Dynamical signature of vortex mass in Fermi superfluids

TL;DR

The paper demonstrates that vortices in Fermi superfluids possess a finite inertial mass arising from normal component trapped in the vortex core, yielding observable small-amplitude transverse oscillations that agree with a simple massive point-vortex model. Using large-scale time-dependent SLDA/DFT simulations across the BCS-BEC crossover and at finite temperature, the authors extract the vortex mass $M_c$ from oscillation frequencies and from static core analyses via the core-normal ratio $\\mathfrak{m}=M_c/M_s$, finding $M_c$ scales with the core area $\\propto\\xi^2$ with a prefactor of order unity (\\alpha \\approx 1.5). Finite temperature enhances core-normal density and thus inertia, increasing oscillation amplitudes while maintaining low dissipation up to about $0.3\\,T_c$, making the inertial signature accessible to experiments. The work combines microscopic DFT results with a generalized point-vortex description, offering a route to study dissipation, vortex-sound interactions, and vortex dynamics across the BCS-BEC crossover in both 2D and 3D settings.

Abstract

Quantum vortices are commonly described as funnel-like objects around which the superfluid swirls, and their motion is typically modeled in terms of massless particles. Here we show that in Fermi superfluids the normal component confined in the vortex core provides the vortex with a finite inertial mass. This inertia imparts an unambiguous signature to the dynamic behavior of vortices, specifically manifesting as small-amplitude transverse oscillations which remarkably follow the prediction of a simple point-like model supplemented by an effective mass. We demonstrate this phenomenon through large-scale time-dependent simulations of Fermi superfluids across a wide range of interaction parameters, at both zero and finite temperatures, and for various initial conditions. Our findings pave the way for the exploration of inertial effects in superfluid vortex dynamics.

Figures (8)

• Figure 1: (a) Pictorial illustration of a superfluid (blue) confined in a circular trap and hosting an off-centered vortex whose core is filled by some normal component (orange). Panel (b) shows the trajectory (solid blue line) of the massive vortex characterized by small-amplitude radial oscillations around the circular trajectory of a massless vortex (dashed line). (c) Evolution of the radial coordinate of a vortex orbiting within a Fermi superfluid at zero temperature (blue solid line, the red dashed line is a sinusoidal fit) as the parameter $k_F a$ is changed. Our simulations start with a static vortex at $r_0(t=0)=0.54\, R$. Moving from the deep BCS regime to the strongly-attractive regime (i.e., from the left to the right panel), the oscillation frequency increases, while the amplitude is reduced. The superfluid (d) and normal (e) densities as extracted from static calculations of a vortex in a container of radius $R=90\, k_F^{-1}$ at $k_F a=-0.7$. Yellow (blue) color corresponds to high (zero) density.
• Figure 2: Dependence of the vortex mass $\mathfrak{m}$ on the interaction strength as obtained from the frequency $\omega$ of transverse oscillations through Eq. (\ref{['eq:omega']}) (blue dots) and from the ratio $N_n/N_s$ (red dots). The gray dashed line corresponds to Eq. (\ref{['eq:m_equal_const_xi_squared']}). Inset: $\omega(k_Fa)$ extracted from time-dependent DFT simulations. Gray areas correspond to values of $k_Fa$ for which $\omega$ cannot be extracted from the trajectory in a reliable way.
• Figure 3: Dependence of the vortex mass $\mathfrak{m}$ on temperature $T$ for fixed $k_Fa=-0.85$ and fixed initial conditions. (a) Comparison from the values inferred from the oscillation frequency $\omega$ (blue dots) and the ratio $N_n/N_s$ (red dots). Error bars would be smaller than the symbols. Inset: $\omega(T)$ extracted from the time-dependent DFT simulations. (b) Time evolution of the vortex radial position: oscillations are less frequent and wider at higher temperatures [lines are color-coded as in panel (c)]. (c) Temperature initially increases the normal component in the vortex core, and, for larger values, it also enhances $\rho_n$ in the bulk.
• Figure S1: (a) Spectrum of the quasi-particle states as a function of the quantum number $\ell$. Yellow (blue) color corresponds to states whose energy is smaller (greater) than $E^*=0.9\,\bar{\Delta}$. (b) Cross-section of the density profiles along a path passing through the center, where $x=0$ denotes the vortex core.
• Figure S2: Left panel: plot of the synthetic state (\ref{['eq:Artificial_Delta']}), at time $i=1$, used to benchmark the vortex-tracking algorithm employed to extract the vortex position $\bm{r}_0(t)$ from DFT simulations. Right panel: the position of the vortex extracted from our DFT simulations (red line) is characterized by regular oscillations significantly ($\sim 12$ times) wider than the irregular fluctuations (blue line) resulting from vortex tracking in synthetic states. For comparison, the radius of the box is $R=90\,dx$.