Normal Fluid Component Research Articles

Quantum analog to flapping of flags: interface instability for co-flow binary superfluids

We study the interface dynamics in immiscible binary superfluids using its holographic description, which naturally consists of an inviscid superfluid component and a viscous normal fluid component. We give the first theoretical realization of interface instability for two superfluid components moving with identical velocity, providing a quantum analog to the flapping of flags that is common in daily life. This behavior is in sharp contrast to the one from Gross-Pitaevskii equation for which no such co-flow instability develops in an isolated uniform system because of Galilean invariance. The real time evolution triggered by the dynamical instability exhibits intricate nonlinear patterns leading to quantum turbulence reminiscent of the quantum Kelvin-Helmholtz instability. Moreover, we show that such interface dynamics is essentially different from the Landau instability for which the frictionless flow becomes thermodynamically unstable above a critical superfluid velocity. Our study uncovers the rich interface dynamics of quantum fluids and the emergence of complex flow phenomena.

Orthostatic Hemifacial Spasm in Idiopathic Intracranial Hypertension.

Among the symptoms seen in idiopathic intracranial hypertension (IIH), hemifacial spasm (HFS) is rare. Orthostatic-induced HFS preceding lumbar puncture (LP) is previously unreported. We treated two patients with unusual IIH presentations. This case series reviews the few reports of HFS in IIH and proposes a mechanism for spasm occurrence. Case 1: A woman in her mid-40s with previously controlled IIH developed daily headache, pulsatile tinnitus, right-sided trigeminal paresthesia, and right-sided HFS. The latter 2 symptoms occurred exclusively when moving from a sitting to a standing position. Imaging was unremarkable; opening pressure (OP) on LP was 46 cmH2O with normal cerebrospinal fluid (CSF) components. Case 2: A woman in her late 40s presented with severe daily headache, pulsatile tinnitus, and left-sided HFS following weight gain. Imaging was unremarkable; OP on LP was 32 cmH2O with normal CSF components. HFS episodes persisted following LP in both patients. Increasing and initiating acetazolamide, respectively, resolved all symptoms. Earlier suggested mechanisms of HFS are based on elevated intracranial pressure (ICP) shifting the facial nerve into proximity of a vascular structure. HFS appearing upon standing and continuing after LP, and thus a lower ICP, contradicts this. We propose a mechanism based on the degree of ICP change. This theory is grounded in the lack of intracranial compliance in IIH, wherein substantial pressure changes occur following small volume changes.

Cross-Component Energy Transfer in Superfluid Helium-4

The reciprocal energy and enstrophy transfers between normal fluid and superfluid components dictate the overall dynamics of superfluid 4He including the generation, evolution and coupling of coherent structures, the distribution of energy among lengthscales, and the decay of turbulence. To better understand the essential ingredients of this interaction, we employ a numerical two-way model which self-consistently accounts for the back-reaction of the superfluid vortex lines onto the normal fluid. Here we focus on a prototypical laminar (non-turbulent) vortex configuration which is simple enough to clearly relate the geometry of the vortex line to energy injection and dissipation to/from the normal fluid: a Kelvin wave excitation on two vortex anti-vortex pairs evolving in (a) an initially quiescent normal fluid, and (b) an imposed counterflow. In (a), the superfluid injects energy and vorticity in the normal fluid. In (b), the superfluid gains energy from the normal fluid via the Donnelly–Glaberson instability.

Current-density functional theory for bosonic superfluids

A finite-temperature current-density functional theory for bosonic superfluids (sf-CDFT) in the thermal equilibrium state is proposed herein. In the sf-CDFT, hydrodynamic physical quantities, such as particle number density, current density, and the order parameter of the Bose–Einstein condensation, are chosen as the basic variables. This theory enables the simultaneous reproduction of the particle number and current densities of both the superfluid and normal fluid components with incorporating effects of the interaction between these components. Specifically, these components are determined by solving two single-particle equations, i.e., the Gross–Pitaevskii–Kohn–Sham and Kohn–Sham equations. Furthermore, using the continuity equation of superfluids, we present the sum rule for the exchange-correlation energy functional of the sf-CDFT, which is useful for developing the approximate form.

