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Physica C Superconductivity

Multiply quantized vortices and finite temperature effects in the BEC/BCS crossover regime

Jacques Tempere, Jozef T. Devreese

Published Jan 27, 2006• 2 citations
Publisher
DOI
10.1016/j.physc.2005.12.019

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The structures of multiply quantized vortices (MQVs) of an equal-population atomic Fermi superfluid in a rotating spherical bubble trap approximated as a thin shell are analyzed by solving the Bogoliubov--de Gennes (BdG) equation throughout the Bardeen-Cooper-Schrieffer (BCS)--Bose-Einstein condensation (BEC) crossover. Consistent with the Poincar\'e-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of a normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on a topological correspondence is provided.
We compute the orbital angular momentum L_{z} of an s-wave paired superfluid in the presence of an axisymmetric multiply quantized vortex. For vortices with a winding number |k|>1, we find that in the weak-pairing BCS regime, L_{z} is significantly reduced from its value ℏNk/2 in the Bose-Einstein condensation (BEC) regime, where N is the total number of fermions. This deviation results from the presence of unpaired fermions in the BCS ground state, which arise as a consequence of spectral flow along the vortex subgap states. We support our results analytically and numerically by solving the Bogoliubov-de Gennes equations within the weak-pairing BCS regime.
The splitting instability of a doubly quantized vortex in the BEC-BCS crossover of a superfluid Fermi gas is investigated by means of a low-energy effective field theory. Our linear stability analysis and nonequilibrium numerical simulations reveal that the character of the instability drastically changes across the crossover. In the BEC limit, the splitting of the vortex into two singly quantized vortices occurs through the emission of phonons, while such an emission is completely absent in the BCS limit. In the crossover regime, the instability and phonon emission are enhanced and the lifetime of a doubly quantized vortex becomes minimal. The emitted phonon can be observed as a spiraling pattern amplified due to the rotational superradiance, known as a mechanism to carry away energy and angular momentum from a spinning black hole. We also investigate the influence of temperature, population imbalance, and three-dimensional effects.