Superfluid Vortex Research Articles

Vortices in chiral, spin-triplet superconductors and superfluids

Superconductors exhibit unconventional electronic and magnetic properties if the Cooper pair wave function breaks additional symmetries of the normal phase. Rotational symmetries in spin and orbital spaces, as well as discrete symmetries such as space and time inversion, may be spontaneously broken. When this occurs in conjunction with broken global U(1) gauge symmetry, new physical phenomena are exhibited below the superconducting transition that are characteristic of the broken symmetries of the pair condensate. This is particularly true of vortices and related defects. Superconductors with a multi-component order parameter exhibit a variety of different vortex structures and closely related defects that are not possible in condensates belonging to a one-dimensional (1D) representation. In this paper, we discuss the structure of vortices in fermionic superfluids and superconductors which break chiral symmetry, i.e. combined broken time inversion and 2D parity. In particular, we consider the structure of vortices and defects that might be realized in thin films of 3He-A and the layered superconductor Sr2RuO4, and identify some of the characteristic signatures of broken chiral symmetry that should be revealed by these defects.

Periodic flow instabilities in the wake of an ion

Sudden periodical discontinuities in ionic mobilities, first observed in the 1960s in liquid helium II, are suggested to be due to the excitation of the shedding mode harmonics of the vortex ring formed in the wake of the ion. Thus, this phenomenon would parallel the first monoperiodical regime displayed by other flow systems, where the presence of these harmonics has been detected recently in the velocity spectrum. Since the shedding Reynolds number is found to retain its validity in a low-polarizability medium such as liquid helium, the critical velocities for the onset of these instabilities have been derived in a temperature range where dimensional analysis can be applied. Predicted critical velocities are in good agreement with the experimental ones, both for positive and negative ions, postulating the existence of a vortex ring in the roton gas of the ion wake. The shedding mode frequency of this vortex ring is evaluated, and experiments are suggested to test its presence. The critical velocity for the formation of a superfluid vortex ring by an ion has been identified, in good agreement with values extrapolated from larger size objects.

Elementary Vortex Processes in Thermal Superfluid Turbulence

By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics.

Dynamics of Quantum Vorticity in a Random Potential

I study the dynamics of a superfluid vortex in a random potential, as in the inner crust of a neutron star. Below a critical flow velocity of the ambient superfluid, a vortex is effectively immobilized by lattice forces even in the limit of zero dissipation. Low-velocity, translatory motion is not dynamically possible, a result with important implications for understanding neutron star precession and the dynamical properties of superfluid nuclear matter.

Do superfluid instabilities prevent neutron star precession?

We discuss short wavelength (inertial wave) instabilities present in the standard two-fluid neutron star model when there is sufficient relative flow along the superfluid neutron vortex array. We demonstrate that these instabilities may be triggered in precessing neutron stars, since the angular velocity vectors of the neutron and proton fluids are misaligned during precession. Our results suggest that the standard (Eulerian) slow precession that results for weak drag between the vortices and the charged fluid (protons and electrons) is not seriously affected by the instability. In contrast, the fast precession, which results when vortices are strongly coupled to the charged component, is generally unstable. The presence of this instability renders the standard (solid body) rotation model for free precession inconsistent and makes unsafe conclusions that have recently been drawn regarding neutron star interiors based on observations of precession in radio pulsars.

Extremely High Frequency Dependence of Two-Dimensional Superfluid Onset

We observed the frequency dependence of the superfluid transition of 4 He films adsorbed on planar gold up to a very high frequency of 180 MHz, using the overtone harmonic modes of a quartz crystal microbalance. The superfluid onset was observed at a temperature markedly higher than the Kosterlitz–Thouless (KT) transition temperature, the onset temperature in the low-frequency limit. The observed frequency dependence is surprisingly well reproduced by the dynamic theory close to the high-frequency condition where the vortex diffusion length in a period becomes as small as the vortex core diameter. We also observed that the superfluid vortex parameters depend strongly on the kind of substrate as well as on 4 He film thickness.

Looking at electrons

Imaging and tracking of bubbles in liquid helium formed by individual electrons allows study of superfluid vortices, and may permit analysis of unusual ionic species in fluids.

