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arXiv:0804.0355 · Physical Review A

Pair breaking in rotating Fermi gases

Mi­chael Urban, Peter Schuck

Published Jul 9, 2008• 29 citations
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Abstract

We study the pair-breaking effect of rotation on a cold Fermi gas in the BCS-BEC crossover region. In the framework of BCS theory, which is supposed to be qualitatively correct at zero temperature, we find that in a trap rotating around a symmetry axis, three regions have to be distinguished: (A) a region near the rotational axis where the superfluid stays at rest and where no pairs are broken, (B) a region where the pairs are progressively broken with increasing distance from the rotational axis, resulting in an increasing rotational current, and (C) a normal-fluid region where all pairs are broken and which rotates like a rigid body. Due to region B, density and current do not exhibit any discontinuities.

DOI
10.1103/physreva.78.011601

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We study the pair-breaking effect of rotation on a cold Fermi gas in the BCS-BEC crossover region. In the framework of BCS theory, which is supposed to be qualitatively correct at zero temperature, we find that in a trap rotating around a symmetry axis, three regions have to be distinguished: (A) a region near the rotational axis where the superfluid stays at rest and where no pairs are broken, (B) a region where the pairs are progressively broken with increasing distance from the rotational axis, resulting in an increasing rotational current, and (C) a normal-fluid region where all pairs are broken and which rotates like a rigid body. Due to region B, density and current do not exhibit any discontinuities.
We investigate the dynamical properties of a superfluid gas of trapped fermionic atoms in the BCS phase. As a simple example we consider the reaction of the gas to a slow rotation of the trap. It is shown that the currents generated by the rotation can be understood within a two-fluid model similar to the one used in the theory of superconductors, but with a position-dependent ratio of normal and superfluid densities. The rather general result of this paper is that already at very low temperatures, far below the critical one, an important normal-fluid component appears in the outer regions of the gas. This renders the experimental observation of superfluidity effects more difficult and indicates that reliable theoretical predictions concerning other dynamical properties, like the frequencies of collective modes, can only be made by taking into account temperature effects.
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 analyze the interplay of adiabatic rotation and Rashba spin-orbit coupling on the BCS-BEC evolution of a harmonically trapped Fermi gas in two dimensions under the assumption that vortices are not excited. First, by taking the trapping potential into account via both the semiclassical and exact quantum-mechanical approaches, we firmly establish the parameter regime where the noninteracting gas forms a ring-shaped annulus. Then, by taking the interactions into account via the BCS mean-field approximation, we study the pair-breaking mechanism that is induced by rotation, i.e., the Coriolis effects. In particular, we show that the interplay allows for the possibility of creating either an isolated annulus of rigidly rotating normal particles that is disconnected from the central core of nonrotating superfluid pairs or an intermediate mediator phase where the superfluid pairs and normal particles coexist as a partially rotating gapless superfluid.
In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature μ-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation, to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.
We study the finite temperature TTT behavior of trapped Fermi gases as they undergo BCS--Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $T\ensuremath{\ne}0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the ``pseudogap phase.''
The pair correlation function of an expanding gas is investigated with an emphasis on the BEC-BCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin up-down channel which, at short distances, is larger than that exhibited by thermal bosons in the Hanbury-Brown-Twiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, in contrast with the behavior of the density. The isotropy of the pair correlation function is an experimentally accessible signature, which makes a clear distinction with respect to the case of noninteracting gases and can be understood as a consequence of the violation of scaling.