Probing "cosmological" defects in superfluid 3He-B with a vibrating-wire resonator

We report on the observation of an anomalously high damping measured by a vibrating-wire resonator (VWR) immersed into superfluid at ultralow temperatures. The observed dissipation is orders of magnitude above that corresponding to friction with the dilute normal fraction and superfluid vortices. A clear pinning behavior is also observed, as well as a strong magnetic field dependence. Our analysis points to the interaction of the VWR with a planar topological defect, analogue to cosmological vacua defects, as proposed by Salomaa and Volovik.     

Observation of wave energy accumulation in the turbulent spectrum of capillary waves on the He-II surface under harmonic pumping

Recent results of the experimental study of capillary turbulence on superfluid helium-4 surface are presented. For the first time wave energy accumulation was observed in the wave turbulent spectrum at high frequencies when the surface was excited by harmonic pumping. We suggest a qualitative explanation of this phenomenon in the frames of weak wave turbulence approach that takes into account discreteness of the eigenfrequencies spectrum of surface oscillations in the cylindrical resonator.     

Topological noise scalings in superfluid and classical turbulence

We calculate the topological noise characterizing the direction of line vortices in superfluid and classical turbulence by finding the intersection of line vortices with square surfaces of edge length l_s positioned normal to three orthogonal axes. In the case of homogeneous superfluid turbulence in thermal counterflow, we find that the noise scales as l_s along the two directions normal to the counterflow and as l _s ^3/2 along the direction parallel to it. In homogeneous isotropic superfluid turbulence, at T→0 K, the noise scales as l _s ^7/4 . In homogeneous isotropic classical turbulence, the scaling is l _s ² . We offer possible interpretations of the computed scalings, as well as justification for their differences.     

Decay of counterflow turbulence in superfluid <Superscript>4</Superscript>He

We summarize recent experiments on thermal counterflow turbulence in superfluid ⁴He, emphasizing the observation of turbulence in the normal fluid and its effect on the decay process when the heat flux is turned off. We argue that what is observed as turbulence in the normal fluid is a novel form of coupled turbulence in the superfluid and normal components, with injection of energy on the scales of both the (large) channel width and the (small) spacing between quantized vortices. Although an understanding of this coupled turbulence remains challenging, a theory of its decay is developed which accounts for the experimental observations.     

Classical and quantum regimes of superfluid turbulence

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q^?1 playing the same role as the Reynolds number Re=UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re?1 in classical hydrodynamics, and q?1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re_s=UR/κ, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.     

Detection and imaging of He2 molecules in superfluid helium

We present data that show a cycling transition can be used to detect and image metastable He2 triplet molecules in superfluid helium. We demonstrate that limitations on the cycling efficiency due to the vibrational structure of the molecule can be mitigated by the use of repumping lasers. Images of the molecules obtained using the method are also shown. This technique gives rise to a new kind of ionizing radiation detector. The use of He2 triplet molecules as tracer particles in the superfluid promises to be a powerful tool for visualization of both quantum and classical turbulence in liquid helium.     

Analysis of the turbulent boundary layer in the vicinity of a self-excited cylindrical Helmholtz resonator

This study investigates the changes in the structure of a turbulent boundary layer downstream of a flow-excited Helmholtz resonator. To this end, a fully developed turbulent boundary layer over a resonator mounted flush with a flat plate was simulated by implementing a large eddy simulation (LES). To assist in understanding the effect of the resonator on the flow structure, a sensitivity study was undertaken by changing the main geometrical parameters of the resonator. The results demonstrated that when the boundary layer thickness equals the orifice length, the cross-stream component of velocity fluctuations penetrates the boundary layer, resulting in a reduction of the turbulence intensity by up to 12%. Therefore, it is concluded that a Helmholtz resonator has the potential to reduce the instabilities within the boundary layer. These investigations also assist in identifying the optimal parameters to delay turbulence events within the grazing flow using Helmholtz resonators.     

Decay of pure quantum turbulence in superfluid 3He-B

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.     

Quantum hydrodynamics

Quantum hydrodynamics in superfluid helium and atomic Bose–Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function (order parameter) appears because of Bose–Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in ⁴${}^4$He, which has no analog with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), “Quantized vortices in superfluid helium and atomic Bose–Einstein condensates”, and other review articles.     

Quantum-limited sensitivity of single-electron-transistor-based displacement detectors

We consider a model of a quantum-mechanical resonator capacitively coupled to a single electron transistor (SET). The tunnel current in the SET is modulated by the vibrations of the resonator, and thus the system operates as a displacement detector. We analyze the effect of the backaction noise of charge fluctuations in the SET onto the dynamics of the resonator and evaluate the displacement sensitivity of the system. The relation between the "classical" and "quantum" parts of the SET charge noise and their effect on the measured system are also discussed.     

