Quantum dynamics of a model for two Josephson-coupled Bose–Einstein condensates

Tonel, Arlei Prestes; Links, Jon; Foerster, Angela

doi:10.1088/0305-4470/38/6/004

Cited by 74 publications

(104 citation statements)

References 25 publications

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“…Due to its simplicity, this model has been investigated widely by many authors using various methods, such as the Gross-Pitaevskii approximation [2], mean-field theory [3,4], the quantum phase model [5] and the Bethe ansatz method [6], providing insights into many intriguing phenomena. For example, it is well known that this model may present a Quantum Phase Transition (QPT) separating a delocalised from a self-trapped phase [7,8].…”

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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“…Using expression (18) and the coefficients c m obtained through exact diagonalization of the Hamiltonian (11) as done in the atom-molecule model [30], we plot in Fig. 2 the entropy of entanglement of the ground state as a function of the parameters λ and γ.…”

Section: Entanglement Of the Ground Statementioning

confidence: 99%

Quantum entanglement and phase transition in a two-dimensional photon–photon pair model

Zhang

Yuan

Zhang

et al. 2013

Physica B: Condensed Matter

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We propose a two-dimensional model consisting of photons and photon pairs. In the model, the mixed gas of photons and photon pairs is formally equivalent to a two-dimensional system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phases. Using the variational method, we discuss the quantum phase transition of the mixed gas and obtain the critical coupling line analytically. Moreover, we also find that the phase transition of the photon gas can be interpreted as second harmonic generation. We then discuss the entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement between photons and photon pairs can be associated with the phase transition of the system.

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“…Pairs of eigenstates with energies beyond this threshold show exponentially decreasing energy splitting. In a similar quantum model [67,68], it was shown that at the mentioned energy threshold the entanglement (using the von Neumann entropy) becomes maximum and then decreases with energy. From these two results we expect that QB states in our case show decreasing entanglement ∆ with energy, tending to 0.5.…”

Section: Entanglement Of Qb Statesmentioning

confidence: 99%

Quantum breathers in capacitively coupled Josephson junctions: Correlations, number conservation, and entanglement

Pinto

Flach

2008

Phys. Rev. B

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We consider the classical and quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. In the classical case the equations of motion admit discrete breather solutions, which are time periodic and localized predominantly on one of the junctions. In the quantum case breather states are found in the central part of the energy spectrum of the confined nonescaping states of the system. We perform a systematic analysis of their tunneling frequency, site correlations, fluctuations of the number of quanta, and entanglement. Quantum breather states show strong site correlation of quanta and are characterized by a strong excitation of quanta on one junction which perform slow coherent tunneling motion from one junction to the other. They suppress fluctuations of the total number of excited quanta. Quantum breather states are the least entangled states among the group of eigenstates in the same range of the energy spectrum. We describe how quantum breather excitations could be experimentally observed by employing the already developed techniques for quantum information processing using Josephson junctions.

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Quantum dynamics of a model for two Josephson-coupled Bose–Einstein condensates

Cited by 74 publications

References 25 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

Quantum entanglement and phase transition in a two-dimensional photon–photon pair model

Quantum breathers in capacitively coupled Josephson junctions: Correlations, number conservation, and entanglement

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