Bose-Hubbard model in a ring-shaped optical lattice with high filling factors
arXiv:1107.1188 · doi:10.1103/PhysRevA.84.013602
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
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- Effects of a rotating periodic lattice on coherent quantum states in a ring topology: The case of positive nonlinearity
- Bose-Einstein condensates in rotating ring-shaped lattices: a multimode model
- Blocked populations in ring-shaped optical lattices
- Vortex nucleation processes in rotating lattices of Bose-Einstein condensates ruled by the on-site phases
- Rotation Sensitive Quench and Revival of Coherent Oscillations in a Ring Lattice
- Entangled Collective Spin States of Two Species Ultracold atoms in a Ring
- Modeled vortex dynamics on a Bose-Einstein condensate in a rotating lattice
- Instability and particle current control of a parametrically driven Bose-Einstein condensate in a ring-shaped lattice
- dc atomtronic quantum interference device: quantum superposition of persistent-current states and a parity-protected qubit
- Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation