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arXiv:2507.05817 · New Journal of Physics

Quantum vortex dipole as a probe of the normal component distribution

Andrea Barresi, Piotr Magierski, Gabriel Wlazłowski

Published Oct 20, 2025• 0 citations
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Abstract

Abstract We investigate the dynamics of quantum vortex dipoles in a strongly interacting, spin-imbalanced Fermi superfluid at zero temperature. Using fully microscopic time-dependent density functional theory, we demonstrate that the dipole trajectory is strongly influenced by the spatial distribution of spin polarization. The resulting forces on the vortices include both longitudinal and transverse components, leading to deflection and shrinking of the dipole during propagation. For moderate polarization, vortex dipoles are deflected and lose energy, while for larger imbalances, they are rapidly annihilated. Our findings provide compelling evidence that spin-imbalanced Fermi gases contain a spatially nonuniform normal component even at zero temperature. We show that vortex dipoles serve as sensitive probes of this component, offering a route to indirectly detect exotic superfluid phases such as the Fulde–Ferrell–Larkin–Ovchinnikov state and related inhomogeneous condensates.

DOI
10.1088/1367-2630/ae1528

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Abstract We investigate the dynamics of quantum vortex dipoles in a strongly interacting, spin-imbalanced Fermi superfluid at zero temperature. Using fully microscopic time-dependent density functional theory, we demonstrate that the dipole trajectory is strongly influenced by the spatial distribution of spin polarization. The resulting forces on the vortices include both longitudinal and transverse components, leading to deflection and shrinking of the dipole during propagation. For moderate polarization, vortex dipoles are deflected and lose energy, while for larger imbalances, they are rapidly annihilated. Our findings provide compelling evidence that spin-imbalanced Fermi gases contain a spatially nonuniform normal component even at zero temperature. We show that vortex dipoles serve as sensitive probes of this component, offering a route to indirectly detect exotic superfluid phases such as the Fulde–Ferrell–Larkin–Ovchinnikov state and related inhomogeneous condensates.
We investigate the properties of a spin-imbalanced and rotating unitary Fermi gas. Using a density functional theory, we provide insight into states that emerge from a competition between Abrikosov lattice formation, spatial phase separation, and the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. A confrontation of the experimental data [M. Zwierlein et al., Science 311, 492 (2006)] with theoretical predictions provides a remarkable qualitative agreement. In the case of gas confined in a harmonic trap, the phase separation into a superfluid core populated by the Abrikosov lattice and a spin-polarized corona is the dominant process. Changing confinement to a boxlike trap reverts the spatial location of the component: gas being in the normal state is surrounded by superfluid threaded by quantum vortices. The vortex lattice no longer exhibits the triangular symmetry, and the emergence of exotic geometries may be an indirect signature of the FFLO-like state formation in the system.
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 investigate the temperature effects in an imbalanced superfluid atomic Fermi gas. We consider a bilayer system of two-component dipolar fermionic atoms with one layer containing atoms of one component and the other layer the atoms of other component with an imbalance between the populations of the two components. This imbalance results in uniform and nonuniform superfluid phases such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and normal Fermi liquid phases for different system parameters. Using the mean-field BCS theory together with the superfluid mass-density criterion we classify different phases in thermodynamic phase diagram. Our results indicate that for a dipolar Fermi system the Sarma phase is stable for large imbalance at finite temperature below the critical temperature, and the FFLO phase is stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The phase diagram in the temperature and population imbalance plane indicate three Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi liquid phase while the other two correspond to the coexistance of the Sarma phase, FFLO phase and normal Fermi phase for dipolar interactions.
Motivated by the recent experimental realization of a candidate to the Fulde-Ferrell (FF) and the Larkin-Ovchinnikov (LO) states in one dimensional (1D) atomic Fermi gases, we study the quantum phase transitions in these enigmatic, finite momentum-paired superfluids. We focus on the FF state and investigate the effects of the induced interaction on the stability of the FFLO phase in homogeneous spin-imbalanced quasi-1D Fermi gases at zero temperature. When this is taken into account we find a direct transition from the fully polarized to the FFLO state. Also, we consider the effect of a finite lifetime of the quasi-particles states in the normal-superfluid instability. In the limit of long lifetimes, the lifetime effect is irrelevant and the transition is directly from the fully polarized to the FFLO state. We show, however, that for sufficiently short lifetimes there is a quantum critical point (QCP), at a finite value of the mismatch of the Fermi wave-vectors of the different quasi-particles, that we fully characterize. In this case the transition is from the FFLO phase to a normal partially polarized state with increasing mismatch.
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.
We investigate the finite-temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a nonpolarized Bardeen-Cooper-Schrieffer superfluid (P<Pc)(P<{P}_{c})(P<Pc​) or a fully polarized normal gas (P>Pc)(P>{P}_{c})(P>Pc​), depending on the smallness of the spin polarization PPP, relative to a critical value Pc{P}_{c}Pc​. In this work, we show how these two phase-separation phases evolve with increasing temperature, and thereby construct a finite-temperature phase diagram. For typical interactions, we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy temperature, which seems to be accessible in the current experiment. The density profile, equation of state, and specific heat of the polarized system have been calculated and discussed in detail. Our results are useful for the ongoing experiment at Rice University on the search for FFLO states in quasi-one-dimensional polarized Fermi gases.