The Two-Site Bose–Hubbard Model

Links, Jon; Foerster, Angela; Tonel, Arlei Prestes; Santos, G.

doi:10.1007/s00023-006-0295-3

Cited by 27 publications

(33 citation statements)

References 16 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These bifurcations allow us to divide the coupling parameter space in three regions. A standard analysis shows the boundary between the regions obey the relation (see [20] for details). Eq.…”

Section: Classical Analysismentioning

confidence: 99%

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

et al. 2017

View full text Add to dashboard Cite

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.

show abstract

Section: Classical Analysismentioning

confidence: 99%

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

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Moreover this technique was already used to construct a two-mode integrable model (the two-site Bose-Hubbard model) [2,3,4] which has been used with success to describe experimental results [5,6].…”

Section: Introductionmentioning

confidence: 99%

Quantum integrable multi-well tunneling models

Ymai

Tonel

Foerster

et al. 2017

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this work we present a general construction of integrable models for boson tunneling in multi-well systems. We show how the models may be derived through the Quantum Inverse Scattering Method and solved by algebraic Bethe ansatz means. From the transfer matrix we find only two conserved operators. However, we construct additional conserved operators through a different method. As a consequence the models admit multiple pseudovacua, each associated to a set of Bethe ansatz equations. We show that all sets of Bethe ansatz equations are needed to obtain a complete set of eigenstates.

show abstract

“…This quest encouraged the search for new solvable models that could be related to the properties of such condensates, including the possibility of interaction among condensates [4][5][6][7][8][9][10][11][12][13][14]. The motivation that underlies those proposed models is that, by the study of exactly solvable models, quantum fluctuations may be fully taken into account providing tools that allows one to go beyond the results obtained by mean field approximations.…”

Section: Introductionmentioning

confidence: 99%

A bosonic multi-state two-well model

Santos¹,

Foerster²,

Roditi³

2013

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

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.

show abstract

The Two-Site Bose–Hubbard Model

Cited by 27 publications

References 16 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 integrable multi-well tunneling models

A bosonic multi-state two-well model

Contact Info

Product

Resources

About