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arXiv:0902.2275 · Physical Review B

Angular Fulde-Ferrell-Larkin-Ovchinnikov state in cold fermion gases in a toroidal trap

Youichi Yanase

Published Dec 29, 2009• 32 citations
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Abstract

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 $T$-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.

DOI
10.1103/physrevb.80.220510

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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.
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 theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS-BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov-de Gennes equation coupled with the regularized gap and number equations. The zero-temperature phase diagram in the crossover regime is presented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state governs the weak-coupling BCS region of a resonance. It is found that the FFLO oscillation vanishes in the BEC side, in which the system under population imbalance turns into a phase separation (PS) between locally binding superfluid and fully polarized spin domains. We also demonstrate numerical calculations with a large particle number O(10^5), comparable to that observed in recent experiments. The resulting density profile on a resonance yields the PS, which is in good agreement with the recent experiments, while the FFLO modulation exists in the pairing field. It is also proposed that the most favorable location for the detection of the FFLO oscillation is in the vicinity of the critical population imbalance in the weak coupling BCS regime, where the oscillation periodicity becomes much larger than the interparticle spacing. Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalanced system. The clear difference in the RF spectroscopy between BCS and BEC sides reveals the structure of the pairing field and local ``magnetization''.
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 sss-wave superconductivity in the two-dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via a Monte Carlo approach. The method requires iterative solution of the Bogoliubov--de-Gennes equations for amplitude- and phase-fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong-coupling problem. At low field we observe the magnetized but homogeneous ``breached pair'' superfluid phase. It reveals that Tc{T}_{c}Tc​ scales an order of magnitude below the mean-field estimate, spontaneous inhomogeneity in the field-induced magnetization, and a strong nonmonotonicity in the temperature dependence of the low-energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. At higher field we obtain the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. The thermal transition from the FFLO phases to the normal state is strongly first order. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into the normal state. The pairing structure factor retains weak signature of finite momentum pairing to a high temperature despite the low Tc{T}_{c}Tc​ itself, while the spin-resolved density of states changes from the ``pseudogapped'' FFLO character to gapless and pseudogapped again with increasing temperature.
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.
We consider a trapped Fermi gas with population imbalance at finite temperatures and map out the detailed phase diagram across a wide Feshbach resonance. We take the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state into consideration and minimize the thermodynamical potential to ensure stability. Under the local density approximation, we conclude that a stable LOFF state is present only on the BCS side of the Feshbach resonance, but not on the BEC side or at unitarity. Furthermore, even on the BCS side, a LOFF state is restricted at low temperatures and in a small region of the trap, which makes a direct observation of a LOFF state a challenging task.