Quantized Vortex Lines Research Articles

On the electric charge of quantized vortices and the dipole moment of vortex pairs and rings in a magnetic field

It is shown that, in the presence of a magnetic field, a quantized vortex line in a superfluid liquid acquires a linear polarization charge, which is localized near the vortex axis over a length on the order of the coherence length. It is found that the total charge of a rectilinear vortex is nonzero, while the vortex pair and vortex ring have a nonzero dipole moment. The electric fields of rectilinear vortices near the end surface of a cylindrical vessel filled with a superfluid liquid are calculated. The electric polarization of superfluid systems in the presence of thermally activated vortex pairs and vortex rings has been studied. It is shown that such a polarization arises in the presence of relative motion of the normal and superfluid components.

Dissipation anomaly in a turbulent quantum fluid

In this work we show evidence for a superfluid analog to the classical dissipation anomaly: When the friction tends to zero, the dissipation does not vanish, but levels off to a constant non-zero value. This characteristic stems from the generation of smaller and smaller structures on the quantized vortex lines as the friction is lowered. This property of quantum turbulence is universal, not depending on the dynamics of the large scales.

Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence

Generic scaling laws, such as Kolmogorov's 5/3 law, are milestone achievements of turbulence research in classical fluids. For quantum fluids such as atomic Bose-Einstein condensates, superfluid helium, and superfluid neutron stars, turbulence can also exist in the presence of a chaotic tangle of evolving quantized vortex lines. However, due to the lack of suitable experimental tools to directly probe the vortex-tangle motion, so far little is known about possible scaling laws that characterize the velocity correlations and trajectory statistics of the vortices in quantum-fluid turbulence, i.e., quantum turbulence (QT). Acquiring such knowledge could greatly benefit the development of advanced statistical models of QT. Here we report an experiment where a tangle of vortices in superfluid 4He are decorated with solidified deuterium tracer particles. Under experimental conditions where these tracers follow the motion of the vortices, we observed an apparent superdiffusion of the vortices. Our analysis shows that this superdiffusion is not due to Lévy flights, i.e., long-distance hops that are known to be responsible for superdiffusion of random walkers. Instead, a previously unknown power-law scaling of the vortex-velocity temporal correlation is uncovered as the cause. This finding may motivate future research on hidden scaling laws in QT.

Simulating pulsar glitches: anN-body solver for superfluid vortex motion in two dimensions

ABSTRACTA rotating superfluid forms an array of quantized vortex lines that determine its angular velocity. The spasmodic evolution of the array under the influence of deceleration, dissipation, and pinning forces is thought to be responsible for the phenomenon of pulsar glitches, sudden jumps in the spin frequency of rotating neutron stars. We describe and implement an N-body method for simulating the motion of up to 5000 vortices in two dimensions and present the results of numerical experiments validating the method, including stability of a vortex ring and dissipative formation of an Abrikosov array. Vortex avalanches occur routinely in the simulations, when chains of unpinning events are triggered collectively by vortex–vortex repulsion, consistent with previous, smaller scale studies using the Gross–Pitaevskii equation. The probability density functions of the avalanche sizes and waiting times are consistent with both exponential and lognormal distributions. We find weak correlations between glitch sizes and waiting times, consistent with astronomical data and meta-models of pulsar glitch activity as a state-dependent Poisson process or a Brownian stress-accumulation process, and inconsistent with a threshold-triggered stress-release model with a single, global stress reservoir. The spatial distribution of the effective stress within the simulation volume is analysed before and after a glitch.

Coarse-grained pressure dynamics in superfluid turbulence

Coarse-grained superfluid dynamics are investigated through detailed numerical simulation at the level of individual quantized vortex lines. Simulations show a strong correlation between the formation of quantized vortex bundles and the production of extreme negative pressure regions in excess of 3 standard deviations. This motivates the use of experimental pressure measurements for probing superfluid turbulence at low temperatures.

Formula omitted]-[formula omitted]-[formula omitted] model in turbulent superfluid helium

We generalize the K−ϵ model of classical turbulence to superfluid helium. In a classical viscous fluid the phenomenological eddy viscosity characterizing the effects of turbulence depends on the turbulent kinetic energy K and the dissipation function ϵ, which are mainly related to the fluctuations of the velocity field and of its gradient. In superfluid helium, instead, we consider the necessary coefficients for describing the effects of classical and quantum turbulence, involving fluctuations of the velocity, the heat flux, and the vortex line density of the quantized vortex lines. By splitting the several fields into a time-average part and a fluctuating part, some expressions involving the second moments of the turbulent fluctuations appear in the evolution equations for the average quantities. As in the K−ϵ model, a practical way of closing such equations is to tentatively express such fluctuating terms as a function of the average quantities. In this context we propose how the turbulent coefficients so introduced could depend on the second moments of the fluctuations of v, q and L (respectively denoted as K, Kq and KL), and on their respective dissipation functions (related to the second moments of their gradients) ϵ, ϵq and ϵL.

