Effect of Population Imbalance on Vortex Mass in Superfluid Fermi Gases

TL;DR

This work extends an effective-field-theory framework for superfluid Fermi gases to include population imbalance and finite temperature, focusing on the vortex mass as a measurable inertial property. The vortex mass is decomposed into an associated part from expelled superfluid and an internal part from excess normal density, both computed from radial vortex profiles obtained in the EFT, with the imbalance introduced via the chemical-potential difference $\zeta$. The study finds a strong, temperature-dependent interplay between imbalance and vortex mass: at low $T$ the mass grows with imbalance, while at higher $T$ the mass can diminish, with nonmonotonic behavior near critical imbalance especially on the BEC side where the mass can significantly increase around $T/T_c \sim 0.2$. These results identify experimental parameter regimes—across the BEC-BCS crossover and near unitary—to observe vortex mass in imbalanced Fermi gases and establish imbalance as a tunable knob for testing vortex dynamics in quantum fluids.

Abstract

One of the fundamental parameters associated with quantized vortices in superfluids is the vortex mass, which is the inertia of a vortex. As of yet, this mass has not been observed in a superfluid. However, ultracold Fermi gases provide a promising platform in which recently much experimental progress was made, offering tunability of the interaction as well as control on the single-vortex level. Not only can the scattering length be freely tuned, allowing exploration of the BEC-BCS crossover, but also an imbalance between different pseudospin states can be introduced. We study the effect of introducing this imbalance on the vortex mass, using a method based on an effective field theory for superfluid Fermi gases. We find that it is crucial to consider the imbalance in conjunction with nonzero temperatures; at some temperatures, the vortex mass is significantly enhanced while at others, the vortex mass is diminished. This pronounced temperature dependence highlights the need for careful tuning of experimental conditions and identifies favorable parameter regimes in which the vortex mass is likely to be observed.

Figures (6)

• Figure 1: This figure shows the total density $\rho_{\text{tot}}$ (solid blue line), superfluid density $\rho_s$ (solid orange line) and normal density $\rho_n$ (solid green line), as well as the density imbalance $\Delta \rho$ (dotted black line) as a function of the radial distance $r$ from the center of the vortex, calculated at temperature zero. All densities are scaled by the bulk total density $\rho_\infty = m k_F^3/3\pi^2$ and the radial distance is scaled by the healing length $\xi$. These are shown for various values of the $s$-wave scattering length $a_s$ and imbalance chemical potential $\zeta$. Also plotted are the asymptotes of the superfluid density (dashed purple line) and the normal density (dashed brown line).
• Figure 2: (a) Total vortex mass for a system size $k_F R = 150$ as a function of the inverse scattering length at various values of the imbalance chemical potential $\zeta$. (b) Correction factors $\alpha_a$ and $\alpha_i$ as a function of the inverse scattering length.
• Figure 3: Total, associated and internal vortex masses at zero temperature are given as a function of the imbalance chemical potential $\zeta$, for various values of the scattering length. Also the mass of the imbalanced component is shown. All masses are normalized by the total vortex mass at $\zeta = 0$.
• Figure 4: Total vortex mass as a function of temperature at various values of the critical imbalance potential, given for inverse scattering lengths -1, 0 and 1. The critical imbalance chemical potential $\zeta_c$ is computed at temperature zero. All masses are normalized by the total vortex mass at $\zeta = T = 0$.
• Figure 5: Order parameter profiles at various values of the $s$-wave scattering length $a_s$ and imbalance chemical potential $\zeta$, for temperature zero. At zero temperature, the asymptotic behavior does not depend on $\zeta$, except in the polarized superfluid phase.