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arXiv:0711.0653 · Physical Review Letters

Destroying Superfluidity by Rotating a Fermi Gas at Unitarity

I. Bausmerth, Alessio Recati, S. Stringari

Published Feb 19, 2008• 21 citations
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Abstract

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity n(N)/n(S)=0.85, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.

DOI
10.1103/physrevlett.100.070401

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We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity n(N)/n(S)=0.85, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.
We discuss the effect of an adiabatic rotation on the phase separation between the superfluid and normal component of a trapped polarized Fermi gas at unitarity and zero temperature, under the assumption that quantized vortices are not formed. We show that the Chandrasekhar-Clogston limit ${n}_{\ensuremath{\downarrow}}∕{n}_{\ensuremath{\uparrow}}$ characterizing the local polarization in the normal phase at the interface is enhanced by the rotation as a consequence of the centrifugal effect. The density profiles (local and column integral) of the two spin species are calculated as a function of the angular velocity for different values of the polarization. The critical value of the angular velocity at which the superfluid exhibits a spontaneous quadrupole deformation is also calculated for the unpolarized case.
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.
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.
The dynamic behavior of a Fermi gas confined in a deformed trap rotating at low angular velocity is investigated in the framework of hydrodynamic theory. The differences exhibited by a normal gas in the collisional regime and a superfluid are discussed. Special emphasis is given to the collective oscillations excited when the deformation of the rotating trap is suddenly removed or when the rotation is suddenly stopped. The presence of vorticity in the normal phase is shown to give rise to precession and beating phenomena which are absent in the superfluid phase.
We study the hydrodynamic expansion of a rotating strongly interacting Fermi gas by releasing a cigar-shaped cloud with a known angular momentum from an optical trap. As the aspect ratio of the expanding cloud approaches unity, the angular velocity increases, indicating quenching of the moment of inertia I to as low as 0.05 of the rigid body value I(rig). Remarkably, we observe this behavior in both the superfluid and collisional normal fluid regimes, which obey nearly identical zero-viscosity irrotational hydrodynamics. We attribute irrotational flow in the normal fluid to a decay of the rotational part of the stream velocity during expansion, which occurs when the shear viscosity is negligible. Using conservation of angular momentum, we directly observe a fundamental result of irrotational hydrodynamics, I/I(rig) = delta2, where delta is the deformation parameter of the cloud.
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.