Crossover from interaction to driven regimes in quantum vortex reconnections

Reconnections of coherent filamentary structures play a key role in the dynamics of fluids, redistributing energy and helicity among the length scales, triggering dissipative effects, and inducing fine-scale mixing. Unlike ordinary (classical) fluids where vorticity is a continuous field, in superfluid helium and in atomic Bose-Einstein condensates (BECs) vorticity takes the form of isolated quantized vortex lines, which are conceptually easier to study. New experimental techniques now allow visualization of individual vortex reconnections in helium and condensates. It has long being suspected that reconnections obey universal laws, particularly a universal scaling with time of the minimum distance between vortices δ. Here we perform a comprehensive analysis of this scaling across a range of scenarios relevant to superfluid helium and trapped condensates, combining our own numerical simulations with the previous results in the literature. We reveal that the scaling exhibits two distinct fundamental regimes: a [Formula: see text] scaling arising from the mutual interaction of the reconnecting strands and a [Formula: see text] scaling when extrinsic factors drive the individual vortices.

Inviscid diffusion of vorticity in low-temperature superfluid helium

We numerically study the spatial spreading of quantized vortex lines in low temperature liquid helium. The vortex lines, initially concentrated in a small region, diffuse into the surrounding vortex-free helium, a situation which is typical of many experiments. We find that this spreading, which occurs in the absence of viscosity, emerges from the interactions between the vortex lines, and can be interpreted as a diffusion process with effective coefficient equal to approximately 0.5$\kappa$ where $\kappa$ is the quantum of circulation.

Creation of a Dirac monopole-antimonopole pair in a spin-1 Bose-Einstein condensate

We theoretically demonstrate that a pair of Dirac monopoles with opposite synthetic charges can be created within a single spin-1 Bose-Einstein condensate by steering the spin degrees of freedom by external magnetic fields. Although the net synthetic magnetic charge of this configuration vanishes, both the monopole and the antimonopole are accompanied by vortex filaments carrying opposite angular momenta. Such a Dirac dipole can be realized experimentally by imprinting a spin texture with a nonlinear magnetic field generated by a pair of coils in a modified Helmholtz configuration. We also investigate the case where the initial state for the dipole-creation procedure is pierced by a quantized vortex line with a winding number k. It is shown that if k = -1, the resulting monopole and antimonopole lie along the core of a singly quantized vortex whose sign is reversed at the locations of the monopoles. For k = -2, the monopole and antimonopole are connected by a vortex line segment carrying two quanta of angular momentum, and hence the dipole as a whole is an isolated configuration. In addition, we simulate the long-time evolution of the dipoles in the magnetic field used to create them. For k = 0, each of the semi-infinite doubly quantized vortices splits into two singly quantized vortices, as in the case of a single Dirac monopole. For k = -1 and k = -2, the initial vortices deform into a vortex with a kink and a vortex ring, respectively.

Characterizing vortex tangle properties in steady-state He II counterflow using particle tracking velocimetry

Historically, there is little faith in particle tracking velocimetry (PTV) as a tool to make quantitative measurements of thermal counterflow in He II, since tracer particle motion is complicated by influences from the normal fluid, superfluid, and quantized vortex lines, or a combination thereof. Recently, we introduced a scheme for differentiating particles trapped on vortices (G1) from particles entrained by the normal fluid (G2). In this paper, we apply this scheme to demonstrate the utility of PTV for quantitative measurements of vortex dynamics in He II counterflow. We estimate $\ell$, the mean vortex line spacing, using G2 velocity data, and $c_2$, a parameter related to the mean curvature radius of vortices and energy dissipation in quantum turbulence, using G1 velocity data. We find that both estimations show good agreement with existing measurements that were obtained using traditional experimental methods. This is of particular consequence since these parameters likely vary in space, and PTV offers the advantage of spatial resolution. We also show a direct link between power-law tails in transverse particle velocity probability density functions (PDFs) and reconnection of vortex lines on which G1 particles are trapped.