Flow of the normal component of He-II about bluff objects observed with He2* excimers

Flow of the normal fluid component of He II about a cylinder and flat plate in a channel with a square cross-section was observed by tracking clouds of ${\text{He}}_{2}^{*}$ excimers. Flow was produced using a lithographically patterned heater. The direction and speed of flow projected onto a plane parallel to the axis of the channel and perpendicular to the heater exhibited significant change with time even after the heater was turned off. Flow was recorded in movies. Excimers moved at least as fast as could be recorded by the camera. Velocity vector field maps of flow suggest formation of structures downstream of the cylinder object that are consistent with parts of eddies. In this paper, we establish a foundation to observe normal component flow of a quantum fluid over centimeters.

Motion of a superfluid vortex according to holographic quantum dissipation

Vortices are topological defects associated with superfluids and superconductors, which, when mobile, dissipate energy destroying the dissipationless nature of the superfluid. The nature of this ``quantum dissipation'' is rooted in the quantum physical nature of the problem, which has been the subject of an extensive literature. However, this has mostly been focused on the measures applicable in weakly interacting systems wherein they are tractable via conventional methods. Recently, it became possible to address such dynamical quantum thermalization problems in very strongly interacting systems using the holographic duality discovered in string theory, mapping the quantum problem on a gravitational problem in one higher dimension, having as benefit offering a more general view on how dissipation emerges from such intricate quantum physical circumstances. We study here the elementary problem of a single vortex in two space dimensions, set in motion by a sudden quench in the background superflow formed in a finite-density Reissner-Nordstrom holographic superfluid. This reveals a number of surprising outcomes addressing questions of principle. By fitting the trajectories unambiguously to the Hall-Vinen-Iordanskii phenomenological equation of motion we find that these are characterized by a large inertial mass at low temperature that, however, diminishes upon raising temperature. For a weak drive the drag is found to increase when temperature is lowered, which reveals a simple shear drag associated with the viscous metallic vortex cores, supplemented by a conventional normal fluid component at higher temperatures. For a strong drive we discover a unique dynamical phenomenon: the core of the vortex deforms accompanied by a large increase of the drag force.

Superfluid helium forced flow in the Gorter-Mellink regime

A dimensional study of the momentum equations of superfluid helium is presented together with a parametric analysis of newly derived dimensionless numbers. The study is performed with a focus on the role of forced flows in the Gorter-Mellink regime. The dimensionless numbers are derived in such a way they become dependent solely on the total fluid velocity, heat flux, and thermophysical properties in order to facilitate their application to engineering problems where the velocity of the single fluid components might be difficult to measure directly. With a similar approach, a novel form of the superfluid Reynolds number is obtained. This form takes into account the velocity of a forced flow and allows to make considerations about the contribution of both forced flow and heat flux to the establishment of the ordinary turbulence in the normal fluid component. It is also presented a formula for a channel critical dimension at which the critical heat flux for the onset of superfluid turbulence causes ordinary turbulence too.

On the linearized system of equations for the condensate–normal fluid interaction at very low temperature

AbstractThe linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate density is studied. A simple and transparent argument gives a necessary and sufficient condition for the existence of global solutions satisfying the conservation of the total number of particles and energy. The global solutions describe the evolution in time of the density of the thermal cloud and, unlike in previous work, that of the condensate's density. Their convergence to a suitable stationary state is also shown and rates of convergence for the normal fluid and superfluid components are obtained.

A new self-consistent approach of quantum turbulence in superfluid helium

We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that describes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is governed by a modified Navier–Stokes equation. The superfluid vortex lines and normal fluid components are fully coupled in a self-consistent manner by the friction force, which induces local disturbances in the normal fluid in the vicinity of vortex lines. The main focus of this work is the numerical scheme for distributing the friction force to the mesh points where the normal fluid is defined (stemming from recent advances in the study of the interaction between a classical viscous fluid and small active particles) and for evaluating the velocity of the normal fluid on the Lagrangian discretisation points along the vortex lines. In particular, we show that if this numerical scheme is not careful enough, spurious results may occur. The new scheme which we propose to overcome these difficulties is based on physical principles. Finally, we apply the new method to the problem of the motion of a superfluid vortex ring in a stationary normal fluid and in a turbulent normal fluid.

