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arXiv:cond-mat/9609013 · Physical Review A

Vortex waves in a cloud of Bose-Einstein-condensed, trapped alkali-metal atoms

Carlo F. Barenghi

Published Dec 1, 1996• 7 citations
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Abstract

We consider the vortex state solution for a rotating cloud of trapped, Bose-Einstein-condensed alkali-metal atoms and study finite-temperature effects. We find that thermally excited vortex waves can distort the vortex state significantly, even at the very low temperatures relevant to the experiments. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.5445

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We consider the vortex state solution for a rotating cloud of trapped, Bose-Einstein-condensed alkali-metal atoms and study finite-temperature effects. We find that thermally excited vortex waves can distort the vortex state significantly, even at the very low temperatures relevant to the experiments. \textcopyright{} 1996 The American Physical Society.
Atom optic techniques are proposed to control the excitation of a Bose-Einstein condensate in an atomic trap. We show that by employing the dipole potential induced by four highly detuned traveling-wave laser beams with appropriate phases and frequencies, one can coherently excite a trapped Bose-Einstein condensate composed of ultracold alkali-metal atoms into a state rotating around the trap center. Pure vortex states can be created with this scheme if the condensate is trapped in an anharmonic trap.
A quantized vortex in Bose-Einstein condensation (BEC) of an alkali-metal atom gas is known to be unstable intrinsically at zero temperature. We examine two stabilization mechanisms of a vortex theoretically. (i) The finite temperature effect is shown to stabilize a vortex. (ii) An additional pinning potential, which may be produced by a focused laser beam at the vortex center, is also shown to stabilize it even at zero temperature. The mean-field calculation for BEC confined by a harmonic potential is employed. The detailed properties of a stable vortex are given, such as the spatial profiles of the condensate and noncondensate, the particle current density around the core, the whole excitation spectrum, and their temperature dependence.
The properties of vortex states in a Bose-Einstein-condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods, we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of atoms containing a vortex is released from a trap. In two dimensions we find the simple result that the time dependence of the cloud radius is given by $(1+{\ensuremath{\omega}}^{2}{t}^{2}{)}^{1/2},$ where $\ensuremath{\omega}$ is the trap frequency. We calculate and compare the expansion of the vortex core and the cloud radius for different numbers of particles and interaction strengths, in both two and three dimensions, and discuss the circumstances under which vortex states may be observed experimentally.
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
We investigate the low-lying excitations of Bose-Einstein condensate of confined alkali-metal atoms, with repulsive interaction. Vortex excitation energy of the condensate containing a large number of atoms is estimated semiclassically. We also investigate the asymptotic form of the low-energy quasiparticle excitation of the condensate in the presence of a vortex, in the large-N limit. The dispersion relation remains the same as that of a condensate without a vortex, except the z component of angular momentum of the modes is shifted by the angular momentum of the vortex. The first-order correction of the energy eigenvalues due to finite-size effects is calculated.
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes, and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (`anomalous') mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.