Vortex lines and vortex lattices in a Bose-Einstein condensate

Haljan,; Coddington, P.D.; Engels,; Cornell,

doi:10.1109/qels.2002.1031243

Cited by 8 publications

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“…Although the mechanisms for the spin-up of the superfluid are not fully understood, at equilibrium the vortices must flow with the normal velocity due to the the mutual friction between superfluid and normal components [2]. In addition to considerable indirect evidence for this hypothesis, small numbers of vortices have been imaged directly in rotating superfluid 4 He [3].In this work we show how the presence of quantized vortices can allow a Bose-Einstein condensate (BEC) to mimic a classical fluid under rotation, as has been suggested by recent experiments at JILA [4]. In these experiments, a trapped gas of ultracold 87 Rb atoms is spun up, and then cooled through the Bose-Einstein condensation transition.…”

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Superfluid-to-Solid Crossover in a Rotating Bose-Einstein Condensate

Feder

Clark

2001

Phys. Rev. Lett.

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The properties of a rotating Bose-Einstein condensate confined in a prolate cylindrically symmetric trap are explored both analytically and numerically. As the rotation frequency increases, an ever greater number of vortices are energetically favored. Though the cloud anisotropy and moment of inertia approach those of a classical fluid at high frequencies, the observed vortex density is consistently lower than the solid-body estimate. Furthermore, the vortices are found to arrange themselves in highly regular triangular arrays, with little distortion even near the condensate surface. These results are shown to be a direct consequence of the inhomogeneous confining potential. 03.75.F, 05.30.Jp, 47.37.+q One of the most striking properties of liquid 4 He(II) is its ability to mimic the behavior of a solid body when subjected to uniform rotation. Since the superfluid velocity field v s is irrotational (∇ × v s = 0), the superfluid component of 4 He(II) might be expected to remain at rest while the normal component rotates with the container. In fact, for sufficiently large values of the rotation frequency Ω, the entire fluid is found to rotate like a classical liquid at all temperatures [1]. The paradox may be resolved by assuming that the superfluid is threaded by quantized vortices. These are singularities of v s , around which the phase of the superfluid order parameter increases by 2π. Although the mechanisms for the spin-up of the superfluid are not fully understood, at equilibrium the vortices must flow with the normal velocity due to the the mutual friction between superfluid and normal components [2]. In addition to considerable indirect evidence for this hypothesis, small numbers of vortices have been imaged directly in rotating superfluid 4 He [3].In this work we show how the presence of quantized vortices can allow a Bose-Einstein condensate (BEC) to mimic a classical fluid under rotation, as has been suggested by recent experiments at JILA [4]. In these experiments, a trapped gas of ultracold 87 Rb atoms is spun up, and then cooled through the Bose-Einstein condensation transition. For small values of Ω, the condensate density is found to assume its usual non-rotating shape, while the thermal cloud bulges outward. This corroborates previous evidence that the condensate behaves as an irrotational superfluid [5,6]. The condensate density profile undergoes a sudden change at a value of Ω that is comparable to the thermodynamic critical frequency for the stability of a single vortex [7]. As Ω increases further, the shape of the condensate gradually approaches that of the thermal cloud. This suggests that for any given value of Ω and temperature, the condensate contains the appropriate number and distribution of vortices for thermodynamic equilibrium. In contrast, when no appreciable thermal fraction is present, higher rotation frequencies are generally required to nucleate vortices in .We present two key results, which also bear on issues raised by recent experiments at MIT [9]. First, the vortices are a...

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confidence: 57%

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Superfluid-to-Solid Crossover in a Rotating Bose-Einstein Condensate

Feder

Clark

2001

Phys. Rev. Lett.

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“…This is a quantitative measure for the rotation frequency, Ω, of the lattice, and therefore the number of vortices [14]. Such distorted shapes have been observed previously for rotating clouds [9,11,12].The shape of a rotating condensate is determined by the magnetic trapping potential and the centrifugal potential − 1 2 M Ω 2 r 2 , where M is the atomic mass. From the effective radial trapping frequency ω r → ω ′ r = ω 2 r − Ω 2 , one obtains the aspect ratio of the rotating cloud,…”

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confidence: 81%

“…These include vortex nucleation [3,4], crystallization of the vortex lattice [5], and decay [6,7]. Experimental study has focused mainly on the nucleation of vortices, either by stirring condensates directly with a rotating anisotropy [8][9][10] or creating condensates out of a rotating thermal cloud [11]. Here we report the first quantitative investigation of vortex dynamics at finite temperature.…”

