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

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.

Accepted in PRA

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Cold Bosons in Optical Lattices
• Bose-Hubbard model with occupation dependent parameters
• Dynamics of a Bose-Einstein condensate in a symmetric triple-well trap
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Cited by in corpus (2)

• Quench from Mott Insulator to Superfluid
• Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation