Bose-Hubbard model that includes interaction-driven tunneling, crucial for understanding phase transitions.

Contribution

It introduces a generalized Bose-Hubbard Hamiltonian incorporating interaction-driven tunneling processes, especially significant at high filling factors, and analyzes their impact on system properties.

Findings

Interaction-driven tunneling is essential at high fillings.

Effective hopping rate remains positive due to interaction effects.

Level crossings indicate a transition to macroscopically occupied states.

Abstract

The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of `vortex' Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the energy and atomic current of a Bloch state, we show that such a hopping rate must be replaced by an effective hopping rate parameter containing the additional contribution an interaction-driven hopping rate. Such a contribution turns out to be crucial at high filling factors, since it preserves the positivity of the effective hopping rate parameter. Level crossings between the energies per particle of a Wannier-like state and the superfluid ground state are interpreted as a signature of the transition to configurations with macroscopically occupied states at each lattice site.