Extended two-site Bose–Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation

Zhu, Qizhong; Zhang, Qi; Wu, Biao

doi:10.1088/0953-4075/48/4/045301

Cited by 18 publications

(34 citation statements)

References 46 publications

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“…In the model under consideration, a novel atom-pair hopping term is included to describe the two-body interaction recently reported experimental observation of correlated tunnelling. There has been a great deal of effort devoted to this subject recently [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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: selftrapping, 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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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“…The above formulae complement the asymptotic results of [9], which were derived for the repulsive case k > 0. Finally, we can also use the above results to associate the quantum phase transition point λ = 1 [12,18,36] with the onset of condensate fragmentation. Following [12,18,36], denoting the ground state by |ψ consider the one-body density matrix ρ (1) = 1 N ψ|â 1 †â 1 |ψ ψ|â 1 †â 2 |ψ ψ|â 2 †â 1 |ψ ψ|â 2 †â 2 |ψ…”

Section: Ground-state Energy and Correlation Functionsmentioning

confidence: 99%

Ground-state Bethe root densities and quantum phase transitions

Links¹,

Marquette²

2015

J. Phys. A: Math. Theor.

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Abstract. Exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe Ansatz equations, to identify quantum phase transitions. Here we expand on this approach, in a quantitative manner, for two models of Bose-Einstein condensates. The first model deals with the interconversion of bosonic atoms and molecules. The second is the two-site Bose-Hubbard model, widely used to describe tunneling phenomena in Bose-Einstein condensates. For these systems we calculate the ground-state root density. This facilitates the determination of analytic forms for the ground-state energy, and associated correlation functions through the Hellmann-Feynman theorem. These calculations provide a clear identification of the quantum phase transition in each model. For the first model we obtain an expression for the molecular fraction expectation value. For the two-site Bose-Hubbard model we find that there is a simple characterisation of condensate fragmentation.Ground-state Bethe root densities and quantum phase transitions 2

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“…At low temperatures the secondquantized Hamiltonian of the system beyond the onsite approximation can be written as [28,29,31,38,39] …”

Section: Modelmentioning

confidence: 99%

“…[29]. These theoretical investigations [27][28][29] concerning to the pair tunneling are confined to the regime of repulsive interatomic interactions. In addition, the analyses in Refs.…”

Section: Introductionmentioning

confidence: 99%

Stationary states and quantum quench dynamics of Bose–Einstein condensates in a double-well potential

Wen¹,

Zhu²,

Xu³

et al. 2015

J. Phys. B: At. Mol. Opt. Phys.

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We consider the properties of stationary states and the dynamics of Bose-Einstein condensates (BECs) in a double-well (DW) potential with pair tunneling by using a full quantum-mechanical treatment. Furthermore, we study the quantum quench dynamics of the DW system subjected to a sudden change of the Peierls phase. It is shown that strong pair tunneling evidently influences the energy spectrum structure of the stationary states. For relatively weak repulsive interatomic interactions, the dynamics of the DW system with a maximal initial population difference evolves from Josephson oscillations to quantum self-trapping as one increases the pair tunneling strength, while for large repulsion the strong pair tunneling inhibits the quantum self-trapping. In the case of attractive interatomic interactions, strong pair tunneling tends to destroy the Josephson oscillations and quantum self-trapping, and the system eventually enters a symmetric regime of zero population difference. Finally, the effect of the Peierls phase on the quantum quench dynamics of the system is analyzed and discussed. These new features are remarkably different from the usual dynamical behaviors of a BEC in a DW potential.

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Extended two-site Bose–Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation

Cited by 18 publications

References 46 publications

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

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

Ground-state Bethe root densities and quantum phase transitions

Stationary states and quantum quench dynamics of Bose–Einstein condensates in a double-well potential

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