Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions [Phys. Rev. Lett. 75, 1687 (1995)]

Bradley, C. C.; Sackett, C. A.; Tollett, J. J.; Hulet, R. G.

doi:10.1103/physrevlett.79.1170

Cited by 412 publications

(501 citation statements)

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“…The experimental achievement of Bose-Einstein condensation in confined alkali-atom gases [1][2][3] has stimulated great interest in the generation and observation of vortices in such systems [4][5][6]. Rotating a totally anisotropic harmonic trap at an angular frequency Ω can, in principle, generate vortices; they are energetically stable for Ω > Ω c [7][8][9][10].…”

Section: Abstract: Bose Condensate; Vortices; Nonaxisymmetric Trapmentioning

confidence: 99%

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Vortex state structure of a Bose condensate in an asymmetric trap

Svidzinsky

Fetter

2000

Physica B: Condensed Matter

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Based on an analytic solution of the Gross-Pitaevskii equation in the large-condensate (Thomas-Fermi) limit we determine the structure of a stationary vortex in a Bose-Einstein condensate in a nonaxisymmetric rotating trap. The condensate velocity field has cylindrical symmetry only near the vortex core and becomes intrinsically anisotropic near the condensate boundaries. Rotating the anisotropic trap induces an additional irrotational velocity field even for a vortex-free condensate. Keywords: Bose condensate; vortices; nonaxisymmetric trapThe experimental achievement of Bose-Einstein condensation in confined alkali-atom gases [1][2][3] has stimulated great interest in the generation and observation of vortices in such systems [4][5][6]. Rotating a totally anisotropic harmonic trap at an angular frequency Ω can, in principle, generate vortices; they are energetically stable for Ω > Ω c [7][8][9][10].This work determines the condensate velocity field for a stationary vortex when the completely anisotropic harmonic trap potential V tr = 1 2 M (ω 2 x x 2 + ω 2 y y 2 + ω 2 z z 2 ) rotates about a principal axis. We consider a zero-temperature condensate in the Thomas-Fermi (TF) limit, when the vortex core radius ξ ∼ d 2 /R is small compared to the mean oscillator length d and the mean dimension R of the condensate [here,author. E-mail: asvid@leland.Stanford.EDU with d i = h/M ω i and trap frequencies ω i (i = x, y, z)].We assume that the trap rotates with an angular velocity Ω around the z axis. At zero temperature in the rotating frame, the equilibrium condensate wave function Ψ satisfies the Gross-Pitaevskii equation: (1) where g = 4πh 2 a/M > 0 is the effective interparticle interaction strength, µ is the chemical potential in the rotating frame, and φ is the azimuthal angle in cylindrical polar coordinates (r, φ, z). Consider a q-fold vortex, oriented along the z axis, with a condensate wave function Ψ = |Ψ|e iS . Its phase must have the form S = qφ + S 1 , where S 1 is an odd 2π-periodic function of φ.Multiplying the imaginary part of (1) by |Ψ| yields the equation of current continuity in the rotating frame:

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Section: Abstract: Bose Condensate; Vortices; Nonaxisymmetric Trapmentioning

confidence: 99%

“…Further, let us consider distances x, y, z ≪ R x , R y, R z , where R i are the TF dimensions of the condensate (M ω 2 i R 2 i = 2µ, i = x, y, z). At these intermediate distances we can omit terms of higher order in the parameter (x i /R i ) 2 . As a result, we find the following inhomogeneous equation:…”

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confidence: 99%

Vortex state structure of a Bose condensate in an asymmetric trap

Svidzinsky

Fetter

2000

Physica B: Condensed Matter

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“…In 1995, BEC was spectacularly observed in dilute gases of alkali atoms confined in traps [10][11][12] . In these dilute gases, essentially 100 % of the gas can condense into a single particle state.…”

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Bose-Einstein condensation in liquidHe4under pressure

et al. 2011

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“…Equivalently, a peak in the structure factor will appear at such a wavevector. The smallness of the roton gap or the largeness of the structure factor peak are experimental signatures of the proximity to the Mott transition.In the present work we focus attention in the possible existence or nonexistence of roton excitations in artificially engineered Bose Einstein Condensates (BECs) [1,2,3]. BECs are superfluid as they posses a finite sound speed [4,5,6] and reduced long wavelength scattering [7,8].…”

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On the Existence of Roton Excitations in Bose?Einstein Condensates: Signature of Proximity to a Mott Insulating Phase

Nazario

Santiago

2004

Journal of Low Temperature Physics

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Within the last decade, artificially engineered Bose Einstein Condensation has been achieved in atomic systems. Bose Einstein Condensates are superfluids just like bosonic Helium is and all interacting bosonic fluids are expected to be at low enough temperatures. One difference between the two systems is that superfluid Helium exhibits roton excitations while Bose Einstein Condensates have never been observed to have such excitations. The reason for the roton minimum in Helium is its proximity to a solid phase. The roton minimum is a consequence of enhanced density fluctuations at the reciprocal lattice vector of the stillborn solid. Bose Einstein Condensates in atomic traps are not near a solid phase and therefore do not exhibit roton minimum. We conclude that if Bose Einstein Condensates in an optical lattice are tuned near a transition to a Mott insulating phase, a roton minimum will develop at a reciprocal lattice vector of the lattice. Equivalently, a peak in the structure factor will appear at such a wavevector. The smallness of the roton gap or the largeness of the structure factor peak are experimental signatures of the proximity to the Mott transition.In the present work we focus attention in the possible existence or nonexistence of roton excitations in artificially engineered Bose Einstein Condensates (BECs) [1,2,3]. BECs are superfluid as they posses a finite sound speed [4,5,6] and reduced long wavelength scattering [7,8]. The other important bosonic superfluid is He 4 [5,9]. Since BECs and He 4 are the same universal phase of matter, they share a large commonality. For example, they are both superfluids whose elementary long wavelength excitation spectrum is phononic, their ground states spontaneously break gauge invariance [10], that is their ground states exhibit macroscopic quantum coherence, and they both posses vortex excitations [11]. This is an example of universality of stable fixed points of matter. In these cases the superfluid ground state is such a fixed point. The similarities will become ever more apparent as the low energy properties BECs are studied more carefully.On the other hand, at shorter wavelengths Helium possesses a roton minimum [5,6,12] in its excitation spectrum leading to low energy excitations occurring at a specific wavevector, which are gapped and are different than long wavelength sound. These excitations can make important contributions to the dynamics and thermodynamics of the system. In BECs no such excitation has been observed and the lack of a peak in the structure factor [7] leads to the conclusion that they do not posses roton excitations. We review some of the properties of rotons in Helium and determine under what conditions will they occur in BECs.All quantum many particle systems are described by a Hamiltonian[5]where m v · ρ v/2 is the kinetic energy operator, U [ρ] is the potential energy operator, which in general can be a functional of the density operator. The density operator in first quantized notation iswith r i being the position of the ith partic...

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Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions [Phys. Rev. Lett. 75, 1687 (1995)]

Cited by 412 publications

References 2 publications

Vortex state structure of a Bose condensate in an asymmetric trap

Vortex state structure of a Bose condensate in an asymmetric trap

Bose-Einstein condensation in liquidHe4under pressure

On the Existence of Roton Excitations in Bose?Einstein Condensates: Signature of Proximity to a Mott Insulating Phase

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