Vortex Mass in Superfluid Fermi Gases along the BEC-BCS Crossover

TL;DR

The paper addresses the long-standing problem of the inertial vortex mass in superfluid Fermi gases along the BEC-BCS crossover. It adopts a two-fluid framework and an effective field theory to compute both the associated (global) and internal (local) vortex masses, revealing a logarithmic dependence on the system size R driven by the asymptotic tails of the superfluid and normal densities: M_a ≈ π ξ^2 ρ_{s,∞} log(R/(α_a ξ)) and M_i ≈ π ξ^2 δρ_{n,∞} log(R/(α_i ξ)), with ξ defined by ξ = sqrt( (ħ^2/m) (C/(Δ^2 G)) ). Across the crossover, M_i vanishes in the BEC limit while M_a grows, and in the BCS limit M_i ≈ M_a; finite-temperature effects can shift these contributions in opposite directions depending on coupling. For realistic system sizes, the total vortex mass exceeds the naive local estimate by about a factor of five, suggesting that vortex inertia could be observable in current ultracold-atom experiments. The work provides a quantitative benchmark for experiments and clarifies how core structure and system size determine vortex dynamics in two-component superfluids.

Abstract

Vortex mass is a key concept in the study of superfluid dynamics, referring to the inertia of vortices in a superfluid, which affects their motion and behavior. Despite being an important quantity, the vortex mass has never been observed experimentally, and remains an unresolved issue in this field. As of now, a large body of research assumes that the vortex mass is a local parameter. In contrast, we present a calculation that suggests a logarithmic dependence on the system size, agreeing with some earlier predictions in the context of Bose gases. We analyze the problem using an effective field theory that describes ultracold atomic Fermi gases over the BEC-BCS crossover at both zero and nonzero temperatures. Our study reveals a strong dependence of the vortex mass on the scattering length; in particular, the vortex mass grows rapidly when moving towards the BCS side. Furthermore, we find that the system-size dependence of the vortex mass results in values an order of magnitude larger than those predicted by other models for realistic system sizes. This implies that the vortex mass could be observable in a wider parameter range than was previously expected. This is particularly relevant considering recent advances in experimental techniques that place the observation of vortex mass in superfluid Fermi gases within reach.

Figures (4)

• Figure 1: (a) Total density $\rho_{\text{tot}}$ (solid blue line), superfluid density $\rho_s$ (solid orange line) and normal density $\rho_n$ (solid green line) as a function of the radial coordinate, calculated in the EFT framework at temperature zero. The densities are normalized by the total density at $r=\infty$. Also plotted are the asymptotic expressions for the superfluid (dashed purple line) and normal (dashed brown line) densities. In the $r < \xi$ region, the asymptotics are continued by dash-dotted lines indicating the simplified analytic vortex profile introduced in Eqs. \ref{['eq:simplified-rhos']} and \ref{['eq:simplified-rhon']}. (b) Healing length as defined in Eq. \ref{['eq:eft-xi1']} over the crossover, for various temperatures. These are compared to analytic expressions in the BCS and BEC limits at zero temperature, which are derived in Appendix \ref{['app:healing']}.
• Figure 2: (a) The vortex mass for a system size of $k_FR = 150$ at zero temperature is plotted, alongside the contributions of the internal and associated mass. The dotted purple and brown lines show the simplified analytic model given by Eqs. \ref{['eq:approximate-associated-mass']} and \ref{['eq:approximate-internal-mass']}, respectively. The solid gray line represents $\pi \xi^2 \rho_{s,\infty}$ and the dashed black line $\pi \xi^2 \,\delta\rho_{n,\infty}$. (b) The ratio of the internal vortex mass to the total vortex mass for different system sizes, including the $R\to\infty$ limit. (c) The correction factors $\alpha_a$ and $\alpha_i$. The dotted line shows the value from the analytical model $\alpha_{\text{ana}}$.
• Figure 3: Total density $\rho_{\text{tot}}$ (solid blue line), superfluid density $\rho_s$ (solid orange line) and normal density $\rho_n$ (solid green line) as a function of the radial coordinate, calculated in the EFT framework at nonzero temperatures. The densities are normalized by the total density at $r=\infty$. Also plotted are the asymptotic expressions for the superfluid (dashed purple line) and normal (dashed brown line) densities. The gray dotted lines correspond to the simplified analytic vortex profile introduced in Eqs. \ref{['eq:simplified-rhos']} and \ref{['eq:simplified-rhon']}.
• Figure 4: (a) The (total) vortex mass for a system size of $k_FR = 150$ at various temperatures. (b) The ratio of the internal vortex mass to the total vortex mass at various temperatures in the $R\to\infty$ limit. (c) The correction factors $\alpha_a$ and $\alpha_i$ at temperatures $T/T_c = 0.5$ and $T/T_c = 0.9$.