An experimental setup for creating and imaging 4He2 * excimer cluster tracers in superfluid helium-4 via neutron-3He absorption reaction.

For the purpose of future visualization of the flow field in superfluid helium-4, clusters of the triplet state excimer 4He2 * are generated along the micro-scale recoil tracks of the neutron-absorption reaction n + 3He → 3T + p. This reaction is induced by neutron irradiation of the 3He fraction contained in natural isotopic abundance liquid helium with neutron beams either from the Japan Proton Accelerator Research Complex, Materials and Life Science Experimental Facility (JPARC)/Materials and Life Science Experimental Facility or from the Kyoto University Institute for Integrated Radiation and Nuclear Science. These 4He2 * clusters are expected to be ideal tracers of the normal-fluid component in superfluid helium with several advantageous properties. Evidence of the excimer generation is inferred by detection of laser induced fluorescence emitted from the 4He2 * clusters excited by a purpose-built short pulse gain-switched titanium:sapphire (Ti:sa) laser operating at a wavelength of 905 nm. The setup and performance characteristics of the laser system including the Ti:sa and two continuous wave re-pumping lasers are described. Detection at the fluorescence wavelength of 640 nm is performed by using optical bandpass filtered photomultiplier tubes (PMT). Electrical noise in the PMT acquisition traces could successfully be suppressed by post-processing with a simple algorithm. Despite other laser-related backgrounds, the excimer was clearly identified by its fluorescence decay characteristics. Production of the excimer was found to be proportional to the neutron flux, adjusted via insertion of different collimators into the neutron beam. These observations suggest that the apparatus we constructed does function in the expected manner and, therefore, has the potential for groundbreaking turbulence research with superfluid helium.

Hydrodynamical instabilities in the superfluid interior of neutron stars with background flows between the components

The interiors of mature neutron stars are expected to be superfluid. Superfluidity of matter on the microscopic scale can have a number of large scale, potentially observable consequences, as the superfluid component of the star can now flow relative to the `normal' component that is tracked by electromagnetic emission. The most spectacular of such phenomena are pulsar glitches, sudden spin-ups observed in many pulsars. A background flow of a normal-fluid component with respect to the superfluid is also known to lead to a number of instabilities in laboratory superfluids, possibly leading to turbulence and modifying the nature of the mutual friction coupling between the two fluids. In this paper we consider modes of oscillation in the crust and core of a superfluid neutron star, by conducting a plane-wave analysis. We explicitly account for a background flow between the two components (as would be expected in the presence of pinning) and the entrainment, and we consider both standard (Hall-Vinen) and isotropic (Gorter-Mellink) forms of the mutual friction. We find that for standard mutual friction there are families of unstable inertial and sound waves both in the case of a counter-flow along the superfluid vortex axis and for counterflow perpendicular to the vortex axis and find that entrainment leads to a quantitative difference between instabilities in the crust and core of the star. For isotropic mutual friction we find no unstable modes, and speculate that instabilities in a straight vortex array may be linked to glitching behaviour, which then ceases until the turbulence has decayed.

Strong anisotropy of superfluid He4 counterflow turbulence

We report on a combined theoretical and numerical study of counterflow turbulence in superfluid $^{4}$He in a wide range of parameters. The energy spectra of the velocity fluctuations of both the normal-fluid and superfluid components are strongly anisotropic. The angular dependence of the correlation between velocity fluctuations of the two components plays the key role. A selective energy dissipation intensifies as scales decrease, with the streamwise velocity fluctuations becoming dominant. Most of the flow energy is concentrated in a wavevector plane which is orthogonal to the direction of the counterflow. The phenomenon becomes more prominent at higher temperatures as the coupling between the components depends on the temperature and the direction with respect to the counterflow velocity.

