Oscillations of rotating trapped Bose-Einstein condensates

Abstract

The tensor-virial method is applied for a study of oscillation modes of uniformly rotating Bose-Einstein condensed gases, whose rigid body rotation is supported by an vortex array. The second order virial equations are derived in the hydrodynamic regime for an arbitrary external harmonic trapping potential assuming that the condensate is a superfluid at zero temperature. The axisymmetric equilibrium shape of the condensate is determined as a function of the deformation of the trap; its domain of stability is bounded by the constraint $\Omega <1$ on the rotation rate (measured in units of the trap frequency ${\omega }_0$.) The oscillations of the axisymmetric condensate are stable with respect to the transverse-shear, toroidal and quasi-radial modes of oscillations, corresponding to the $l=2$, $|m|=0,1,2$ surface deformations. In non-axisymmetric traps, the equilibrium constrains the (dimensionless) deformation in the plane orthogonal to the rotation to the domain $A_2>{\Omega }^2$ with $\Omega <1$. The second harmonic oscillation modes in non-axisymmetric traps separate into two classes which have even or odd parity with respect to the direction of the rotation axis. Numerical solutions show that these modes are stable in the parameter domain where equilibrium figures exist.

16 pages, including 4 figures, uses Revtex; v2 includes a treatment of modes in unisotropic traps; PRA in press

References in corpus (7)

• Vortex formation in a stirred Bose-Einstein condensate
• Vortices in a Bose-Einstein Condensate
• Bose Condensates with 1/r Interatomic Attraction: Electromagnetically Induced ``Gravity''
• Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas
• Vortex stability of interacting Bose-Einstein condensates confined in anisotropic harmonic traps
• The Yrast Spectra of Weakly Interacting Bose-Einstein Condensates
• Perturbations of self-gravitating, ellipsoidal superfluid-normal fluid mixtures

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• Ground and Low-Lying Collective States of Rotating Three-Boson System
• The axial breathing mode in rapidly rotating Bose-Einstein condensates and uncertainty of the rotation velocity
• Spontaneous symmetry breaking in rotating condensates of ultracold atoms
• Oscillations of Bose-Einstein condensates with vortex lattices. II. Finite temperatures
• Scan calculation of the density of states: real space cluster perturbation theory applied to inhomogeneous Hubbard model in one dimension
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