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Physical Review A

Location of the vortex phase in the phase diagram of a rotating two-component Fermi gas

Harmen J. Warringa

Published Oct 15, 2012• 8 citations
Publisher

Abstract

We determine the conditions under which superfluidity with and without quantized vortices appears in a weakly interacting two-component atomic Fermi gas that is trapped in a rotating cylindrical symmetric harmonic potential. We compute the phase diagram as a function of rotation frequency, scattering length, temperature, total number of trapped atoms, and population imbalance. Our analysis is based on solving the Bogoliubov--de Gennes equation.

DOI
10.1103/physreva.86.043615

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We determine the conditions under which superfluidity with and without quantized vortices appears in a weakly interacting two-component atomic Fermi gas that is trapped in a rotating cylindrical symmetric harmonic potential. We compute the phase diagram as a function of rotation frequency, scattering length, temperature, total number of trapped atoms, and population imbalance. Our analysis is based on solving the Bogoliubov--de Gennes equation.
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.
We consider quantized vortices in two-component Bose-Einstein condensates and three-component Fermi gases with attractive interactions. In these systems, the vortex core can be either empty (normal in the fermion case) or filled with another superfluid. We determine critical values of the parameters---chemical potentials, scattering lengths, and, for Fermi gases, temperature---at which the transition between the two types of vortices occurs. Population imbalance can lead to superfluid core (coreless) vorticity in multicomponent superfluids which otherwise support only usual vortices. For multicomponent Fermi gases, we construct the phase diagram, including regions of coreless vorticity. We extend our results to trapped bosons and fermions using an appropriate local approximation, which goes beyond the usual Thomas-Fermi approximation for trapped bosons.
The behavior of a dilute two-component neutral superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.
We use the Bogoliubov--de Gennes formalism to analyze the effects of rotation on the ground-state phases of harmonically trapped Fermi gases, under the assumption that quantized vortices are not excited. We find that the rotation breaks Cooper pairs that are located near the trap edge, and that this leads to a phase separation between the nonrotating superfluid (fully paired) atoms located around the trap center and the rigidly rotating normal (nonpaired) atoms located toward the trap edge, with a coexistence (partially paired) region in between. Furthermore, we show that the superfluid phase that occurs in the coexistence region is characterized by a gapless excitation spectrum, and that it is distinct from the gapped phase that occurs near the trap center.
We report the equilibrium vortex phase diagram of a rotating two-band Fermi gas confined to a cylindrically symmetric parabolic trapping potential, using the recently developed finite-temperature effective field theory (Klimin et al 2016 Phys. Rev. A 94 023620). A non-monotonic resonant dependence of the free energy as a function of the temperature and the rotation frequency is revealed for a two-band superfluid. We particularly focus on novel features that appear as a result of interband interactions and can be experimentally resolved. The resonant dependence of the free energy is directly manifested in vortex phase diagrams, where areas of stability for both integer and fractional vortex states are found. The study embraces the BCS–BEC crossover regime and the entire temperature range below the critical temperature T c . Significantly different behavior of vortex matter as a function of the interband coupling is revealed in the BCS and BEC regimes.