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arXiv:cond-mat/0607569 · Physical Review Letters

Nonuniform Mixed-Parity Superfluid State in Fermi Gases

Kirill V. Samokhin, M. S. Mar’enko

Published Nov 9, 2006• 23 citations
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Abstract

We study the effects of dipole interaction on the superfluidity in a homogeneous Fermi gas with population imbalance. We show that the Larkin-Ovchinnikov-Fulde-Ferrell phase is replaced by another nonuniform superfluid phase, in which the order parameter has a nonzero triplet component induced by the dipole interaction.
DOI
10.1103/physrevlett.97.197003

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Abstract Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent opportunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of great interest in condensed matter physics. However, the FFLO states have not been observed experimentally in Fermi gases in three dimensions (3D), possibly due to their small phase space volume and extremely low temperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainly in a 6Li–40K mixture, on the one-plane-wave FFLO phases for a 3D homogeneous case at the mean-field level. We present various phase diagrams related to the FFLO states at both zero and finite temperatures, throughout the BCS-BEC crossover, and show that a large mass ratio may enhance substantially FFLO type of pairing.
The possibility of a Fulde-Ferrell-Larkin-Ovchinnikov-like (FFLO-like) state in a population-imbalanced Fermi gas with a vortex is proposed. Employing the Bogoliubov-de Gennes formalism, we determine self-consistently the superfluid order parameter and the particle number density in the presence of a vortex. We find that, upon increasing the population imbalance, the superfluid order parameter spatially oscillates around the vortex core in the radial direction, indicating that the FFLO-like state becomes stable. We find that the radial FFLO-like states cover a wide region of the phase diagram in the weak-coupling regime at T=0T=0T=0, in contrast with the conventional case without a vortex. We show that this inhomogeneous superfluidity can be detected as peak structures of the local polarization rate associated with the node structure of the superfluid order parameter. Since the vortex in the three-dimensional Fermi gas with population imbalance has been already realized in experiments, our proposal is a promising candidate of a FFLO-like state in cold atom physics.
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 $\mathrm{\ensuremath{\Delta}}$.
In ultracold Fermi gases, the effect of spin imbalance on superfluidity has been the subject of intense study. One of the reasons for this is that spin imbalance frustrates the Bardeen-Cooper-Schrieffer (BCS) superfluid pairing mechanism, in which fermions in different spin states combine into Cooper pairs with zero momentum. In 1964, it was proposed that an exotic superfluid state called the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the Cooper pairs have nonzero momentum, could exist in a spin-imbalanced Fermi gas. At the saddle-point (mean-field) level, it has been shown that the FFLO state only occupies a very small sliver in the ground-state phase diagram of a three-dimensional (3D) Fermi gas. However, a question that remains to be investigated is as follows: What is the influence of phase fluctuations on the FFLO state? In this work, we show that phase fluctuations only lead to relatively small quantitative corrections to the presence of the FFLO state in the saddle-point phase diagram of a 3D spin-imbalanced Fermi gas. Starting from the partition function of the system, we calculate the effective action within the path-integral adiabatic approximation. The action is then expanded up to second order in the fluctuation field around the saddle point, leading to the fluctuation free energy. Using this free energy, we calculate corrections due to phase fluctuations to the BCS-FFLO transition in the saddle-point phase diagram. At temperatures at which the FFLO state exists, we find only small corrections to the size of the FFLO area. Our results suggest that fluctuations of the phase of the FFLO order parameter, which can be interpreted as an oscillation of its momentum vector, do not cause an instability of the FFLO state with respect to the BCS state.