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arXiv:cond-mat/0108195 · Physical Review Letters

Formation and Decay of Vortex Lattices in Bose-Einstein Condensates at Finite Temperatures

J. R. Abo-Shaeer, Chandra Raman, Wolfgang Ketterle

Published Feb 1, 2002• 155 citations
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Abstract

The dynamics of vortex lattices in stirred Bose-Einstein condensates have been studied at finite temperatures. The decay of the vortex lattice was observed nondestructively by monitoring the centrifugal distortions of the rotating condensate. The formation of the vortex lattice could be deduced from the increasing contrast of the vortex cores observed in ballistic expansion. In contrast to the decay, the formation of the vortex lattice is insensitive to temperature change.

DOI
10.1103/physrevlett.88.070409

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The dynamics of vortex lattices in stirred Bose-Einstein condensates have been studied at finite temperatures. The decay of the vortex lattice was observed nondestructively by monitoring the centrifugal distortions of the rotating condensate. The formation of the vortex lattice could be deduced from the increasing contrast of the vortex cores observed in ballistic expansion. In contrast to the decay, the formation of the vortex lattice is insensitive to temperature change.
We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. The vortex cores were observed using time-of-flight absorption imaging. Depending on the stirrer size, either discrete resonances or a broad response was visible as the stir frequency was varied. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices.
We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex-lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex-lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.
We show that the formation of a vortex lattice in a weakly interacting Bose condensed gas can be modeled with the nonlinear Schrödinger equation for both T=0 and finite temperatures without the need for an explicit damping term. Applying a weak rotating anisotropic harmonic potential, we find numerically that the turbulent dynamics of the field produces an effective dissipation of the vortex motion and leads to the formation of a lattice. For T=0, this turbulent dynamics is triggered by a rotational dynamic instability of the condensate. For finite temperatures, noise is present at the start of the simulation and allows the formation of a vortex lattice at a lower rotation frequency, the Landau frequency. These two regimes have different vortex dynamics. We show that the multimode interpretation of the classical field is essential.
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Quantized vortices play a key role in superfluidity and superconductivity. We have observed the formation of highly ordered vortex lattices in a rotating Bose-condensed gas. These triangular lattices contained over 100 vortices with lifetimes of several seconds. Individual vortices persisted up to 40 seconds. The lattices could be generated over a wide range of rotation frequencies and trap geometries, shedding light on the formation process. Our observation of dislocations, irregular structure, and dynamics indicates that gaseous Bose-Einstein condensates may be a model system for the study of vortex matter.