Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Vortex Mutual Friction, Orbital Inertia, and History-Dependent Textures in Rotating Superfluid 3He−A

Antti J. Manninen, T. D. C. Bevan, J. B. Cook, Harry Alles, John R. Hook, Henry Edgar Hall

Published Dec 16, 1996• 58 citations
Publisher

Abstract

We have measured the resistive and reactive mutual friction coefficients in rotating superfluid ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A$ at $29.3\mathrm{bars}$ pressure. The results agree with those predicted from the equation of orbital hydrodynamics for two quantum continuous vortices if the previously measured value of the orbital viscosity is used. Our results put an upper limit on the orbital inertia of less than $0.005\ensuremath{\Elzxh}$ per Cooper pair. We explain our observation of history-dependent textures by noting that the ease of formation of continuous vortices depends on the relative direction of $\mathbf{l}$ and the rotation axis.

DOI
10.1103/physrevlett.77.5086

Related papers

Critical Velocity of Vortex Nucleation in Rotating Superfluid 3 He- A

V. M. H. Ruutu, Juha Kopu, M. Krusius +4 more

We have measured the critical velocity ${\ensuremath{\upsilon}}_{\mathrm{c}}$ at which ${}^{3}\mathrm{He}\ensuremath{-}\mathrm{A}$ in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that ${\ensuremath{\upsilon}}_{\mathrm{c}}$ is distributed between a maximum and a minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentun axis $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ in the cylinder. Slow cooldown through ${T}_{\mathrm{c}}$ in rotation yields $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ textures for which the measured ${\ensuremath{\upsilon}}_{\mathrm{c}}$'s are in good agreement with the calculated instability of the expected $\stackrel{^}{\mathbf{l}}$ texture.

arXiv:cond-mat/9708226•Physical Review Letters•Dec 22, 1997•99 citations

Collective motion of quantized vortex lines in rotating superfluid B3

M. Krusius, J. S. Korhonen, Y. Kondo +1 more

Insight in the dynamics of quantized vortex lines has been obtained by performing NMR measurements in uniformly rotating superfluid $^{3}\mathit{B}$. Compared to superfluid $^{4}\mathrm{He}$, in $^{3}\mathit{B}$ the viscosity of the normal component is three orders of magnitude larger and the pinning of vortices is weaker. The collective modes governing the hydrodynamic response of an array of vortex lines are highly overdamped. Two distinct modes are identified: (1) a relatively fast mutual-friction-resisted mode, which controls the redistribution of the vortex density on a time scale of a few seconds, and (2) an exponentially relaxing slow mode with a time constant of a few minutes, which governs asymptotically the approach to equilibrium at nearly constant vortex density. Measurement of the fast motion allows us to extract the dissipative mutual friction. The slow mode is dominated by the elastic tension along the vortex line and by weak pinning at the top and bottom surfaces of the rotating container. With increasing vortex density the surface pinning becomes a collective process, in which coherently moving groups of vortices are pinned in unison. Collective pinning is a result of the shear elasticity related to the crystalline order of the vortex lattice. Our measurements on the slow mode indicate that the crystalline correlation extends over many lattice spacings.

Physical review. B, Condensed matter•Jun 1, 1993•80 citations

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

N. Grani, Diego Hernández-Rajkov, Cyprien Daix +8 more

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.

arXiv:2503.21628•Nature Communications•Nov 21, 2025•3 citations

Measuring mutual friction in superfluids: the role of initial vortex configuration fluctuations

N. Grani, Diego Hernández-Rajkov, Marcia Frómeta Fernández +2 more

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 ′ .

arXiv:2508.21546•The European Physical Journal Special Topics•Oct 6, 2025•2 citations

Spectral Flow in Vortex Dynamics of 3 He-B and Superconductors

Nikolai B. Kopnin, Григорий Ефимович Воловик, Ülo Parts

A non-dissipative force F nd acting on a vortex in Fermi superfluids and superconductors is calculated taking into account the spectral flow of fermion zero modes in the vortex core. The spectral-flow effect casts a new light on the problem of mutual friction in superfluids. We demonstrate that, for vortices in an isotropic system, the reactive mutual friction parameter D ' ( T ) is negative in the collisionless regime and it is positive in the hydrodynamic regime. This agrees with 3 He-B measurements, which thus give the experimental verification of the spectral-flow effect on the vortex dynamics.

arXiv:cond-mat/9509157•Europhysics Letters (EPL)•Dec 10, 1995•94 citations

Orbital Damping of the Oscillating Superfluid $$^3$$ 3 He A–B Interface at Low Temperatures

Manuel Arrayás, S. N. Fisher, R. P. Haley +2 more

We present a model for the friction and effective mass of an oscillating superfluid $$^3$$ 3 He A–B interface due to orbital viscosity in the B-phase texture close to the interface. The model is applied to an experiment in which the A–B interface was stabilised in a magnetic field gradient at the transition field $$B_c = 340$$ B c = 340 mT at 0 bar pressure and at a very low temperature $$T \approx 0.155$$ T ≈ 0.155 mK. The interface was then oscillated by applying a small additional field at frequencies in the range 0.1–100 Hz. The response of the interface is governed by friction and by its effective mass. The measured dissipation does not fit theoretical predictions based either on the Andreev scattering of thermal quasiparticles or by pair-breaking from the moving interface. We describe a new mechanism based on the redistribution of thermal quasiparticle excitations in the B-phase texture engendered by the moving interface. This gives rise to friction via orbital viscosity and generates a significant effective mass of the interface. We have incorporated this mechanism into a simple preliminary model which provides reasonable agreement with the measured behaviour.

