Surface of a Bose-Einstein condensed atomic cloud

Khawaja, U. Al; Pethick, C. J.; Smith, H.

doi:10.1103/physreva.60.1507

Cited by 46 publications

(60 citation statements)

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“…The group velocity dω/dk = R(ω 2 ⊥ − Ω 2 )/(2 √ k) agrees with the propagation velocity of the surface wave in our simulation. As discussed by Al Khawaja et al [16], the surface waves are connected with the low energy excitations studied by Stringari and Dalfovo et al [17], and Isoshima and Machida [10].…”

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Vortex lattice formation in a rotating Bose-Einstein condensate

2002

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We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The origin of the peculiar surface-mode excitations is identified to be phase fluctuations at the low-density surface regime. The obtained dependence of a distortion parameter on time and that on the driving frequency agree with the recent experiments by Madison et al. [Phys. Rev. Lett. 86, 4443 (2001)].PACS numbers: 03.75. Fi, 67.40.Db Quantized vortices have long been studied in superfluid 4 He as the topological defects characteristic of superfluidity [1,2]. However, the relatively high density and strong repulsive interaction complicate the theoretical treatments of the Bose-Einstein condensed liquid, and the healing length of the atomic scale makes the experimental visualization of the quantized vortices difficult. The recent achievement of Bose-Einstein condensation in trapped alkali-metal atomic gases at ultra low temperatures has stimulated intense experimental and theoretical activity. The atomic Bose-Einstein condensates(BECs) have the weak interaction because they are dilute gases, thus being free of the above difficulties that superfluid 4 He is subject to. Quantized vortices in the atomic BECs have recently been created experimentally by Matthews et al. By rotating an asymmetric trapping potential, Madison et al. at ENS succeeded in forming a quantized vortex in 87 Rb BEC for a stirring frequency that exceeds a critical value [4]. Vortex lattices were obtained for higher frequencies. The ENS group subsequently observed that vortex nucleation occurs via a dynamical instability of the condensate [6]. For a given modulation amplitude and stirring frequency, the steady state of the condensate was distorted to an elliptic cloud, stationary in the rotating frame, as predicted by Recati et al. [7]. An intrinsic dynamical instability [8] of the steady state transformed the elliptic state into a more axisymmetric state with vortices. However, the origin of that instability and how it leads to the formation of vortex lattices remains to be investigatedThe ENS group found that the minimum rotation frequency Ω nuc at which one vortex appears is 0.65ω ⊥ , where ω ⊥ is the transverse oscillation frequency of the cigar-shaped trapping potential, independent of the number of atoms or the longitudinal frequency ω z [9]. There is a discrepancy between the observations and the theoretical considerations based on the stationary solution of the Gross-Pitaevskii equation(GPE) [10,11]; Ω nuc is significantly larger than its equilibrium estimates.The present paper addresses these issues by numerically solving the GPE that governs the time evolution of the order parameter ψ(r, t):Here g = 4πh 2 a/m is the coupling constant, proportional to the 87 Rb scattering length a ≈5.77 nm. The high anisotropy of the cig...

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“…The dispersion relation of the surface waves [16] of a rotating condensate is obtained as follows. The substitution of the Madelung transformation ψ = |ψ|e iθ into Eq.…”

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Vortex lattice formation in a rotating Bose-Einstein condensate

2002

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“…The dispersion law, ω (0) 2 +1 ∝ k, is analogous to that of surface waves on a boundary between a single component BEC and vacuum [16]. Now it is necessary to explain why in the present problem one cannot choose…”

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“…The analytic approximation given by Eqs. (15,16) is justified by numerical calculations. The difference between the 0 analytic and numerical solutions behaves as O(γ ∈ ) in a wide range of γ less than 0.1.…”

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Waves on an interface between two phase-separated Bose-Einstein condensates

Mazets

2002

Phys. Rev. A

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We examine waves localized near a boundary between two weakly segregated Bose-Einstein condensates. In the case of a wavelength of order of or larger than the thickness of the overlap region the variational method is used. The dispersion laws for the two oscillation branches are found in analytic form. The opposite case of a wavelength much shorter than the healing length in the bulk condensate is also discussed.PACS numbers: 03.75. Fi, 05.30.Jp, The studies of mixtures of two superfluid Bose liquids ascend to the early work by Khalatnikov [1] who determined the possible sound modes in such a system within a macroscopic (hydrodynamical) approach. Later a microscopic theory was developed: Bassichis [2] considered a neutral mixture of two charged Bose gases with Coulomb interactions, and Nepomnyashchii [3] considered a system composed of bosons of two kinds interacting via shortrange potentials. In Ref.[3], most closely related to the case of a two-component degenerate dilute atomic vapor, the two-branch spectrum of elementary excitations and following from it criterion for stability of the ground state were found.The advances in experiments on Bose-Einstein condensation of trapped alkali atoms gave rise to an interest to this subject. The ground state configuration of a two-component atomic Bose-Einstein condensate (BEC) in the presence of a harmonic confining potential at zero temperature was calculated by Ho and Shenoy [4] in the Thomas-Fermi limit. The collective oscillation frequencies for trapped binary BECs were also determined [5][6][7]. Interesting numerical results are obtained by Pu and Bigelow [8]. These studies reveal that if the number of trapped atoms of each kind is large enough, the ground state physics can be qualitatively understood from the arguments valid for a case of absence of a trap [3]. In the latter case, the ground state properties are determined by a certain relation between the coupling constants. Namely, if the intercomponent repulsion (we do not consider attractive potentials in the present paper) is small enough, i.e., if g 12 < √ g 11 g 22 , where g ij = 2πh[m i m j /(m i + m j )] −1 a ij , a ij is the corresponding s-wave scattering length of a pair of ultracold atoms when one of them is of the jth kind and another is of the ith kind, m j is the mass of an atom for the jth component of the mixed BEC, i j = 1, 2, then the two degenerate Bose gases are miscible, i.e. they co-exist in all the volume. In the opposite case, g 12 > √ g 11 g 22 , the two components are immiscible and separated in space. In the latter case, a new physics related to the intercomponent boundary arises. The steady-state energetics of such an interface was estimated by Timmermans [9]. Ao and Chui [10] performed more detailed analysis, in particular, they found that there are two different regimes called, correspondingly, weakly and strongly segregated phase. The former one takes place if g 12 exceeds √ g 11 g 22 only slightly. In such a case the component interpenetration depth is quite large and proportiona...

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Experimental Studies Of Bose-Einstein Condensates In Sodium

Ketterle

Bose-Einstein Condensates and Atom Lasers

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Surface of a Bose-Einstein condensed atomic cloud

Cited by 46 publications

References 8 publications

Vortex lattice formation in a rotating Bose-Einstein condensate

Vortex lattice formation in a rotating Bose-Einstein condensate

Waves on an interface between two phase-separated Bose-Einstein condensates

Experimental Studies Of Bose-Einstein Condensates In Sodium

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