Quantum phase transitions in Bose–Einstein condensates from a Bethe ansatz perspective

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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“…In future work it is planned to extend the methods adopted in [27,28] for the TMBH model to meet this need.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2017

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“…In particular, as our models are solvable, one can obtain precise results, for instance, of properties related to the energy gap, entanglement and ground state fidelity [48]. Also, as mentioned above, increasingly sophisticated NMR techniques [44,49] allows manipulation of qubits and we believe that with our models we add an interesting possibility to the usual NMR nuclear quadrupole Hamiltonian.…”

Section: Introductionmentioning

confidence: 75%

A bosonic multi-state two-well model

Santos¹,

Foerster²,

Roditi³

2013

J. Phys. A: Math. Theor.

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Abstract. Inspired by the increasing possibility of experimental control in ultracold atomic physics we introduce a new Lax operator and use it to construct and solve models with two wells and two on well states together with its generalization for n on well states. The models are solved by the algebraic Bethe ansatz method and can be viewed as describing two Bose-Einstein condensates allowing for an exchange interaction through Josephson tunneling.

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“…[11][12][13]15]. Here the energy gap is defined as the energy difference between the first excited state E 1 and the ground state E 0 , i.e., ∆E = E 1 − E 0 .…”

Section: A Energy Gapmentioning

confidence: 99%

“…One Rydberg molecule consists of a single kind of atoms in different states, and the atoms can jump between the ground state and Rydberg states, which provides probability to study the QPT in atom-molecule conversion system with atomic hopping. Although the quantum phase transition of the ground state has been studied in the atom-molecule system [9][10][11][12][13], the atoms in that system were in the same state and the hopping between different hyperfine atomic states was not considered. So it is need to consider the atom-molecule conversion system with atomic hopping and study the effect of the hopping strength between different hyperfine atomic states on the quantum phase transition.…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transition in an atom–molecule conversion system with atomic transition

Hui¹,

Lu²,

Xu³

et al. 2013

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

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The quantum phase transition in an atom-molecule conversion system with atomic hopping between different hyperfine states is studied. In mean field approximation, we give the phase diagram whose phase boundary only depends on the atomic hopping strength and the atom-molecule energy detuning but not on the atomic interaction. Such a phase boundary is further confirmed by the fidelity of the ground state and the energy gap between the first-excited state and the ground one. In comparison to mean field approximation, we also study the quantum phase transition in full quantum method, where the phase boundary can be affected by the particle number of the system. Whereas, with the help of finite-size scaling behaviors of energy gap, fidelity susceptibility and the first-order derivative of entanglement entropy, we show that one can obtain the same phase boundary by the MFA and full quantum methods in the limit of N → ∞. Additionally, our results show that the quantum phase transition can happen at the critical value of the atomic hopping strength even if the atom-molecule energy detuning is fixed on a certain value, which provides one a new way to control the quantum phase transition.

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Quantum phase transitions in Bose–Einstein condensates from a Bethe ansatz perspective

Cited by 18 publications

References 43 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

A bosonic multi-state two-well model

Quantum phase transition in an atom–molecule conversion system with atomic transition

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