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arXiv:0904.4034 · Physical Review A

Rotating Larkin-Ovchinnikov-Fulde-Ferrell state of the two-dimensional ultracold Fermi superfluid gas: Reentrant behavior of the critical angular velocity

Miodrag L. Kulić, Armen Sedrakian, Dirk H. Rischke

Published Oct 15, 2009• 6 citations
arXivHTMLPDF

Abstract

A rotating ultracold $S$-wave superfluid Fermi gas is studied when the mismatch in chemical potentials $\ensuremath{\delta}\ensuremath{\mu}$ (and the population imbalance $\ensuremath{\delta}n$) corresponds to the Larkin-Ovchinnikov-Fulde-Ferrell state in the vicinity of the Lifshitz critical point. It is shown that under these conditions the critical angular velocity ${\ensuremath{\Omega}}_{c2}$ in two-dimensional systems is an oscillating function of temperature and $\ensuremath{\delta}n$ giving rise to reentrant superfluid phases. The reason for this behavior is the population by Cooper pairs of the Landau levels $(n\ensuremath{\ge}1)$ above the lowest one $(n=0)$.

DOI
10.1103/physreva.80.043610

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A rotating ultracold SSS-wave superfluid Fermi gas is studied when the mismatch in chemical potentials \ensuremathδ\ensuremathμ\ensuremath{\delta}\ensuremath{\mu}\ensuremathδ\ensuremathμ (and the population imbalance \ensuremathδn\ensuremath{\delta}n\ensuremathδn) corresponds to the Larkin-Ovchinnikov-Fulde-Ferrell state in the vicinity of the Lifshitz critical point. It is shown that under these conditions the critical angular velocity \ensuremathΩc2{\ensuremath{\Omega}}_{c2}\ensuremathΩc2​ in two-dimensional systems is an oscillating function of temperature and \ensuremathδn\ensuremath{\delta}n\ensuremathδn giving rise to reentrant superfluid phases. The reason for this behavior is the population by Cooper pairs of the Landau levels (n\ensuremath≥1)(n\ensuremath{\ge}1)(n\ensuremath≥1) above the lowest one (n=0)(n=0)(n=0).
The ground-state phase diagram of attractively interacting Fermi gases in two dimensions with a population imbalance is investigated. We find the regime of stability for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, in which pairing occurs at a finite wave vector, and determine the magnitude of the pairing amplitude $\mathrm{\ensuremath{\Delta}}$ and FFLO wave vector qqq in the ordered phase, finding that $\mathrm{\ensuremath{\Delta}}$ can be of the order of the two-body binding energy. Our results rely on a careful analysis of the zero-temperature gap equation for the FFLO state, which possesses nonanalyticities as a function of $\mathrm{\ensuremath{\Delta}}$ and qqq, invalidating a Ginzburg-Landau expansion in small $\mathrm{\ensuremath{\Delta}}$.
We have studied the distinctive features of the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) instability and phase transitions in two-dimensional (2D) mesoscopic superconductors placed in magnetic field of arbitrary orientation and rotating superfluid Fermi gases with imbalanced state populations. Using a generalized version of the phenomenological Ginzburg-Landau theory we have shown that the FFLO states are strongly modified by the effect of the trapping potential confining the condensate. The phenomenon of the inhomogeneous state formation is determined by the interplay of three length scales: (i) length scale of the FFLO instability; (ii) 2D system size; (iii) length scale associated with the orbital effect caused either by the Fermi condensate rotation or magnetic field component applied perpendicular to the superconducting disk. We have studied this interplay and resulting quantum oscillation effects in both superconducting and superfluid finite-size systems with FFLO instability and described the hallmarks of the FFLO phenomenon in a restricted geometry. The finite size of the system is shown to affect strongly the conditions of the observability of switching between the states with different vorticities.
We study superconducting properties of population-imbalanced ultracold Fermi mixtures in the honeycomb lattice that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain ground-state phase diagrams including the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by atypical behavior of the Cooper-pair total momentum. We show that the momentum changes its value as well as direction with a change of the system parameters. We discuss the influence of Van Hove singularities on the possibility of the reentrant FFLO phase occurrence, without a BCS precursor.
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.
We study an effect of rotation on the two component Fermi superfluid gases with population imbalance in a toroidal trap. We investigate how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is changed by the rotation using the Bogoliubov-de Gennes equation in the quasi-one-dimensional regime. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in T -Φ plane. We show the order parameter of these states.
We investigate, in three spatial dimensions, the transition from the normal state to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phases. We make use of a Fourier expansion for the order parameter and the Green's functions to handle the quasiclassical equations in the vicinity of the transition. We show that, below the tricritical point, the transition is always first order. We find that, at the transition, the higher Fourier components in the order parameter are always essentially negligible. Below the tricritical point we have the already known result that the order parameter has a spatial dependence which is essentially cos(q∙r)\mathrm{cos}(\mathbf{q}∙\mathbf{r})cos(q∙r). However, when the temperature is lowered the order parameter switches to a sum of two cosines, with equal weights and wave vectors with the same length, but orthogonal directions. Finally, by further lowering the temperature, and down to T=0T=0T=0, one finds another transition toward an order parameter that is the sum of three cosines with, again, equal weights and orthogonal directions. Hence the structure of the order parameter gets more complex as the temperature is lowered. On the other hand, the resulting critical temperatures are found to be only slightly higher than the ones corresponding to the standard second-order FFLO transition. We apply our results to the specific case of ultracold Fermi gases and show that the differences in atomic populations of the two hyperfine states involved in the BCS condensation display sizeable variations when one goes from the normal state to the superfluid FFLO phases, or from one FFLO phase to another. Experimentally this should allow us to clearly identify the various phase transitions.