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arXiv:2503.21628 · Nature Communications

Mutual friction and vortex Hall angle in a strongly interacting Fermi superfluid

N. Grani, Diego Hernández-Rajkov, Cyprien Daix, P. Pieri, Michele Pini, Piotr Magierski, Gabriel Wlazłowski, Marcia Frómeta Fernández, Francesco Scazza, Giulia Del Pace, G. Roati

Published Nov 21, 2025• 3 citations

Abstract

We investigate the two-dimensional motion of a single vortex orbiting a pinned anti-vortex in a unitary Fermi superfluid. By analyzing its trajectory, we measure the yet-unknown longitudinal and transverse mutual friction coefficients, which quantify the vortex-mediated coupling between the normal and superfluid components. Both coefficients increase while approaching the superfluid transition. They provide access to the vortex Hall angle, which is linked to the relaxation time of the localized quasiparticles occupying Andreev bound states within the vortex core, and to the vortex Reynolds number Reα associated with the transition from laminar to quantum turbulent flows. We compare our results with numerical simulations and an analytic model originally formulated for superfluid 3He, finding good agreement. Our work suggests that vortex dynamics in unitary Fermi superfluids is essentially affected by the interplay between delocalized thermal excitations and vortex-bound quasiparticles. Further, it provides a novel testbed for studying vortex dynamics at finite temperatures. Vortex dynamics and mutual friction in quantum fluids are intimately connected to the fundamental properties of superfluids. Here, the authors reveal previously unexplored mechanisms underlying the mutual friction coefficients in ultracold Fermi superfluids in the unitary limit, suggesting bound quasiparticles within the vortex core play a significant role.

DOI: 10.1038/s41467-025-64992-w

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We investigate the two-dimensional motion of a single vortex orbiting a pinned anti-vortex in a unitary Fermi superfluid. By analyzing its trajectory, we measure the yet-unknown longitudinal and transverse mutual friction coefficients, which quantify the vortex-mediated coupling between the normal and superfluid components. Both coefficients increase while approaching the superfluid transition. They provide access to the vortex Hall angle, which is linked to the relaxation time of the localized quasiparticles occupying Andreev bound states within the vortex core, and to the vortex Reynolds number Reα associated with the transition from laminar to quantum turbulent flows. We compare our results with numerical simulations and an analytic model originally formulated for superfluid 3He, finding good agreement. Our work suggests that vortex dynamics in unitary Fermi superfluids is essentially affected by the interplay between delocalized thermal excitations and vortex-bound quasiparticles. Further, it provides a novel testbed for studying vortex dynamics at finite temperatures. Vortex dynamics and mutual friction in quantum fluids are intimately connected to the fundamental properties of superfluids. Here, the authors reveal previously unexplored mechanisms underlying the mutual friction coefficients in ultracold Fermi superfluids in the unitary limit, suggesting bound quasiparticles within the vortex core play a significant role.

Abstract The physical origin of mutual friction in quantum fluids is deeply connected to the fundamental nature of superfluidity. It stems from the interaction between the superfluid and normal components, mediated by the dynamics of quantized vortices that induce the exchange of momentum and energy. Despite the complexity of these interactions, their essential features can be effectively described by the dissipative point vortex model—an extension of classical vortex dynamics that incorporates finite-temperature dissipation. Mutual friction is parametrized by the longitudinal (dissipative) coefficient

\alpha

α and the transverse (reactive) coefficient

\alpha '

α ′ . Accurate measurement of these parameters provides critical insights into the microscopic mechanisms governing vortex motion and dissipation in quantum fluids, serving as a key benchmark for theoretical models. In this work, we employ the dissipative point vortex model to study how fluctuations in the initial conditions influence the inference of

\alpha

α and

\alpha '

α ′ from the time evolution of the vortex trajectories. Using experimentally realistic parameters, we show that fluctuations can introduce significant biases in the extracted values of the mutual friction coefficients. We compare our findings with recent experimental measurements in strongly interacting atomic superfluids. Applying this analysis to our recent experimental results allowed us to account for fluctuations in the correct determination of

\alpha

α and

\alpha '

α ′ .