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Formation and Decay of Vortex Lattices in Bose-Einstein Condensates at Finite Temperatures

2002

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The dynamics of vortex lattices in stirred Bose-Einstein condensates have been studied at finite temperatures. The decay of the vortex lattice was observed non-destructively by monitoring the centrifugal distortions of the rotating condensate. The formation of the vortex lattice could be deduced from the increasing contrast of the vortex cores observed in ballistic expansion. In contrast to the decay, the formation of the vortex lattice is insensitive to temperature change.PACS 03.75.Fi, 67.40.Vs, 32.80.Pj Gaseous Bose-Einstein condensates (BEC) have become a testbed for many-body theory. The properties of a condensate at zero temperature are accurately described by a nonlinear Schrödinger equation. More recently, theoretical work on the ground state properties of condensates [1] has been extended to rotating condensates containing one or several vortices [2] and their dynamics. These include vortex nucleation [3,4], crystallization of the vortex lattice [5], and decay [6,7]. Experimental study has focused mainly on the nucleation of vortices, either by stirring condensates directly with a rotating anisotropy [8][9][10] or creating condensates out of a rotating thermal cloud [11]. Here we report the first quantitative investigation of vortex dynamics at finite temperature. The crystallization and decay of a vortex lattice have been studied and a striking difference is found between the two processes: while the crystallization is essentially temperature independent, the decay rate increases dramatically with temperature.The method used to generate vortices has been outlined in previous work [9,12]. Condensates of up to 75 million sodium atoms (> 80% condensate fraction) were prepared in a cigar-shaped Ioffe-Pritchard magnetic trap using evaporative cooling. The radial and axial trap frequencies of ω x = 2π × (88.8 ± 1.4) Hz, ω y = 2π × (83.3 ± 0.8) Hz, and ω z = 2π × (21.1 ± 0.5) Hz, respectively, corresponded to a radial trap asymmetry of ǫ r = (ω2)% and an aspect ratio of A = ω x /ω z = (4.20 ± 0.04). The relatively large value of the radial trap asymmetry is due to gravitational sag and the use of highly elongated pinch coils (both estimated to contribute equally). The radio frequency used for evaporation was held at its final value to keep the temperature of the condensate roughly constant throughout the experiment. The condensate's ThomasFermi radii, chemical potential, and peak density were R r = 28 µm, R z = 115 µm, 300 nK, and 4 × 10 14 cm −3 , respectively, corresponding to a healing length ξ ≃ 0.2 µm.Vortices were produced by spinning the condensate for 200 ms along its long axis with a scanning, blue-detuned laser beam (532 nm) [8,13]. For this experiment two symmetric stirring beams were used (Gaussian waist w = 5.3 µm, stirring radius 24 µm). The laser power of 0.16 mW per beam corresponded to an optical dipole potential of 310 nK. After the stirring beams were switched off, the rotating condensate was left to equilibrate in the static magnetic trap for various hold times. As in our previous work,...

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“…Specifically, the effective radial trap frequency ω 2 ⊥ − Ω 2 1/2 produces an observable centrifugal distortion of the condensate [10][11][12] for currently attainable values of Ω/ω ⊥ < ∼ 1. As seen below, this behavior means that ω ⊥ effectively acts like Ω c2 for pure harmonic radial confinement, and direct experimental study of the limiting behavior for Ω → ω ⊥ would be difficult.…”

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confidence: 99%

Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials

Fetter

2001

Phys. Rev. A

147

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A dense vortex lattice in a rotating dilute Bose-Einstein condensate is studied with the ThomasFermi approximation. The upper critical angular velocity Ωc2 occurs when the intervortex separation b becomes comparable with the vortex core radius ξ. For a radial harmonic trap, the loss of confinement as Ω → ω ⊥ implies a singular behavior. In contrast, an additional radial quartic potential provides a simple model for which Ωc2 is readily determined. Unlike the case of a type-II superconductor at fixed temperature, the onset of Ωc2 arises not only from decreasing b but also from increasing ξ caused by the vanishing of the chemical potential as Ω → Ωc2. 03.75.Fi, 67.40.Vs, 47.37.+q

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Vortex lines and vortex lattices in a Bose-Einstein condensate

Cited by 8 publications

References 0 publications

Superfluid-to-Solid Crossover in a Rotating Bose-Einstein Condensate

Superfluid-to-Solid Crossover in a Rotating Bose-Einstein Condensate

Formation and Decay of Vortex Lattices in Bose-Einstein Condensates at Finite Temperatures

Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials

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