Generation of $$^4$$ 4 He $$_2^*$$ 2 ∗ Clusters via Neutron- $$^3$$ 3 He Absorption Reaction Toward Visualization of Full Velocity Field in Quantum Turbulence

For flow visualization study of quantum turbulence in superfluid $$^4$$ He, He $$_2^*$$ excimers are unique tracers which follow only normal-fluid component flow above 1 K. To generate detectable small He $$_2^*$$ clouds (clusters) required for full-space velocity field measurements, we have adopted a new method based on neutron absorption reaction of $$^3$$ He impurities in $$^4$$ He and conducted proof-of-principle experiments. Generation of the He $$_2^*$$ excimers was detected by laser-induced fluorescence using photomultiplier tubes. The fluorescence was observed to increase proportionally to the neutron flux, suggesting that a sufficient amount of He $$_2^*$$ excimers were generated by neutrons. We also estimated the number of He $$_2^*$$ excimers possibly generated by $$\gamma $$ -rays and found that the relevant contribution was less than 40%. Thus, the majority of the He $$_2^*$$ excimers was confirmed to be generated via n- $$^3$$ He absorption reactions.

Statistics of turbulence and intermittency enhancement in superfluid He4 counterflow

We report a detailed analysis of the energy spectra, second- and high-order structure functions of velocity differences in superfluid $^4$He counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the one-dimensional energy spectrum $E_{xz} (k_y)$ (averaged over the $xz$-plane, parallel to the channel wall), directly measured as a function of the wall-normal wave-vector $k_y$, gives more detailed information on the energy distribution over scales than the corresponding second-order structure function $S_{2}(\delta_y)$. In particular, we discover two intervals of $k_y$ with different apparent exponents: $E_{xz} (k_y)\propto k_y^{-m_C}$ for $k\lesssim k_\times$ and $E_{xz} (k_y)\propto k_y^{-m_F}$ for $k\gtrsim k_\times$. Here $k_\times$ denotes wavenumber that separate scales with relatively strong (for $k\lesssim k_\times$) and relatively weak (for $k\gtrsim k_\times$) coupling between the normal-fluid and superfluid velocity components. We interpret these $k$-ranges as cascade-dominated and mutual friction-dominated intervals, respectively. General behavior of the experimental spectra $E_{xz}(k_y)$ agree well with the predicted spectra [Phys. Rev. B 97, 214513 (2018)]. Analysis of the $n$-th order structure functions statistics shows that in the energy-containing interval the statistics of counterflow turbulence is close to Gaussian, similar to the classical hydrodynamic turbulence. In the cascade- and mutual friction-dominated intervals we found some modest enhancement of intermittency with respect of its level in classical turbulence. However, at small scales, the intermittency becomes much stronger than in the classical turbulence.

Exploration of thermal counterflow in He II using particle tracking velocimetry

Visualization of thermal counterflow in He II using PIV (particle image velocimetry) and PTV (particle tracking velocimetry) is difficult because tracer particle motion can be influenced by both the normal fluid and superfluid components of He II as well as the quantized vortex tangle. For instance, an early PTV experiment observed particles moving at the normal fluid velocity $v_n$, while a PIV experiment observed particles moving at $v_n/2$, though the range of heat flux applied in these experiments differed by an order of magnitude. To resolve this apparent discrepancy and explore statistics of particle motion in thermal counterflow, we have applied PTV to a wide range of heat flux at several fluid temperatures. We introduce a scheme for analyzing the velocity of particles presumably moving with the normal fluid separately from those presumably influenced by the vortex tangle. Our results show two distinct peaks in the streamwise particle velocity PDF (probability density function) for lower heat flux, one centered at the normal fluid velocity $v_n$ ("G2") and one near $v_n/2$ ("G1"). For higher heat flux there is a single peak centered near $v_n/2$ ("G3"). Using our separation scheme we show there is no size difference between particles contributing to G1 and G2. We also show that non-classical features of the transverse velocity PDF arise entirely from G1, while the corresponding PDF for G2 exhibits classical Gaussian form. G2 transverse velocity fluctuation, backed up by second sound attenuation in decaying counterflow, suggests large scale turbulence in the normal fluid is absent from the two peak region. We offer a brief discussion of physical mechanisms that may be responsible for our observations, revealing that G1 velocity fluctuations may be linked to fluctuations of vortex line velocity, and suggest numerical simulations that may reveal underlying physics in detail.

