Quantum vortex dipole as a probe of the normal component distribution

TL;DR

The paper addresses how spin imbalance in strongly interacting Fermi superfluids at zero temperature affects vortex dipole dynamics. It applies fully microscopic time-dependent density functional theory in the ASLDA framework to simulate a vortex dipole propagating through spin-polarized regions and analyzes how spatially inhomogeneous normal components reshape its trajectory and energy. The results show observable dipole deflection and shrinkage driven by mutual-friction forces, with stronger effects at higher polarization, and demonstrate energy transfer from vortex motion to internal excitations via a Helmholtz decomposition that separates rotational and compressive flow components. These findings suggest vortex dipoles as sensitive probes of the normal component distribution and possible inhomogeneous pairing states (e.g., LOFF-like phases), offering a pathway for indirect experimental detection and a benchmark for future studies.

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.

Figures (9)

• Figure 1: Comparison of forces acting on vortex cores under different density regimes. a) Both normal and superfluid component are isotropic ($\rho_s = \textrm{const}, \rho_n = \textrm{const}$); b) Both components are distributed inhomogeneously ($\rho_s = \rho_s(\bm{r}), \rho_n = \rho_n(\bm{r})$), but their sum is isotropic $\rho_s(\bm{r})+\rho_n(\bm{r})\approx \textrm{const}$.
• Figure 2: Example of the initial setup, represented on the spatial mesh of size $100\times 64\times 16$. The vortex dipole is imprinted in the region where the system is locally spin-balanced. During the dynamics, the dipole will propagate toward the region where the system is spin-imbalanced. The trajectory of the vortex dipole will be used as a probe for studies of the underlying structure of the spin-imbalanced environment. The color map shows the spatial distribution of the pairing field absolute value $\Delta(\bm{r})$.
• Figure 3: Example of a vortex dipole propagation in a spin-imbalanced environment with global spin-polarization $P=2.89\%$. The initial size of the vortex dipole is $d_{\textrm{i}}=16k_F^{-1}$. Panel a) shows the initial configuration. The vertical stripes visible in $p(\bm{r})$ quantity (color map) are due to the initial state preparation procedure, where we separate the simulation volume into spin-balanced and spin-imbalanced regions by means of the external potential. As the dynamics start, the system relaxes, and this artifact vanishes, as seen in panel b) for the time moment $t \approx 10\varepsilon_{F}^{-1}$. Panel c) $t \approx 420\varepsilon_{F}^{-1}$: the dipole interacts with the ferron; one of the vortices sucks in the spin-polarization which significantly affects the ferron's structure. Panel d) $t \approx 1000\varepsilon_{F}^{-1}$: the dipole size has significantly shrunk, and the cores have now been filled with the spin-polarization. Inset: Cross-section of the order parameter $\Delta$, along the line as shown in panels a) and d). The dipole persists, but its internal structure has significantly changed. Arrows (heat scale) indicate the local intensity and direction of the total current $\bm{j}_\uparrow(\bm{r},t)+\bm{j}_\downarrow(\bm{r},t)$. Red dots indicate positions of vortex cores.
• Figure 4: Panel a) Distance ratio $d_{\textrm{f}}/d_{\textrm{i}}$ as a function of initial dipole size $d_{\textrm{i}}$ for various polarizations. Notably, the series for $P \simeq 3.5\%$ has only one datapoint for which the dipole survives. For lower $d_{\textrm{i}}$, the dipoles annihilate before the trajectory ends. Panel b) Trajectories of vortex dipoles with different initial sizes $d_{\textrm{i}}$ at fixed polarization $P \approx 1.5\%$. The dipole changes the direction of propagation upon colliding with a ferron. For the smallest initial size, the dissipation is high enough that the dipole annihilates.
• Figure 5: Solution of classical equations of motion for the massless vortex dipole, assuming that the dimensionless dissipative coefficients $\tilde{D}$ and $\tilde{D}^\prime$ acquire nonzero values only in selected regions, indicated as grey circles. Two cases are presented: the transverse force dominates over the longitudinal (solid line) and the transverse force is absent (dashed line).