Excitations in vortex cores in superconductors and other Fermi superfluids are single-particle excitations with a peculiar energy spectrum. These excitations are responsible for many important thermodynamic properties such as specific heat, London penetration length, etc. They also determine the dynamic characteristics of superconductors and superfluids through their interaction with vortices. Flux flow resistance, the Hall effect in type II superconductors and the mutual friction in superfluids are the most important phenomena which strongly depend on vortex core excitations. These phenomena determine the electromagnetic responses of type II superconductors and the hydrodynamic behaviour of superfluids and are of great significance for practical applications of superconducting devices and for understanding the most fundamental properties of correlated electrons and other Fermi particles. In this review we consider the dynamic properties of superconductors and superfluids and outline the basic ideas and results on the vortex dynamics in clean superfluid Fermi systems. The forces acting on moving vortices are discussed including the problem of the transverse force which was a matter of confusion for quite some time. We formulate the equations of the vortex dynamics, which include all the forces and the inertial term associated with excitations bound to the moving vortex.

Dissipation of quantum vortex motion is fundamental to superfluid dynamics and quantum turbulence, yet there is currently a large gap between theory and experiments with ultracold atoms. Here we present a microscopic open quantum systems theory of thermally damped vortex motion in oblate atomic superfluids that includes previously neglected energy-damping interactions between superfluid and thermal atoms. This mechanism couples strongly to vortex core motion and causes dissipation of vortex energy due to mutual friction, as well as Brownian motion of vortices due to thermal fluctuations. We derive an analytic expression for the dimensionless mutual friction coefficient that gives excellent quantitative agreement with experimentally measured values, without any fitted parameters. Our work closes an existing two orders of magnitude gap between dissipation theory and experiments, previously bridged by fitted parameters, and provides a microscopic origin for the mutual friction and diffusion of quantized vortices in two-dimensional atomic superfluids.

Abstract Mutual friction caused by scattering of thermal excitations by quantized vortices is a phenomenon of key importance for the understanding of vortex dynamics and quantum turbulence in finite-temperature superfluids. The article reviews theoretical, numerical, and experimental results obtained during the last 40 years in the study of mutual friction in bosonic superfluids such as

^4

4 He and Bose–Einstein condensates. Among several research topics reviewed in this article particular attention is paid to the development of theory and numerical analysis of roton-vortex interactions and mutual friction in superfluid helium; an application of the two-fluid model for the analysis of the flow in the vicinity of the vortex core and the calculation of the longitudinal and transverse forces exerted on a vortex; vortex diffusivity in

^4

4 He films; and theoretical, numerical, and experimental studies of thermal dissipation and mutual friction in finite-temperature Bose–Einstein condensates.

In Fermi superfluids, such as superfluid (3)He, the viscous normal component can be considered to be stationary with respect to the container. The normal component interacts with the superfluid component via mutual friction, which damps the motion of quantized vortex lines and eventually couples the superfluid component to the container. With decreasing temperature and mutual friction, the internal dynamics of the superfluid component becomes more important compared with the damping and coupling effects from the normal component. As a result profound changes in superfluid dynamics are observed: the temperature-dependent transition from laminar to turbulent vortex motion and the decoupling from the reference frame of the container at even lower temperatures.

Recent measurements of mutual friction in strongly interacting Fermi superfluids establish a direct link between the transverse dynamics of quantized vortices and the relaxation of localized core states. Motivated by these results, we investigate the dynamics of knotted vortex filaments within an effective hydrodynamic framework. By extending the vortex Hall angle formalism to non-planar filament geometries, we derive a phenomenologically motivated scaling relation between filament topology and internal relaxation times. We show that a hierarchy of decay times emerges naturally from a topology-dependent Reynolds-like barrier, with lifetimes controlled by writhe-dependent geometric phase lags. While no claim is made of microscopic particle identity, the resulting hierarchy closely parallels the ordering observed in several physical systems exhibiting metastable topological excitations.