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Journal of Low Temperature Physics

Mutual Friction in Bosonic Superfluids: A Review

Yu. A. Sergeev

Published May 18, 2023• 9 citations
Publisher

Abstract

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.

DOI
10.1007/s10909-023-02972-4

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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 4^44 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 4^44 4 He films; and theoretical, numerical, and experimental studies of thermal dissipation and mutual friction in finite-temperature Bose–Einstein condensates.
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 α\alphaα α and the transverse (reactive) coefficient α′\alpha 'α′ 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 α\alphaα α and α′\alpha 'α′ 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 α\alphaα α and α′\alpha 'α′ α ′ .
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.
Like many quantum fluids, superfluid helium-4 (He II) can be considered as a mixture of two miscible fluid components: an inviscid superfluid and a viscous normal fluid consisting of thermal quasiparticles [1]. A mutual friction between the two fluids can emerge due to quasiparticles scattering off quantized vortex lines in the superfluid [2]. This quantum dissipation mechanism is the key for understanding various fascinating behaviors of the two-fluid system [3,4]. However, due to the lack of experimental data for guidance, modeling the mutual friction between individual vortices and the normal fluid remains an unsettled topic despite decades of research [5-10]. Here we report an experiment where we visualize the motion of quantized vortex rings in He II by decorating them with solidified deuterium tracer particles. By examining how the rings spontaneously shrink and accelerate, we provide unequivocal evidences showing that only a recent theory [9] which accounts for the coupled motion of the two fluids with a self-consistent local friction can reproduce the observed ring dynamics. Our work eliminates long-standing ambiguities in our theoretical description of the vortex dynamics in He II, which will have a far-reaching impact since similar mutual friction concept has been adopted for a wide variety of quantum two-fluid systems, including atomic Bose-Einstein condensates (BECs) [11,12], superfluid neutron stars [13-15], and gravity-mapped holographic superfluid [16,17].
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.
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.
Quantum turbulence is recently one of the most important topics in low temperature physics. Physics of quantum turbulence and quantized vortices have been studied chiefly in superfluid helium. The realization of atomic Bose-Einstein condensation has allowed us to study quantized vortives in the fascinating systems too. Generally there are two kinds of cooperative phenomena comprised of quantized vortices, from the research history of superfluid helium. Lots of studies in atomic Bose-Einstein condensates (BECs) are devoted mainly to the issues of vortex lattices under rotation. However, another important state on quantized vortices, namely quantum turbulence, has been never studied in atomic BECs. In this work, we address for the first time quantum turbulence in atomic BECs theoretically and numerically. After reviewing shortly the recent developments on quantum turbulecne, we propose how to make quantum turbulence in a trapped BEC by combining rotation around two axes, and confirm the Kolmogorov spectra by the Gross-Pitaevskii model.