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Journal of Physics Conference Series

Crossover from Fulde-Ferrell state to Larkin-Ovchinnikov state in cold fermion gases

Tomohiro Yoshida, Youichi Yanase

Published Dec 17, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/400/1/012086

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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 study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two-component Fermi superfluid gases in a toroidal trap. We investigate the stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov--de Gennes equation. We find that two FFLO phases, i.e., the half-quantum-vortex state and the intermediate state of the Fulde-Ferrell (FF) state and the 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 both the TTT-PPP plane and the TTT-hhh plane. We demonstrate characteristic features of these states, such as the order parameter, flux quantization, and local polarization. Several related works are discussed, and the advantages of cold Fermi gases are indicated.
We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the rotation symmetry is spontaneously broken, in population imbalanced fermion gases near the BCS-BEC crossover. We investigate the superfluid gases at low temperatures on the basis of the Bogoliubov--de Gennes equation and examine the stability against thermal fluctuations using the TTT-matrix approach beyond the local-density approximation. We find that the angular FFLO state is stabilized in the gases confined in the toroidal trap but not in the harmonic trap. The angular FFLO state is stable near the BCS-BEC crossover owing to the formation of pseudogap. Spatial dependences of number density and local population imbalance are shown for an experimental test.
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 $\mathrm{\ensuremath{\Delta}}$.
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 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.