Uncertainty product of an out-of-equilibrium Bose-Einstein condensate

Klaiman, Shachar; Streltsov, Alexej I.; Alon, Ofir E.

doi:10.1088/1742-6596/826/1/012020

Cited by 8 publications

(13 citation statements)

References 80 publications

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“…6 and 7. The similarity of the out-of-equilibrium results for the same interaction parameter and different numbers of particles (N = 1000 bosons in the present subsection, N = 10 in the Appendix), together with analogous behavior in the dynamics of larger systems in one-dimensional traps [21,27], provide, in our opinion, strong evidences that the effects of the anisotropy of the time-dependent position and momentum variances in essentially fully-condensed BECs persist in the limit of an infinite number of particle.…”

Section: B Dynamicssupporting

confidence: 64%

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Variance of an anisotropic Bose-Einstein condensate

et al. 2018

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The anisotropy of a trap potential can impact the density and variance of a Bose-Einstein condensate (BEC) in an opposite manner. We exemplify this effect for both the ground state and out-of-equilibrium dynamics of structureless bosons interacting by a long-range inter-particle interaction and trapped in a two-dimensional single-well potential. We demonstrate that even when the density of the BEC is, say, wider along the y direction and narrower along the x direction, its position variance can actually be smaller and momentum variance larger in the y direction than in the x direction. This behavior of the variance in a many-particle system is counterintuitive. It suggests using the variance as a tool to characterize the strength of correlations along the y and x directions in a trapped BEC.

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Section: B Dynamicssupporting

confidence: 64%

“…The latter is far away from the infinite-particle limit (where the bosonic system is 100% condensed) which was the focus of previous work [20,21]. We mention that preliminary results in one spatial dimension were recently reported in [27]. The structure of the paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

Variance of an anisotropic Bose-Einstein condensate

et al. 2018

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“…x,density = 0.777, 0.748, 0.519 and 1 N ∆ 2 P X = ∆ 2 px,density = 0.329, 0.340, 0.482, whereas at the many-body level we find 1 N ∆ 2X = 0.781, 0.794, 0.927 and 1 N ∆ 2 P X = 0.328, 0.322, 0.272 for the three interactions parameters Λ = −0.018, −0.18, −1.8, respectively. Just like for their repulsive sibling [42,45,48], the variance and density in the ground state of an attractive trapped BEC behave in an opposite manner. In summary, increasing the attraction amounts to enlarging the position variance, despite narrowing of the density, in as much as increasing the repulsion [42,45,48] leads to decreasing of the position variance, in spite of broadening of the density.…”

Section: Ground Statementioning

confidence: 99%

“…The interaction is quenched at t = 0 from Λ = λ 0 (N − 1) = −0.18 to Λ = −0.36. Following the quench of the interaction, the density performs breathing oscillations [45,48,[117][118][119]. The number of particles is N = 10, 100, .…”

Section: Out-of-equilibrium Dynamicsmentioning

confidence: 99%

Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance

Alon

Cederbaum

2018

Chemical Physics

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The dynamics of attractive bosons trapped in one dimensional anharmonic potentials is investigated. Particular emphasis is put on the variance of the position and momentum many-particle operators. Coupling of the center-of-mass and relative-motion degrees-of-freedom necessitates an accurate numerical treatment. The multiconfigurational time-dependent Hartree for bosons (MCT-DHB) method is used, and high convergence of the energy, depletion and occupation numbers, and position and momentum variances is proven numerically. We demonstrate for the ground state and out-of-equilibrium dynamics, for condensed and fragmented condensates, for small systems and en route to the infinite-particle limit, that intriguing differences between the density and variance of an attractive Bose-Einstein condensate emerge. Implications are briefly discussed.

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“…In this Appendix, a brief introduction of the many-body variance, which is employed in the main text to study many-body excitations involved in the dynamics of trapped BECs, is given. The many-body variance has been of interest in recent studies on correlations between bosons in the ground state [242] and for outof-equilibrium BECs [243,244], in particular in a 1D bosonic Josephson junction [245] or in anharmonic and anisotropic trapping potentials [246,81]. It has also been found that the variance is a sensitive measure for the numerical convergence of MCTDHB [80].…”

Section: A2 Multi-orbital Approachesmentioning

confidence: 99%

Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates

Alon¹,

Beinke²,

Cederbaum³

2021

Preprint

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This review explores the dynamics and the low-energy excitation spectra of Bose-Einstein condensates (BECs) of interacting bosons in external potential traps putting particular emphasis on the emerging manybody effects beyond mean-field descriptions. To do so, methods have to be used that, in principle, can provide numerically exact results for both the dynamics and the excitation spectra in a systematic manner. Numerically exact results for the dynamics are presented employing the well-established multicongurational time-dependent Hartree for bosons (MCTDHB) method. The respective excitation spectra are calculated utilizing the more recently introduced linear-response theory atop it (LR-MCTDHB). The latter theory gives rise to an, in general, non-hermitian eigenvalue problem. The theory and its newly developed implementation are described in detail and benchmarked towards the exactly-solvable harmonic-interaction model. Several applications to BECs in one-and two-dimensional potential traps are discussed. With respect to dynamics, it is shown that both the out-of-equilibrium tunneling dynamics and the dynamics of trapped vortices are of many-body nature. Furthermore, many-body effects in the excitation spectra are presented for BECs in different trap geometries. It is demonstrated that even for essentially-condensed systems, the spectrum of the lowest-in-energy excitations computed at the many-body level can differ substantially from the standard mean-field description. In general, it is shown that bosons carrying angular momentum are more sensitive to many-body effects than bosons without. These effects are present in both the dynamics and the excitation spectrum.

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Uncertainty product of an out-of-equilibrium Bose-Einstein condensate

Cited by 8 publications

References 80 publications

Variance of an anisotropic Bose-Einstein condensate

Variance of an anisotropic Bose-Einstein condensate

Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance

Many-body effects in the excitations and dynamics of trapped Bose-Einstein condensates

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