Oscillation frequencies for a Bose condensate in a triaxial magnetic trap

Cerboneschi, E.; Mannella, R.; Arimondo, E.; Salasnich, Luca

doi:10.1016/s0375-9601(98)00732-4

Cited by 73 publications

(98 citation statements)

References 19 publications

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“…We solved the equations numerically by means of a finite-difference Crank-Nicholson predictorcorrector method with the cylindrical symmetry (details of the method were given in Ref. [20]). To generate the ground-state wave functions ψ 1,2 (r, z), with j = 1, 2, the imaginary-time integration was used.…”

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confidence: 99%

Effects of axial vorticity in elongated mixtures of Bose-Einstein condensates

2008

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We consider a meniscus between rotating and nonrotating species in the Bose-Einstein condensate (BEC) with repulsive inter-atomic interactions, confined to a pipe-shaped trap. In this setting, we derive a system of coupled one-dimensional (1D) nonpolynomial Schrödinger equations (NPSEs) for two mean-field wave functions. Using these equations, we analyze the phase separation/mixing in the pipe with periodic axial boundary conditions, i.e. in a toroidal configuration. We find that the onset of the mixing, in the form of suction, i.e., filling the empty core in the vortical component by its nonrotating counterpart, crucially depends on the vorticity of the first component, and on the strengths of the inter-atomic interactions.PACS numbers: 03.75.Lm, Since the creation of vortices in Bose-Einstein condensates (BECs) [1,2], this topic has been a subject of many experimental and theoretical works, as reviewed in Refs.[3]. In particular, much attention has been drawn to vortices in mixtures of two BEC species; in fact, the first vortices were created in a two-component setting [1], and a theoretical analysis of that setting was developed too [4]. In this connection, a situation of straightforward interest is the interaction of rotating and nonrotating immiscible BEC species. It is natural to expect that the nonrotating component may fill the hollow vortical core(s) in the rotating one. As shown experimentally, vortices and vortex lattices with empty and filled cores feature a great difference in their structure [2,5]. Very recently it has been also predicted the possibility to create vortex with arbitrary topological charge by phase engineering [6].Matter-wave vortices can be created not only in largeaspect ratio settings, but also in narrow cigar-shaped traps ("pipes"), which help to stabilize them [7]. In the pipe geometry, it is interesting too to consider the interaction of rotating and nonrotating BEC species, which is the subject of the present work. In particular, a natural issue in this case is the effect of "suction", i.e., onset of effective mixing between two nominally immiscible species by pushing the nonrotating component into the empty core in the vorticity-carrying one. In other words, the suction implies indefinite stretching of the meniscus separating the immiscible species which originally fill two halves of the tube.In the mean-field approximation, the starting point of the analysis is a system of coupled Gross-Pitaevskii equations (GPEs) for macroscopic wave functions, ψ 1 and ψ 2 , of the two BEC species confined in the tight cylindrical trap. In the scaled form, the equations arewhere z is the axial coordinate, while x and y are the transverse ones. In these equations, lengths are measured in units of a (1) ⊥ = h/(m 1 Ω 1 ), the energy in units ofhΩ 1 , and time in units of 1/Ω 1 , where m 1,2 and Ω 1,2 are masses and transverse trapping frequencies of the two species, while the relative parameters in Eqs. (1) and (2) are m ≡ m 2 /m 1 and Ω ≡ Ω 2 /Ω 1 . The interaction strengths in the equations...

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Effects of axial vorticity in elongated mixtures of Bose-Einstein condensates

2008

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“…(4), using a finite difference spatial representation of the wave function and a norm-preserving Crank-Nicholson integrator, see e.g. [15] for details (a) (b) Fig. 1 Sketch of the experiments we are proposing.…”

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Mean-Field Transport of a Bose-Einstein Condensate

Sekkouri

Wimberger

2017

Emergent Complexity From Nonlinearity, in Physics, Engineering and the Life Sciences

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The expansion of an initially confined Bose-Einstein condensate into either free space or a tilted optical lattice is investigated in a mean-field approach. The effect of the interactions is to enhance or suppress the transport depending on the sign and strength of the interactions. These effects are discusses in detail in view of recent experiments probing non-equilibrium transport of ultracold quantum gases.

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“…Dots in Fig. 10 represent analytical result (26), and lines depict (for the sake of checking the correctness of the analytical result) the numerical solution of Eq. (22) with λ = 0, obtained as in Ref.…”

Section: Self-trapping In the Noninteracting Fermi Gas And Self-rmentioning

confidence: 99%

“…(22) with λ = 0, obtained as in Ref. [26] [in the latter case, the 3D density is numerically integrated in the transverse plane to reduce it to n 1 , see Eq. (23)].…”

Section: Self-trapping In the Noninteracting Fermi Gas And Self-rmentioning

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Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

2013

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We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one-or twodimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermivon Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity.

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Oscillation frequencies for a Bose condensate in a triaxial magnetic trap

Cited by 73 publications

References 19 publications

Effects of axial vorticity in elongated mixtures of Bose-Einstein condensates

Effects of axial vorticity in elongated mixtures of Bose-Einstein condensates

Mean-Field Transport of a Bose-Einstein Condensate

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

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