Hydromagnetic waves in a superfluid neutron star with strong vortex pinning

Neutron star cores may be the hosts of a unique mixture of a neutron superfluid and a proton superconductor. Compelling theoretical arguments have been presented over the years that if the proton superconductor is of type II, then the superconductor fluxtubes and superfluid vortices should be strongly coupled and hence the vortices should be pinned to the proton-electron plasma in the core. We explore the effect of this pinning on the hydromagnetic waves in the core, and discuss two astrophysical applications of our results. (i) We show that, even in the case of strong pinning, the core Alfven waves thought to be responsible for the low-frequency magnetar quasi-periodic oscillations (QPO) are not significantly mass loaded by the neutrons. The decoupling of ∼0.95 of the core mass from the Alfven waves is, in fact, required in order to explain the QPO frequencies, for simple magnetic geometries and for magnetic fields not greater than 10 15 G. (ii) We show that in the case of strong vortex pinning, hydromagnetic stresses exert stabilizing influence on the Glaberson instability, which has recently been proposed as a potential source of superfluid turbulence in neutron stars.

Vortex structure of neutron stars with CFL quark cores

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields of nonabelian semi-superfluid vortex filaments in color superconducting cores of neutron stars containing a diquark CFL condensate. The interaction of the diquark CFL condensate with the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of the energies of these filaments are determined from the quantization conditions. It is shown that a lattice of semi-superfluid vortex filaments with a minimal quantum of circulation develops in the quark superconducting core during rotation of the star. The magnetic field in the core of this vortex is on the order of 1018 G. A cluster of proton vortices, which develops in the hadron phase surrounding every superfluid neutron vortex owing to an entrainment effect, creates new semi-superfluid vortex filaments with a minimal quantum of circulation in the quark superconducting core.

Quantum tunneling of vortices in two-dimensional superfluids

We examine the problem of quantum vortex tunneling in the Gross-Pitaevskii model. The effect of gapless phonons is to produce a super-Ohmic quantum dissipation that renormalizes the effective tunneling parameters but does not destroy quantum coherence. The renormalization of the instanton frequency is computed within a specific model tunneling potential.

Non-Abelian strings in high-density QCD: Zero modes and interactions

The most fundamental strings in high density color superconductivity are the non-Abelian semi-superfluid strings which have color gauge flux tube but behave as superfluid vortices in the energetic point of view. We show that in addition to the usual translational zero modes, these vortices have normalizable orientational zero modes in the internal space, associated with the color-flavor locking symmetry broken in the presence of the strings. The interaction among two parallel non-Abelian semi-superfluid strings is derived for general relative orientational zero modes to show the universal repulsion. This implies that the previously known superfluid vortices, formed by spontaneously broken U(1)_B, are unstable to decay. Moreover, our result proves the stability of color superconductors in the presence of external color gauge fields.

Vortex Locking in Direct Numerical Simulations of Quantum Turbulence

Direct numerical simulations are used to examine the locking of quantized superfluid vortices and normal fluid vorticity in evolving turbulent flows. The superfluid is driven by the normal fluid, which undergoes either a decaying Taylor-Green flow or a linearly forced homogeneous isotropic turbulent flow, although the back reaction of the superfluid on the normal fluid flow is omitted. Using correlation functions and wavelet transforms, we present numerical and visual evidence for vortex locking on length scales above the intervortex spacing.

A cellular automaton model of pulsar glitches

A cellular automaton model of pulsar glitches is described, based on the superfluid vortex unpinning paradigm. Recent analyses of pulsar glitch data suggest that glitches result from scale-invariant avalanches \citep{Melatos07a}, which are consistent with a self-organized critical system (SOCS). A cellular automaton provides a computationally efficient means of modelling the collective behaviour of up to $10^{16}$ vortices in the pulsar interior, whilst ensuring that the dominant aspects of the microphysics are not lost. The automaton generates avalanche distributions that are qualitatively consistent with a SOCS and with glitch data. The probability density functions of glitch sizes and durations are power laws, and the probability density function of waiting times between successive glitches is Poissonian, consistent with statistically independent events. The output of the model depends on the physical and computational paramters used. The fitted power law exponents for the glitch sizes ($a$) and durations ($b$) decreases as the strength of the vortex pinning increases. Similarly the exponents increase as the fraction of vortices that are pinned decreases. For the physical and computational parameters considered, one finds $-4.3\leq a \leq -2.0$ and $-5.5\leq b\leq -2.2$, and mean glitching rates in the range $0.0023\leq\lambda\leq0.13\$ in units of inverse time.

Vortex pseudomomentum and dissipation in a superfluid vortex lattice

We propose an alternative approach to the dissipative vortex dynamics occurring in a superfluid vortex lattice at finite temperatures. Focusing upon the pseudomomentum of a vortex and its surrounding quasiparticles, we derive an equation of motion which, in spite of yielding the same evolution as the usual one for massless vortices, does not involve the vortex mass. This picture could provide further insights into the controversy about the nature of the vortex mass.

