Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis

Abstract

The extended Bose-Hubbard model for a double-well potential with atom-pair tunneling is studied. Starting with a classical analysis we determine the existence of three different quantum phases: self-trapping, phase-locking and Josephson states. From this analysis we built the parameter space of quantum phase transitions between degenerate and non-degenerate ground states driven by the atom-pair tunneling. Considering only the repulsive case, we confirm the phase transition by the measure of the energy gap between the ground state and the first excited state. We study the structure of the solutions of the Bethe ansatz equations for a small number of particles. An inspection of the roots for the ground state suggests a relationship to the physical properties of the system. By studying the energy gap we find that the profile of the roots of the Bethe ansatz equations is related to a quantum phase transition.

10 pages, 10 figures

References in corpus (10)

• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Universal space-time scaling symmetry in the dynamics of bosons across a quantum phase transition
• Few-boson dynamics in double wells: From single-atom to correlated-pair tunneling
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• Commutability between Semiclassical Limit and Adiabatic Limit
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• The two-site Bose--Hubbard model
• Quantum phase transitions in Bose-Einstein condensates from a Bethe ansatz perspective
• Extended Bose-Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation
• Ground-state Bethe root densities and quantum phase transitions

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