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arXiv:cond-mat/0404039 · Physical Review Letters

Universal Vortex Formation in Rotating Traps with Bosons and Fermions

M. Toreblad, Magnus O. Borgh, M. Koskinen, M. Manninen, S. M. Reimann

Published Aug 26, 2004• 41 citations
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Abstract

We show that the rotation of trapped quantum mechanical particles with a repulsive interaction can lead to vortex formation, irrespective of whether the particles are bosons or (unpaired) fermions. The exact many-particle wave function constitutes similar structures in both cases, implying that this vortex formation is indeed universal.
DOI
10.1103/physrevlett.93.090407

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A two-component Fermi gas with attractive sss-wave interactions forms a superfluid at low temperatures. When this gas is confined in a rotating trap, fermions can unpair at the edges of the gas and vortices can arise beyond certain critical rotation frequencies. We compute these critical rotation frequencies and construct the phase diagram in the plane of scattering length and rotation frequency for different total numbers of particles. We work at zero temperature and consider a cylindrically symmetric harmonic trapping potential. The calculations are performed in the Hartree-Fock-Bogoliubov approximation which implies that our results are quantitatively reliable for weak interactions.
The main theme of this review is the many-body physics of vortices in quantum droplets of bosons or fermions in the limit of small particle numbers. Systems of interest include cold atoms in traps as well as electrons confined in quantum dots. When set to rotate, these in principle different quantum systems show remarkable analogies. The topics reviewed include the structure of the finite rotating many-body state, universality of vortex formation and localization of vortices in both bosonic and fermionic systems, and the emergence of particle-vortex composites in the quantum Hall regime. An overview of the computational many-body techniques sets focus on the configuration-interaction and density-functional methods. Studies of quantum droplets with one or several particle components, where vortices as well as coreless vortices may occur, are reviewed, and theoretical as well as experimental challenges are discussed.
Vortices can form when finite quantal systems are set to rotate. In the limit of small particle numbers the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. We show that for a larger number of fermions, N≳15N\gtrsim15N≳15, the fermion vortices compete and co-exist with (Chamon-Wen) edge-reconstructed ground states, forcing some ground states, for instance the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could for instance be a semiconductor heterostructure, a quantum dot, and the corresponding boson system a magneto optical trap (MOT).