Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

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

doi:10.1103/physreva.73.023609

Cited by 52 publications

(67 citation statements)

References 28 publications

(61 reference statements)

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“…With λ = 0, another saddle point can appear at θ = π provided λ < λ c = − 1 2 3/2 . The appearance of this saddle point can be understood from the graphical solution of the equation (see also [43]):…”

Section: Figmentioning

confidence: 99%

“…The case λ = 0 in the Hamiltonian (4) corresponds to inclusion of the s-wave scattering interactions. Recently, in [43] a more general quantum Hamiltonian describing the coupling between atomic and diatomic-molecular BECs within two-mode approximation was considered:…”

Section: Figmentioning

confidence: 99%

“…The phenomenon is very important for BEC physics: we consider here nonlinear two-mode models related to tunnelling between coupled BEC in a double well [23], nonlinear Landau-Zener tunnelling [24,25], Feshbach resonance passage in atom-molecule systems [26,27,28]. Nonlinear two-mode models were extensively studied previously (sometimes beyond the mean-field approxima- * Electronic address: alx˙it@yahoo.com tion, [23,24,25,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]), and destruction of adiabaticity was discussed already in [24,25,26], still there are regimes of motion that were not analyzed in these papers from the point of view of nonadiabatic behaviour, that is, when initial populations of both modes are not zero (or very small), but finite. We presented some of our results on that theme in [27,28]; nevertheless destruction of adiabatic invariance has not been studied systematically in BEC-related models yet.…”

Section: Introductionmentioning

confidence: 99%

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Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

Itin

Watanabe

2007

Phys. Rev. E

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We discuss dynamics of approximate adiabatic invariants in several nonlinear models being related to physics of Bose-Einstein condensates (BEC). We show that nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunnelling, and BEC tunnelling oscillations in a double-well can be considered within a unifying approach based on the theory of separatrix crossings. The separatrix crossing theory was applied previously to some problems of classical mechanics, plasma physics and hydrodynamics, but has not been used in the rapidly growing BEC-related field yet. We derive explicit formulas for the change in the action in several models. Extensive numerical calculations support the theory and demonstrate its universal character. We also discovered a qualitatively new nonlinear phenomenon in a NLZ model which we propose to call separated adiabatic tunnelling (AT).

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Section: Figmentioning

confidence: 99%

Section: Figmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

Itin

Watanabe

2007

Phys. Rev. E

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“…We adopt the method of directly diagonalising the Hamiltonian (32) as done in [18], and compute the expectation value of z(t) through…”

Section: Ground-state Expectation Values and Quantum Dynamicsmentioning

confidence: 99%

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

et al. 2007

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We study a three-mode Hamiltonian modelling a heteronuclear molecular BoseEinstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classical analogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wavefunction overlaps to clarify the nature of the ground-state phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance.

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“…Additionally, in (9), we also drop the subscript of the transverse wave-vectors of photons and PPs, i.e. we take k r = k. It is well known that for a general massive Boson-Boson pairs gas, at absolute zero temperature, there exists a BEC consisting of two possible condensate phases [25][26][27]: (i) Both the single boson and the pair of bosons are condensed. (ii) The pair of bosons are condensed but the single boson is not.…”

Section: Bec Of Photons and Photon Pairsmentioning

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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Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

Cited by 52 publications

References 28 publications

Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

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

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