Orthogonal and antiparallel vortex tubes and energy cascades in quantum turbulence

We investigate the dynamics of energy cascades in quantum turbulence by directly observing the vorticity distributions in numerical simulations of the Gross-Pitaevskii equation. By Fourier filtering each scale of the vorticity distribution, we find that antiparallel vortex tubes at a large scale generate small-scale vortex tubes orthogonal to those at the large scale, which is a manifestation of the energy cascade from large to small scales. We reveal the dynamics of quantized vortex lines in these processes.

Vortices in self-bound dipolar droplets

Quantized vortices have been observed in a variety of superfluid systems, from $^4$He to condensates of alkali-metal bosons and ultracold Fermi gases along the BEC-BCS crossover. In this article we study the stability of singly quantized vortex lines in dilute dipolar self-bound droplets. We first discuss the energetic stability region of dipolar vortex excitations within a variational ansatz in the generalized nonlocal Gross-Pitaevskii functional that includes quantum fluctuation corrections. We find a wide region where stationary solutions corresponding to axially-symmetric vortex states exist. However, these singly-charged vortex states are shown to be unstable, either by splitting the droplet in two fragments or by vortex-line instabilities developed from Kelvin-wave excitations. These observations are the results of large-scale fully three-dimensional simulations in real time. We conclude with some experimental considerations for the observation of such states and suggest possible extensions of this work.

Dissipation in quantum turbulence in superfluid He4 above 1 K

There are two commonly discussed forms of quantum turbulence in superfluid $^4$He above 1K: in one there is a random tangle of quantizes vortex lines, existing in the presence of a non-turbulent normal fluid; in the second there is a coupled turbulent motion of the two fluids, often exhibiting quasi-classical characteristics on scales larger than the separation between the quantized vortex lines in the superfluid component. The decay of vortex line density, $L$, in the former case is often described by the equation $dL/dt=-\chi_2 (\kappa/2\pi)L^2$, where $\kappa$ is the quantum of circulation, and $\chi_2$ is a dimensionless parameter of order unity. The decay of total turbulent energy, $E$, in the second case is often characterized by an effective kinematic viscosity, $\nu'$, such that $dE/dt=-\nu' \kappa^2 L^2$. We present new values of $\chi_2$ derived from numerical simulations and from experiment, which we compare with those derived from a theory developed by Vinen and Niemela. We summarise what is presently known about the values of $\nu'$ from experiment, and we present a brief introductory discussion of the relationship between $\chi_2$ and $\nu'$, leaving a more detailed discussion to a later paper.

Dynamics of the density of quantized vortex lines in counterflow turbulence: Experimental investigation

Recently the interest in thermal counterflow of superfluid $^{4}\mathrm{He}$, the most extensively studied form of quantum turbulence, has been renewed. Particularly, an intense theoretical debate has arisen about what form, if any, of the so-called Vinen equation accurately captures the dynamics of vortex line density, $L$. We address this problem experimentally, in a 21 cm long channel of square $7\ifmmode\times\else\texttimes\fi{}7\phantom{\rule{4pt}{0ex}}{\mathrm{mm}}^{2}$ cross section. Based on large statistics of second-sound data measured in nonequilibrium square-wave modulated thermally induced counterflow we investigate the phase portrait of the general form of the governing dynamical equation and conclude that for sparse tangles $(L\ensuremath{\lesssim}{10}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2})$ all proposed forms of this equation based on the concept of a homogeneous random tangle of quantized vortices provide equally adequate descriptions of the growth of $L$, while for dense tangles $(Lg{10}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2})$ none of them is satisfactory or able to account for the significant slow-down in tangle growth rate as the steady state is approached. We claim, however, that agreement with theory is recovered if the geometrical parameter ${c}_{2}$ introduced in numerical studies by K. W. Schwarz [Phys. Rev. B 38, 2398 (1988)] is allowed to vary with vortex line density which also greatly improves the prediction of the observed early decay rate.

Dynamics of the vortex line density in superfluid counterflow turbulence

Describing superfluid turbulence at intermediate scales between the inter-vortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines $\cal{L}$. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides $\cal{L}$ and the normal and superfluid velocity fields. In this paper we offer a minimal closure using one additional anisotropy parameter $I_{l0}$. Using the example of counterflow superfluid turbulence we derive two coupled closure equations for the vortex line density and the anisotropy parameter $I_{l0}$ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.

