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arXiv:cond-mat/0611740 · Physical Review A

Josephson effect in an atomic Fulde-Ferrell-Larkin-Ovchinnikov superfluid

Hui Hu, Xia-Ji Liu

Published Jan 31, 2011• 9 citations
arXivHTMLPDF

Abstract

We study theoretically two spatially separate quasi-one-dimensional atomic Fermi gases in a double-well trap. By tuning independently their spin polarizations, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid or a Bardeen-Cooper-Schrieffer (BCS) superfluid may be formed in each well. We seek the possibility of creating a spatially tunable atomic Josephson junction between two superfluids, which is supposed to be realizable via building a weak link at given positions of the double-well barrier. We show that within mean-field theory the maximum Josephson current is proportional to the order parameter in two wells. Thus, the spatial inhomogeneity of the FFLO order parameter in one well may be directly revealed through the current measurement with the position-tunable link. We anticipate that this type of Josephson measurement can provide useful evidence for the existence of exotic FFLO superfluids. Possible experimental realizations of the Josephson measurements in atomic Fermi gases are discussed.

DOI
10.1103/physreva.83.013631

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We study theoretically two spatially separate quasi-one-dimensional atomic Fermi gases in a double-well trap. By tuning independently their spin polarizations, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid or a Bardeen-Cooper-Schrieffer (BCS) superfluid may be formed in each well. We seek the possibility of creating a spatially tunable atomic Josephson junction between two superfluids, which is supposed to be realizable via building a weak link at given positions of the double-well barrier. We show that within mean-field theory the maximum Josephson current is proportional to the order parameter in two wells. Thus, the spatial inhomogeneity of the FFLO order parameter in one well may be directly revealed through the current measurement with the position-tunable link. We anticipate that this type of Josephson measurement can provide useful evidence for the existence of exotic FFLO superfluids. Possible experimental realizations of the Josephson measurements in atomic Fermi gases are discussed.
We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. By including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field.
We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit-coupled atomic Fermi gases under a Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well known that the system is either a Bardeen-Cooper-Schrieffer superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zero-energy Majorana modes. However, in the weakly interacting regime the topological superfluid prefers to stay at the trap edge, in contrast to a FFLO superfluid, which occurs near the trap center. As a result, it is unlikely to experimentally observe an inhomogeneous FFLO superfluid with topo-logical order without specifically tailoring the geometry or other parameters of the Fermi cloud.
In a very interesting recent Letter\cite{machida}, the authors suggested the possibility of realizing the spatially modulated, or Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state in trapped atomic fermion systems. The authors this Letter used a 1D mean field solution as guidance to estimate the parameter range for the existence of the FFLO phase, and also discussed the possibility of its detection by imaging the atomic density of the system. In this comment I wish to make two points. (i) In 1D there exists an exact solution based on bosonization, which fully takes into account the important quantum fluctuation effects\cite{yang01}; the exact solution suggests a wider parameter range for the FFLO state than that obtained from the mean-field solution of the present Letter. (ii) One can detect the FFLO pairing (in which Cooper pairs carry finite momenta) more directly by extending the methods used to detect BCS pairing\cite{regal,altman,greiner}.
We study s-wave pairing of population imbalanced Fermi atoms in quasi two dimensions using a mean field theory. At zero temperature, we map out the phase diagram in the entire Bardeen, Cooper and Schrieffer-Bose Einstein condensation (BCS-BEC) crossover region by investigating the effect of weak atom tunneling between layers. We find that the superfluid phase stabilizes as one decreases the atom tunneling between layers. This allows one to control the superfluid-normal first order phase transition by tuning a single experimental parameter. Further, we find that a tunneling induced polarized superfluid phase appears in a narrow parameter region in the BEC regime. At Finite temperatures, we use a Landau-Ginzberg functional approach to investigate the possibility of spatially inhomogeneous Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in the weakly interacting BCS limit near the tricritical point of spatially homogenous superfluid, FFLO, and normal phases. We find that the normal-FFLO phase transition is first order transition as opposed to the continues transition predicted in zero temperature theories.
We show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.
We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (NPP{N}_{\text{PP}}NPP​). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.