Dynamics of solid particles in a tangle of superfluid vortices at low temperatures

We present results of numerical study of motion of micron-size, neutrally buoyant, solid particles in liquid helium at temperatures small enough that the normal fluid is negligible and turbulence manifests itself as a tangle of superfluid line vortices. Based on dynamically self-consistent model of interaction between a solid particle and the quantized vortex, we analyze first an influence of temperature on particle trapping on the vortex core. We find that the particle can be trapped only in the case where the particle experiences the damping force, such as the viscous drag force exerted by the normal fluid. However, at temperature below 0.7K, when the normal fluid is practically absent, the moving particle still experiences the damping force caused by the ballistic scattering of quasiparticles (phonons and rotons) off the particle surface. Using, together with our calculation of close interaction between the particle and the quantized vortex, available experimental data and theoretical results for this force, we show that trapping of micron-size, neutrally buoyant particles on quantized vortices becomes impossible at temperatures below 0.5K. At such temperatures, the particle motion in the vortex tangle can be studied based on the simpler, “one-way coupling” model ignoring the backreaction of the particle on the motion and evolution of quantized vortices. Based on such a model, we present results of numerical calculation of particle trajectories in the vortex tangle and show that, due to instability of trajectories and the mismatch of initial velocities of particles and the fluid, the motion of inertial particles does not reveal the motion of turbulent superfluid. We show that particle trajectories between vortex cores are ballistic. Interaction of particles with moving vortices leads to increase of the average particle velocity until it saturates at the value much larger than the fluid rms velocity. These results prevent the use of small tracer particles to study vortex tangles at low temperatures, but open to investigation a new and remarkably simple model of Lagrangian turbulence. We present the probability density function of the turbulent velocity and show that the particle velocity spectrum obeys a simple scaling law.

Population imbalance as a vortex catalyst in Fermi superfluids

Pairing leads to superfluidity in ultracold atomic gases, but this pairing can be frustrated when a population imbalance is present between the pairing partners. Here we investigate how vortices in the fermionic superfluid are affected by imbalance. We show that the vortex core radius is increased by imbalance, accommodating excess component atoms. This has two intriguing consequences. Firstly, a small imbalance acts as a catalyst for vortex formation, decreasing the critical rotation frequency. Secondly, imbalanced gases near critical imbalance can exhibit rotationally induced superfluidity.

Flow of He-II in a Horizontal Capillary in the Presence of a Longitudinal Heat Flux and in a Superfluid Vortex Flow Regime

Flow of He-II in a Horizontal Capillary in the Presence of a Longitudinal Heat Flux and in a Superfluid Vortex Flow Regime

Quantum Turbulence in a Propagating Superfluid Vortex Front

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.

Dissipative Dynamics of Superfluid Vortices at Nonzero Temperatures

We consider the evolution and dissipation of vortex rings in a condensate at nonzero temperatures in the context of the classical field approximation, based on the defocusing nonlinear Schrödinger equation. The temperature in such a system is fully determined by the total number density and the number density of the condensate. The collisions with noncondensed particles reduce the radius of a vortex ring until it completely disappears. We obtain a universal decay law for a vortex line length and relate it to mutual friction coefficients in the fundamental equation of vortex motion in superfluids.

Relaxation of superfluid vortex bundles via energy transfer to the normal fluid

We apply numerical and computational analyses to the decay of a topologically nontrivial, bundle-structured superfluid vortex tangle via mutual friction effected energy transfer to an initially stationary, viscous normal fluid. We demonstrate that, as long as the coherent superfluid vorticity structures remain intact, the induced normal-fluid vorticity acquires a similar to the superfluid vorticity morphology, and the normal-fluid energy spectrum mimics the superfluid energy spectrum presenting a low-wavenumber scaling regime. After a (smaller than the integral advective time scale) transient, the superfluid vorticity bundles disintegrate; this is followed by the decay of normal-fluid energy. The kinetic energies of the two fluids are mismatched throughout the decay period, and the dismantling of coherent vorticity destroys the low-wavenumber energy spectrum scaling in both fluids. At the point of maximum normal-fluid energy, the circulation of the induced normal-fluid vortices is comparable to the ''macroscopic'' circulation of the superfluid vorticity bundles. We show that the superfluid dynamics are dominated throughout the decay period by inertial rather than mutual friction effects, that the formation of bundlelike coherent superfluid vortices cannot be the outcome of pure (reconnecting) Biot-Savart dynamics, and that superfluid vortex length dynamics are not analogous to superfluid energy dynamics. We conjecture that themore » dynamics of fully developed, turbulent thermal superfluid flow could be described in terms of interactions of cyclic coherent vorticity patterns in both fluids.« less