Dynamics of a Single Vortex Line in a Bose-Einstein Condensate

Rosenbusch, P.; Bretin, Vincent; Dalibard, Jean

doi:10.1103/physrevlett.89.200403

Cited by 155 publications

(163 citation statements)

References 26 publications

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“…Near equilibrium, the visibility of the vortices are still different from those in Fig. 2(b-v) and (c-v), because the vortex lines still bend near the edge of the condensates, which is consistent with the previous equilibrium arguments [14]. Animation of the above simulation is in Ref.…”

supporting

confidence: 85%

“…In contrast to 2D simulations, a 3D simulation gives significant improvement for describing real 3D systems. For the present study, these improvements are (i) the 3D simulation includes the axial (z) component, which increases the number of degrees of freedom of the fluctuation modes, and (ii) the 3D simulation can treat observed physical phenomena associated with "vortex lines", such as bending [14], Kelvin waves (helical displacements of the vortex core) [16], and reconnection [17]. These features make the dynamical process of vortex lattice formation richer than that of the 2D case.…”

mentioning

confidence: 99%

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Three-dimensional dynamics of vortex-lattice formation in Bose-Einstein condensates

Kasamatsu

Machida²,

Sasa³

et al. 2005

Phys. Rev. A

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We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped BoseEinstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The simulations reveal previously unknown dynamical features of the vortex nucleation process, in which the condensate undergoes a strongly turbulent stage and the penetrating vortex lines vibrate rapidly. The vibrations arise from spontaneous excitation of Kelvin waves on the proto-vortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.PACS numbers: 03.75. Fi, 67.40.Db Atomic-gas Bose-Einstein condensates (BECs) provide a versatile testing ground for superfluidity, particularly in systems with an externally driven rotation. Several experimental groups have observed the formation of a lattice of quantized vortices in such a rotating BEC [1,2,3,4]. The experiment that largely motivates the present study is a direct observation of nonlinear dynamical phenomena such as vortex nucleation and lattice formation of a rotating BEC in real time [5]. There are some theoretical attempts to understand the dynamical properties of vortex lattice formation in this system [6,7,8,9,10,11,12]. Among these studies, the experimental observations are well reproduced by two-dimensional (2D) numerical simulations of the timedependent Gross-Pitaevskii equation (GPE) with a phenomenological dissipation term [7,8,9,13]. This paper presents the full three-dimensional (3D) dynamics of vortex lattice formation in a rotating BEC through the numerical simulations of the time-dependent GPE with a dissipation term. Except for a few preliminary works [6,11,12] and studies of the static configurations of vortices [14,15], this problem has been analyzed using only 2D simulations. In contrast to 2D simulations, a 3D simulation gives significant improvement for describing real 3D systems. For the present study, these improvements are (i) the 3D simulation includes the axial (z) component, which increases the number of degrees of freedom of the fluctuation modes, and (ii) the 3D simulation can treat observed physical phenomena associated with "vortex lines", such as bending [14], Kelvin waves (helical displacements of the vortex core) [16], and reconnection [17]. These features make the dynamical process of vortex lattice formation richer than that of the 2D case. Recently, Lobo et al. studied the 3D dynamics of rotating atomic-gas BECs using classical field theory in which the dynamics is described by the energy-conserving timedependent GPE and both the condensate wave function and its fluctuation modes are approximated by a single c-number field [11]. The dissipative process and the 3D vortex dynamics of a rotating BEC in a sphericallysymmetric trap was discussed in Ref. [12]. In our present study, we take account of the phenomenological dissipation so as to reproduce the entire vortex formation process that was observed in the experiments ...

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supporting

confidence: 85%

mentioning

confidence: 99%

Three-dimensional dynamics of vortex-lattice formation in Bose-Einstein condensates

Kasamatsu

Machida²,

Sasa³

et al. 2005

Phys. Rev. A

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“…As ℓ is increased the vortex line is closer to the center and it is curved for ℓ < 1; it becomes the axially symmetric vortex at the center of the condensate for ℓ = 1. Following [2,7] we call the vortex mode in Fig. 1 the U-vortex.…”

Section: Precessing Vorticesmentioning

confidence: 99%

“…In the last years there has been intense experimental and theoretical study on the creation and dynamics of single vortices as well as vortex lattices in ultracold atomic Bose-Einstein condensates (BECs) [2,3]. These systems offer the possibility for direct observation of vortex lines and of their dymamics.…”

Section: Introductionmentioning

confidence: 99%

Single vortex states in a confined Bose-Einstein condensate

2005

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It has been demonstrated experimentally that non-axially symmetric vortices precess around the centre of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S-vortex and the U-vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S-vortex has higher energy than the U-vortex in a rotating elongated condensate. We show that the S-vortex is related to the solitonic vortex which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S-vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.

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“…Motivated by the recent advances achieved in the experimental manipulation of rotating condensates [11,12] and of condensates loaded into optical lattices [13], we use the self-consistent HF to study the temperature dependence of the thermodynamic parameters for the rotating interacting BEC in 1D optical lattice. The effects of the rotation rate and optical potential depth are considered simultaneously.…”

Section: Introductionmentioning

confidence: 99%