Beyond the Fermi pseudopotential: A modified Gross-Pitaevskii equation

We derive rigorously one-and two-dimensional mean-field equations for cigar-and pancake-shaped Bose-Einstein condensates (BEC) with higher order interactions (HOI). We show how the higher order interaction modifies the contact interaction of the strongly confined particles. Surprisingly, we find that the usual Gaussian profile assumption for the strongly confining direction is inappropriate for the cigar-shaped BEC case, and a Thomas-Fermi type profile should be adopted instead. Based on the derived mean field equations, the Thomas-Fermi densities are analyzed in presence of the contact interaction and HOI. For both box and harmonic traps in one, two and three dimensions, we identify the analytical Thomas-Fermi densities, which depend on the competition between the contact interaction and the HOI.

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“…(15), TF density (17) and the numerical results from 3D MGPE (4) by integrating the longitudinal z axis out. The results are displayed in Fig.…”

Section: Quasi-2d Bec With Hoimentioning

confidence: 99%

Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions

Ruan

Cai

Bao

2016

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

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“…For λ = 0 one finds the standard GPE (1). The contribution due to the nonvanishing size of the particles r out was found by Collin, Massignan, and Pethick [6] (for earlier work see [7]). In our case it takes the form…”

Section: Modified Gpe For δ-Functions Interactionmentioning

confidence: 79%

Simple model for interactions and corrections to the Gross-Pitaevskii equation

Veksler¹,

Fishman²,

Ketterle³

2014

Phys. Rev. A

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One of the assumptions leading to the Gross-Pitaevskii equation (GPE) is that the interaction between atom pairs can be written effectively as a δ function so that the interaction range of the particles is assumed to vanish. A simple model that takes into account the extension of the interparticle potential is introduced. The correction to the GPE predictions for the energy of a condensate confined by a harmonic trap in the Thomas-Fermi regime is estimated. Although it is found to be small, we believe that in some situations it can be measured using its dependance on the frequency of the confining trap. Due to the simplicity of the model, it may have a wide range of applications.

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“…The dynamic behaviour of the three dimensional (3D) modified GP equation which take into account quantum fluctuations and the shape dependence on the interaction potential can be described by [9]  ,…”

Section: Modified Gross-pitaevskii Equationsmentioning

confidence: 99%

“…For inhomogeneous systems, recent works on two atoms in a trap have shown that the shape-independent approximation becomes less valid under strong confinement [8]. Then, a modified GP equation, which incorporates the energy dependence of the two-body scattering amplitude through an effective-range expansion has been derived [9]. To the best of our knowledge, MI in this system has not been investigated.…”

Section: Introductionmentioning

confidence: 99%

Impact of Quantum Fluctuations on the Modulational Instability of a Modified Gross-Pitaevskii Equation with Two-Body Interaction

Tiofack¹,

Ekogo²,

Moussambi³

et al. 2012

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Modulational instability conditions for the generation of localized structures in the context of matter waves in BoseEinstein condensates are investigated analytically and numerically. The model is based on a modified Gross-Pitaevskii equation, which account for the energy dependence of the two-body scattering amplitude. It is shown that the modified term due to the quantum fluctuations modify significantly the modulational instability gain. Direct numerical simulations of the full modified Gross-Pitaevskii equation are performed, and it is found that the modulated plane wave evolves into a train of pulses, which is destroyed at longer times due to the effects of quantum fluctuations.

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Beyond the Fermi pseudopotential: A modified Gross-Pitaevskii equation

Cited by 70 publications

References 32 publications

Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions

Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions

Simple model for interactions and corrections to the Gross-Pitaevskii equation

Impact of Quantum Fluctuations on the Modulational Instability of a Modified Gross-Pitaevskii Equation with Two-Body Interaction

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