Vortices in a trapped dilute Bose-Einstein condensate

We review the theory of vortices in trapped dilute Bose-Einstein condensate s 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 av ailable experimental results. We discuss various properties of a single vor tex, including its structure, energy, dynamics, normal modes, and stability , as well as vortex arrays. When the nonuniform condensate contains a vorte x, the excitation spectrum includes unstable ('anomalous') mode(s) with neg ative frequency. Trap rotation shifts the normal-mode frequencies and can s tabilize the vortex. We consider the effect of thermal quasiparticles on vo rtex normal modes as well as possible mechanisms for vortex dissipation. Vo rtex states in mixtures and spinor condensates are also discussed.