Journal of Low Temperature Physics•Mar 27, 2014•4 citations
We have measured the resistive and reactive mutual friction coefficients in rotating superfluid 3He\ensuremath−A{}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A3He\ensuremath−A at 29.3bars29.3\mathrm{bars}29.3bars pressure. The results agree with those predicted from the equation of orbital hydrodynamics for two quantum continuous vortices if the previously measured value of the orbital viscosity is used. Our results put an upper limit on the orbital inertia of less than 0.005\ensuremath\Elzxh0.005\ensuremath{\Elzxh}0.005\ensuremath\Elzxh per Cooper pair. We explain our observation of history-dependent textures by noting that the ease of formation of continuous vortices depends on the relative direction of l\mathbf{l}l and the rotation axis.
We have measured the critical velocity ${\ensuremath{\upsilon}}_{\mathrm{c}}$ at which ${}^{3}\mathrm{He}\ensuremath{-}\mathrm{A}$ in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that ${\ensuremath{\upsilon}}_{\mathrm{c}}$ is distributed between a maximum and a minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentun axis $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ in the cylinder. Slow cooldown through Tc{T}_{\mathrm{c}}Tc​ in rotation yields $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ textures for which the measured ${\ensuremath{\upsilon}}_{\mathrm{c}}$'s are in good agreement with the calculated instability of the expected $\stackrel{^}{\mathbf{l}}$ texture.
Insight in the dynamics of quantized vortex lines has been obtained by performing NMR measurements in uniformly rotating superfluid 3B^{3}\mathit{B}3B. Compared to superfluid 4He^{4}\mathrm{He}4He, in 3B^{3}\mathit{B}3B the viscosity of the normal component is three orders of magnitude larger and the pinning of vortices is weaker. The collective modes governing the hydrodynamic response of an array of vortex lines are highly overdamped. Two distinct modes are identified: (1) a relatively fast mutual-friction-resisted mode, which controls the redistribution of the vortex density on a time scale of a few seconds, and (2) an exponentially relaxing slow mode with a time constant of a few minutes, which governs asymptotically the approach to equilibrium at nearly constant vortex density. Measurement of the fast motion allows us to extract the dissipative mutual friction. The slow mode is dominated by the elastic tension along the vortex line and by weak pinning at the top and bottom surfaces of the rotating container. With increasing vortex density the surface pinning becomes a collective process, in which coherently moving groups of vortices are pinned in unison. Collective pinning is a result of the shear elasticity related to the crystalline order of the vortex lattice. Our measurements on the slow mode indicate that the crystalline correlation extends over many lattice spacings.
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 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 ′ .
A non-dissipative force F nd acting on a vortex in Fermi superfluids and superconductors is calculated taking into account the spectral flow of fermion zero modes in the vortex core. The spectral-flow effect casts a new light on the problem of mutual friction in superfluids. We demonstrate that, for vortices in an isotropic system, the reactive mutual friction parameter D ' ( T ) is negative in the collisionless regime and it is positive in the hydrodynamic regime. This agrees with 3 He-B measurements, which thus give the experimental verification of the spectral-flow effect on the vortex dynamics.
Orbital Damping of the Oscillating Superfluid 3^33 3 He A–B Interface at Low Temperatures
We present a model for the friction and effective mass of an oscillating superfluid 3^33 3 He A–B interface due to orbital viscosity in the B-phase texture close to the interface. The model is applied to an experiment in which the A–B interface was stabilised in a magnetic field gradient at the transition field Bc=340B_c = 340Bc​=340 B c = 340 mT at 0 bar pressure and at a very low temperature T≈0.155T \approx 0.155T≈0.155 T ≈ 0.155 mK. The interface was then oscillated by applying a small additional field at frequencies in the range 0.1–100 Hz. The response of the interface is governed by friction and by its effective mass. The measured dissipation does not fit theoretical predictions based either on the Andreev scattering of thermal quasiparticles or by pair-breaking from the moving interface. We describe a new mechanism based on the redistribution of thermal quasiparticle excitations in the B-phase texture engendered by the moving interface. This gives rise to friction via orbital viscosity and generates a significant effective mass of the interface. We have incorporated this mechanism into a simple preliminary model which provides reasonable agreement with the measured behaviour.