Multiple-quantized vortices in rotating LOFF state of ultracold Fermi superfluid gas

A rotating ultracold S-wave superfluid Fermi gas is considered, when the population imbalance (or equivalently the mismatch in chemical potentials) corresponds to the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state in the vicinity of the Lifshitz critical point. It is shown that under these conditions the critical angular velocity in two-dimensional systems is an oscillating function of temperature and population imbalance giving rise to reentrant superfluid phases. This leads to vortex lattices with multiple-quantized circulation quanta. The reason for this behavior is the population by Cooper pairs of the Landau levels above the lowest one.

💡 Research Summary

The authors investigate a two‑component ultracold Fermi gas confined to a quasi‑two‑dimensional (pancake‑shaped) trap, where a population imbalance between the two hyperfine states (or, equivalently, a mismatch of the chemical potentials δµ) drives the system into the Larkin‑Ovchinnikov‑Fulde‑Ferrell (LOFF) phase. Near the Lifshitz critical point (the point in the temperature–δµ plane where the homogeneous superfluid becomes unstable toward a spatially modulated order parameter) the LOFF wave‑vector Q is small, allowing a gradient expansion of the pairing kernel.

When the gas is set into rotation with angular velocity Ω about the z‑axis, the Coriolis term in the single‑particle Hamiltonian plays the role of a synthetic vector potential VΩ = Ω × r. In the rotating frame the kinetic energy becomes (p – 2M VΩ)²/2M, which is mathematically identical to the Hamiltonian of a charged particle in a magnetic field. Consequently the normal‑state quasiparticles acquire Landau quantization. The authors distinguish two regimes: (i) a quasiclassical regime where ℏΩ ≪ π(kBTc)²/µ (µ being the average chemical potential, essentially the Fermi energy) so that Landau level spacing is negligible, and (ii) a quantum regime where ℏΩ ≳ kBTc and genuine Landau quantization must be retained. The paper focuses on the former, which is appropriate close to the Lifshitz point.

Linearizing the gap equation yields a kernel K₀(q) that depends on temperature t = T/Tc₀ and reduced mismatch δ̄µ = δµ/Tc₀ through digamma functions. Expanding K₀(q) up to q⁴ gives coefficients k₂(t,δ̄µ) and k₄(t,δ̄µ). At the Lifshitz point (t* ≈ 0.56, δ̄µ* ≈ 1.04) both k₂ and the linear term in the Ginzburg‑Landau functional vanish, leaving the quartic term to stabilize the modulated phase.

In the rotating system the linearized Ginzburg‑Landau equation becomes