Ultralow-Dissipation Superfluid Micromechanical Resonator

Micro and nanomechanical resonators with ultra-low dissipation have great potential as useful quantum resources. The superfluid micromechanical resonators presented here possess several advantageous characteristics: straightforward thermalization, dissipationless flow, and in situ tunability. We identify and quantitatively model the various dissipation mechanisms in two resonators, one fabricated from borosilicate glass and one from single crystal quartz. As the resonators are cryogenically cooled into the superfluid state, the damping from thermal effects and from the normal fluid component are strongly suppressed. At our lowest temperatures, damping is limited solely by internal dissipation in the substrate materials, and reach quality factors up to 913,000 at 13 mK. By lifting this limitation through substrate material choice and resonator design, modelling suggests that the resonators should reach quality factors as high as 10$^8$ at 100 mK, putting this architecture in an ideal position to harness mechanical quantum effects.

Searching for two-dimensional Weyl superconductors in heterostructures

Two-dimensional Weyl superconductor is the most elusive member of a group of materials with Weyl fermions as low-energy excitations. Here, we propose to realize this state in a heterostructure consisting of thin films of half-metal and spin-singlet superconductor. In particular, for the $d$-wave case, a very robust two-dimensional Weyl superconductor (dWSC) is realized independent of the orientation of the spontaneous magnetization of the half-metal. The quasiparticle spectra of the dWSC show interesting evolution with the direction of the magnetization, featured by a series of Lifshitz transitions in the zero-energy contour of the quasiparticle spectrum. For a general magnetization orientation of the half-metal, the state is a combination of a superconducting component and a normal fluid component and is different from all known forms of pairings. In addition, we find a transition between type-I and type-II Weyl nodes. This is also the first example of a type-II Weyl node in the presence of superconducting correlation. The symmetries and topological properties of the system are analyzed. We also study the phases in the heterostructure with the half-metal replaced by a ferromagnetic metal with a partially spin-polarized Fermi surface.

Numerical Investigation of Thermal Counterflow of He II Past Cylinders.

We investigate numerically, for the first time, the thermal counterflow of superfluid helium past a cylinder by solving with a finite volume method the complete so-called two-fluid model. In agreement with existing experimental results, we obtain symmetrical eddies both up- and downstream of the obstacle. The generation of these eddies is a complex transient phenomenon that involves the friction of the normal fluid component with the solid walls and the mutual friction between the superfluid and normal components. Implications for flow in a more realistic porous medium are also investigated.

Erratum to: Statistical Measurement of Counterflow Turbulence in Superfluid Helium-4 Using $$\hbox {He}^{{*}}_{2}$$ He 2 ∗ Tracer-Line Tracking Technique

We report preliminary results of a systematic study of the flow of normal fluid component in steady-state quantum turbulence in thermal counterflow of superfluid \(^{4}\hbox {He}\) using a high-precision flow visualisation technique based on the tracking of thin lines of \(\hbox {He}_2^{*}\) molecular tracers. Non-trivial profiles of mean velocity and turbulent fluctuation across the channel are observed with complicated temperature- and heat flux-dependencies. Mean turbulence intensity, however, depends on velocity only very weakly and is controlled primarily by the temperature.

Statistical Measurement of Counterflow Turbulence in Superfluid Helium-4 Using $$\hbox {He}_2^*$$ Tracer-Line Tracking Technique

We report preliminary results of a systematic study of the flow of normal fluid component in steady-state quantum turbulence in thermal counterflow of superfluid \(^{4}\hbox {He}\) using a high-precision flow visualisation technique based on the tracking of thin lines of \(\hbox {He}_2^{*}\) molecular tracers. Non-trivial profiles of mean velocity and turbulent fluctuation across the channel are observed with complicated temperature- and heat flux-dependencies. Mean turbulence intensity, however, depends on velocity only very weakly and is controlled primarily by the temperature.