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arXiv:cond-mat/9610093 · Physical Review A

Excitation spectroscopy of vortex states in dilute Bose-Einstein condensed gases

R. J. Dodd, Keith R. Burnett, Mark Edwards, Charles W. Clark

Published Jul 1, 1997• 124 citations
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Abstract

We apply linear-response analysis to the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate in a vortex state, and apply it to a system of rubidium atoms confined in a time-averaged orbiting potential trap. The excitation frequencies of a vortex differ significantly from those of the ground state, and may therefore be used to obtain a spectroscopic signature of the presence of a vortex state.

DOI
10.1103/physreva.56.587

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We apply linear-response analysis to the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate in a vortex state, and apply it to a system of rubidium atoms confined in a time-averaged orbiting potential trap. The excitation frequencies of a vortex differ significantly from those of the ground state, and may therefore be used to obtain a spectroscopic signature of the presence of a vortex state.
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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.
The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmonic potential under forced rotation. By solving the non-linear Bogoliubov equations coupled with the Gross-Pitavskii equation, the elementary excitations and the total energy of the systems are calculated as a function of rotation velocity. There are two distinct criteria of vortex stability; The position of the excitation energy levels relative to the condensate energy level yields the local stability criterion, and the total energy relative to that of the non-vortex state yields the global stability criterion. The vortex stability phase diagram in the rotation velocity vs the particle density of the system is obtained, allowing one to locate the appropriate region to observe the singly quantized vortex.
In this work we compare the results of the Gross-Pitaevskii and modified Gross-Pitaevskii equations with ab initio variational Monte Carlo calculations for Bose-Einstein condensates of atoms in axially symmetric traps. We examine both the ground state and excited states having a vortex line along the zzz axis at high values of the gas parameter and demonstrate an excellent agreement between the modified Gross-Pitaevskii and ab initio Monte Carlo methods, both for the ground and vortex states.
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.