Vortex instability and the onset of superfluid turbulence

Quantized circulation, the absence of Galilean invariance due to a clamped normal component, and the vortex mutual friction are the major factors that make superfluid turbulence behave in a way different from that in classical fluids. The model is developed for the onset of superfluid turbulence that describes the initial avalanchelike multiplication of vortices into a turbulent vortex tangle.     

Kelvin-wave cascade and decay of superfluid turbulence

Kelvin waves (kelvons), the distortion waves on vortex lines, play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that nontrivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; a corresponding kinetic equation is derived. We prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.     

Turbulence in boundary flow of superfluid 4He triggered by free vortex rings

The transition to turbulence in the boundary flow of superfluid 4He is investigated using a vortex-free vibrating wire. At high wire vibration velocities, we found that stable alternating flow around the wire enters a turbulent phase triggered by free vortex rings. Numerical simulations of vortex dynamics demonstrate that vortex rings can attach to the surface of an oscillating obstacle and expand unstably due to the boundary flow of the superfluid, forming turbulence. Experimental investigations indicate that the turbulent phase continues even after stopping the injection of vortex rings, which is also confirmed by the simulations.     

Repetitive single vortex-loop creation by a vibrating wire in superfluid 3He-B

Spectacular features are observed on the velocity-force characteristics of a vibrating wire resonator in superfluid 3He-B at ultralow temperatures. Both plateaus and discontinuities are seen in the characteristics. The plateaus seem to have two separate critical velocities where first some "event" occurs, which causes the wire to lose energy and slow down, followed by a second lower critical velocity where the event decouples. It is suggested that these events are due to vortex-loop creation at protuberances on the vibrating wire. This opens up the possibility of controlling the creation of vorticity through specially prepared protuberances.     

The effects of colored quadratic noise on a turbulent transition in liquid4He

Liquid⁴He presents an important physical system for the experimental study of noise-induced dynamical transitions. At temperatures belowT in the He II phase, the flow of heat in the liquid helium is limited by a kind of superfluid turbulence. The steady-state properties of this turbulence are adequately described by a dense tangle of quantized vortex lines in the superfluid component of the He II. The turbulence undergoes a continuous transition as the heat current is increased. At this transition the intrinsic fluctuations in the dissipation and the relaxation time both become large [D. Griswold, C. P. Lorenson, and J. T. Tough,Phys. Rev. B 35:3149 (1987)]. These observations are consistent with a model of the transition as an imperfect pitchfork bifurcation [M. Schumaker and W. Horsthemke,Phys. Rev. A 36:354 (1987)]. External noise can be easily added to the driving heat current. Small-amplitude noise simply causes the system to fluctuate about the deterministic steady states. Large-amplitude noise causes dramatic changes. The stochastic steady states of the turbulence show noise-induced bistability [D. Grisowld and J. T. Tough,Phys. Rev. A 36:1360 (1987)]. Comparison with the imperfect pitchfork model is difficult because the noise is colored, quadratic, and large. Nevertheless, an approximate result obtained by Schumaker and Horsthemke is in good qualitative agreement with the data.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Quenched Kosterlitz-Thouless superfluid transitions

Rapidly quenched Kosterlitz-Thouless (KT) superfluid transitions are studied by solving the Fokker-Planck equation for the vortex-pair dynamics in conjunction with the KT recursion relations. Power-law decays of the vortex density at long times are found, and the results are in agreement with a scaling proposal made by Minnhagen and co-workers for the dynamical critical exponent. The superfluid density is strongly depressed after a quench, with the subsequent recovery being logarithmically slow for starting temperatures near T(KT). No evidence is found of vortices being "created" in a rapid quench; there is only decay of the existing thermal vortex pairs.     

Attenuation of second sound in superfluid 3He-A1

The attenuation of second sound (spin-entropy) wave in the superfluid A1 phase has been measured in magnetic fields up to 11 T and to sufficiently high frequency to observe the bulk attenuation proportional to the square of frequency. The measured attenuation coefficient is compared with the existing theories of hydrodynamics and dissipative coefficients. The resulting "excess" attenuation is discussed in terms of the temperature dependent spin diffusion coefficient in the superfluid.     

Mutual-friction induced instability of normal-fluid vortex tubes in superfluid helium-4

It is shown that, as a result of its interactions with superfluid vorticity, a normal-fluid vortex tube in helium-4 becomes unstable and disintegrates. The superfluid vorticity acquires only a small (few percents of normal-fluid tube strength) polarization, whilst expanding in a front-like manner in the intervortex space of the normal-fluid, forming a dense, unstructured tangle in the process. The accompanied energy spectra scalings offer a structural explanation of analogous scalings in fully developed finite-temperature superfluid turbulence. A macroscopic mutual-friction model incorporating these findings is proposed.     

Fluctuations and Correlations of Pure Quantum Turbulence in Superfluid 3He-B

We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.