Self-trapping on a dimer: Time-dependent solutions of a discrete nonlinear Schrödinger equation

Kenkre, V. M.; Campbell, D. K.

doi:10.1103/physrevb.34.4959

Cited by 302 publications

(194 citation statements)

References 18 publications

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“…This self-trapping effect, which originally has been established on the mean-field level [3,23,25,26], has recently been observed experimentally for condensates [10]. Self-trapping can also be understood within the N -particle approach (cf.…”

Section: Modelmentioning

confidence: 99%

Coherent control of mesoscopic tunneling in a Bose-Einstein condensate

Weiß

Jinasundera

2005

Phys. Rev. A

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For a weakly interacting Bose-Einstein condensate in a double well, an appropriate time-dependent modulation of the trapping potential counter-acts the "self-trapping" effects of the interactions, thereby allowing tunneling between the wells. It is demonstrated numerically that this modulation can be employed for transferring the condensate from one well to the other in a controlled way. Moreover it allows the production of mesoscopic entangled states on short time scales.

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Section: Modelmentioning

confidence: 99%

Coherent control of mesoscopic tunneling in a Bose-Einstein condensate

Weiß

Jinasundera

2005

Phys. Rev. A

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“…Adopted almost thirty years ago to model small molecular systems and study energy-localization effects [11]- [13], equations (1) still represent the basic theoretic model for studying the dynamics of solitons and of low-energy excitations in lattices [14]- [17] where bosons can experience both attractive (U < 0) and repulsive (U > 0) interactions.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the central-depleted-well regime in the open Bose-Hubbard trimer

Penna

2013

Phys. Rev. E

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We study the quantum dynamics of the central-depleted-well (CDW) regime in a three-mode Bose Hubbard model subject to a confining parabolic potential. By introducing a suitable set of momentum-like modes we identify the microscopic variables involved in the quantization process and the dynamical algebra of the model. We describe the diagonalization procedure showing that the model reduces to a double oscillator. Interestingly, we find that the parameter-space domain where this scheme entails a discrete spectrum well reproduces the two regions where the classical trimer excludes unstable oscillations. Spectral properties are examined in different limiting cases together with various delocalization effects. These are shown to characterize quantum states of the CDW regime in the proximity of the borderline with classically-unstable domains.

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“…In Ref. [10] Kenkre and Campbell studied the self-trapping transition on a nonlinear cubic dimer, finding an exact value for the critical nonlinearity γ c = 4. Then, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Self-trapping transition in nonlinear cubic lattices

Naether

Martínez²,

Guzmán-Silva³

et al. 2013

Phys. Rev. E

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We explore the fundamental question about the critical nonlinearity value needed to dynamically localize energy in discrete nonlinear cubic (Kerr) lattices. We focus on the effective frequency and participation ratio of the profile to determine the transition into localization in one-, two-, and three-dimensional lattices. A simple and general criterion is developed -for the case of an initially localized excitation -to define the transition region in parameter space ("dynamical tongue") from a delocalized to a localized profile. We introduce a method for computing the dynamically excited frequencies, which helps us to validate our stationary ansatz approach and the effective frequency concept. A general analytical estimate of the critical nonlinearity is obtained, with an extra parameter to be determined. We found this parameter to be almost constant for two-dimensional systems, and proved its validity by applying it successfully to two-dimensional binary lattices.

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Self-trapping on a dimer: Time-dependent solutions of a discrete nonlinear Schrödinger equation

Cited by 302 publications

References 18 publications

Coherent control of mesoscopic tunneling in a Bose-Einstein condensate

Coherent control of mesoscopic tunneling in a Bose-Einstein condensate

Dynamics of the central-depleted-well regime in the open Bose-Hubbard trimer

Self-trapping transition in nonlinear cubic lattices

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