Hydrodynamical model of anisotropic, polarized turbulent superfluids. I: constraints for the fluxes

This work is the first of a series of papers devoted to the study of the influence of the anisotropy and polarization of the tangle of quantized vortex lines in superfluid turbulence. A thermodynamical model of inhomogeneous superfluid turbulence previously formulated is here extended, to take into consideration also these effects. The model chooses as thermodynamic state vector the density, the velocity, the energy density, the heat flux, and a complete vorticity tensor field, including its symmetric traceless part and its antisymmetric part. The relations which constrain the constitutive quantities are deduced from the second principle of thermodynamics using the Liu procedure. The results show that the presence of anisotropy and polarization in the vortex tangle affects in a substantial way the dynamics of the heat flux, and allow us to give a physical interpretation of the vorticity tensor here introduced, and to better describe the internal structure of a turbulent superfluid.

Modeling of classical turbulence by quantized vortices

Quantum turbulence in superfluids appears as a stochastic tangle of quantized vortex lines. Interest to this system extends beyond the field of superfluid helium to include a large variety of topics both fundamental and engineering problem. In the article we present a discussion of the hot topic, which is undoubtedly mainstream in this field, and which deals with the quasi-classical properties of quantum turbulence. The idea that classical turbulence can be modeled by a set of slim vortex tubes (or vortex sheets) has been discussed for quite a long time. In classical fluids, the concept of thin vortex tubes is a rather fruitful mathematical model. Quantum fluids, where the vortex filaments are real objects, give an excellent opportunity for the study of the question, whether the dynamics of a set of vortex lines is able to reproduce (at least partially) the properties of real hydrodynamic turbulence. The main goal of this article is to discuss the current state of this activity. We cover such important topics as theoretical justification of this model, and experimental and numerical evidence for quasi-classical turbulence.

Flux-Vortex Pinning and Neutron Star Evolution

G. Srinivasan et al. (1990) proposed a simple and elegant explanation for the reduction of the neutron star magnetic dipole moment during binary evolution leading to low mass X-ray binaries and eventually to millisecond pulsars: Quantized vortex lines in the neutron star core superfluid will pin against the quantized flux lines of the proton superconductor. As the neutron star spins down in the wind accretion phase of binary evolution, outward motion of vortex lines will reduce the dipole magnetic moment in proportion to the rotation rate. The presence of a toroidal array of flux lines makes this mechanism inevitable and independent of the angle between the rotation and magnetic axes. The incompressibility of the flux-line array (Abrikosov lattice) determines the epoch when the mechanism will be effective throughout the neutron star. Flux vortex pinning will not be effective during the initial young radio pulsar phase. It will, however, be effective and reduce the dipole moment in proportion with the rotation rate during the epoch of spindown by wind accretion as proposed by Srinivasan et al. The mechanism operates also in the presence of vortex creep.

Vortex Reconnections and Rebounds in Trapped Atomic Bose-Einstein Condensates

Reconnections and interactions of filamentary coherent structures play a fundamental role in the dynamics of fluids, plasmas and nematic liquid crystals. In fluids, vortex reconnections redistribute energy and helicity among the length scales and induce fine-scale turbulent mixing. Unlike ordinary fluids where vorticity is a continuous field, in quantum fluids vorticity is concentrated into discrete (quantized) vortex lines turning vortex reconnections into isolated events, making it conceptually easier to study. Here we report experimental and numerical observations of three-dimensional quantum vortex interactions in a cigar-shaped atomic Bose-Einstein Condensate (BEC). In addition to standard reconnections, already numerically and experimentally observed in homogeneous systems away from boundaries, we show that double reconnections, rebounds and ejections can also occur as a consequence of the non-homogeneous, confined nature of the system.

Detection of vortex coherent structures in superfluid turbulence

Filamentary regions of high vorticity irregularly form and disappear in the turbulent flows of classical fluids. We report an experimental comparative study of these so-called “coherent structures” in a classical vs. quantum fluid, using liquid helium with a superfluid fraction varied from 0% up to 83%. The low-pressure core of the vorticity filaments is detected by pressure probes located on the sidewall of a 78-cm-diameter von Kármán cell driven up to record turbulent intensity . The statistics of occurrence, magnitude and relative distribution of the filaments in a classical fluid are found indistinguishable from their superfluid counterpart, namely the bundles of quantized vortex lines. This suggests that the internal structure of vortex filaments, as well as their dissipative properties have a negligible impact on their macroscopic dynamics, such as lifetime and intermittent properties.