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Physical Review B

Frequency-dependent drag from quantum turbulence produced by quartz tuning forks in superfluid He4

S. L. Ahlstrom, D. I. Bradley, Marcel Človečko, S. N. Fisher, A. M. Guénault, E. A. Guise, R. P. Haley, Oleg Kolosov, P. V. E. McClintock, G. R. Pickett, M. Poole, V. Tsepelin, Andrew Woods

Published Jan 30, 2014• 27 citations
Publisher

Abstract

We have measured the drag force from quantum turbulence on a series of quartz tuning forks in superfluid helium. The tuning forks were custom made from a 75-$\ensuremath{\mu}$m-thick wafer. They have identical prong widths and prong spacings, but different lengths to give different resonant frequencies. We have used both the fundamental and overtone flexure modes to probe the turbulent drag over a broad range of frequencies $f=\ensuremath{\omega}/2\ensuremath{\pi}$ from 6.5 to 300 kHz. Optical measurements show that the velocity profiles of the flexure modes are well described by a cantilever beam model. The critical velocity for the onset of quantum turbulence at low temperatures is measured to be ${v}_{c}\ensuremath{\approx}\sqrt{0.7\ensuremath{\kappa}\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega}}$ where $\ensuremath{\kappa}$ is the circulation quantum. The drag from quantum turbulence shows a small frequency dependence when plotted against the scaled velocity $v/{v}_{c}$.

DOI
10.1103/physrevb.89.014515

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We have measured the drag force from quantum turbulence on a series of quartz tuning forks in superfluid helium. The tuning forks were custom made from a 75-\ensuremathμ\ensuremath{\mu}\ensuremathμm-thick wafer. They have identical prong widths and prong spacings, but different lengths to give different resonant frequencies. We have used both the fundamental and overtone flexure modes to probe the turbulent drag over a broad range of frequencies f=\ensuremathω/2\ensuremathπf=\ensuremath{\omega}/2\ensuremath{\pi}f=\ensuremathω/2\ensuremathπ from 6.5 to 300 kHz. Optical measurements show that the velocity profiles of the flexure modes are well described by a cantilever beam model. The critical velocity for the onset of quantum turbulence at low temperatures is measured to be vc\ensuremath≈0.7\ensuremathκ\ensuremathω{v}_{c}\ensuremath{\approx}\sqrt{0.7\ensuremath{\kappa}\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega}}vc​\ensuremath≈0.7\ensuremathκ\ensuremathω​ where \ensuremathκ\ensuremath{\kappa}\ensuremathκ is the circulation quantum. The drag from quantum turbulence shows a small frequency dependence when plotted against the scaled velocity v/vcv/{v}_{c}v/vc​.
In this thesis we use quartz tuning fork resonators to probe properties of normal and superfluid 4He and 3He. Our main goal is to study both quantum turbulence and acoustic emission of tuning forks in liquid helium. By employing a multi-frequency lock-in amplifier we contrast single and multi- frequency methods of measuring tuning forks in the linear regime. In the non-linear response of tuning forks during turbulence we create multi-frequency excitations called intermodulation products which are used to find the non-linear forces that created them. We apply this technique to quantum turbulence in superfluid 4He-II and find that the retarding in-phase force on the fork increases at a critical velocity for turbulence nucleation. We also observe that the out-of-phase non-linear force increases, which we attribute to energy loss via vortex ring emission by the fork. Superfluid 3He is a fermionic condensate of Cooper pairs of 3He atoms. At ultra-low temperatures of 120 μK thermally excited unpaired quasiparticles travel ballistically through the condensate. We beam quasiparticles from a black body source towards a 5 × 5-pixel camera and observe that the excitations follow photonic-like trajectories. We apply the source-camera configuration to non-invasively detect and even image quantum vortices, that are topological defects in the superfluid. Lastly, we explore the frequency dependent damping of quartz tuning forks in liquid 3He. We find that at high frequencies the fork damping is governed by acoustic emission. Furthermore, we show that existing models developed for sound emission in 4He can be used to predict observed acoustic damping in 3He. The results also suggest that devices for 3He experiments should be placed in cavities or designed to operate at low frequencies.
In this Thesis, we present an excessive study of the dynamics of quantum fluids em- ploying the detectors in the form of mechanical resonating structures with characteristic dimensions below 1 mm. We operate the devices in normal and superfluid liquid phases of both helium isotopes scanning the wide range of temperatures between 2.17 K and ≈ 150 µK. We show, that the detectors in the form of quartz tuning forks and supercon- ducting vibrating wires are suitable probes in both hydrodynamic and ballistic regimes of superfluids, described by two-fluid model. These devices can be used to initiate and observe turbulent transition in quantum fluids leading to the generation of quantum tur- bulence. The same devices can work as detectors of externally driven turbulent flows. The phenomenon of quantum turbulence, representing any turbulent flow of quantum fluids, is discussed in more detail. We further report observation of turbulent onset in mechanically and thermally driven oscillatory flows. This transition can have origin in both of the components of superfluid 4 He, leading to either classical-like instability or "quantum" instability connected with the generation of quantized vortices. Finally, we discuss the properties and potential of the MEMS and NEMS devices, advancing from much smaller dimensions,...
Quantum turbulence is a conceptually simple form of turbulence, consisting of a tangle of quantised vortex lines. It provides a model system, through which it may be possible to understand features of the complex and not yet fully understood classical turbulence. A novel detector made from arrays of custom-designed tuning forks was developed and used to investigate properties of excitation beams and quantum turbulence in superfluid 3He-B at temperatures below 200 µK. The detector was constructed from 5 arrays of 5 tuning forks mounted in a copper block to create a 25 pixel square detector of excitation flux. The detector was situated in a cell such that it could be illuminated with a beam of thermal excitations, and that turbulence could be generated in the path of the beam, which will cast a shadow on the face. Characterisation of the detector response to beams generated by the black-body radiator and source wire were performed. We observe that the beam generated by a black-body radiator appears approximately symmetric, consistent with being emitted from a point-source of excitations. In addition to this we find that the profile of the beam generated by the black-body radiator was independent of the power applied to it, an important assumption of the properties of the black-body radiator that had not been previously observed. The beam emitted from a vibrating wire was found to be much narrower and has a angular profile that changes as the velocity of the wire is increased. Probing a turbulent tangle generated by a vibrating wire with this beam showed that the turbulence appears to fill all of the volume in between the radiator and detector. The vortex line density of the tangle appeared the be greatest in the vicinity of the wire, consistent with previous measurements of the vortex tangle generated by vibrating wires. In addition, we find that there are reproducible features in the development of the shadow as a function of the wire velocity, indicating that there is some structure in the development. The shadow is independent of the power of the beam used to probe the tangle. Measurements of fluctuations in the shadow cast by the vortex tangle show that the turbulence has a spectrum reminiscent of the Kolmogorov spectrum. In addition to this the resolution of the detector is such that it is possible in principle to measure the shadow cast by a single vortex line, and we examine candidate events for such a measurement. This represents the first such measurement of the motion of vortex lines in 3He-B.
Vortex Shedding from a Microsphere Oscillating in Superfluid 4^44He at mK Temperatures and from a Laser Beam Moving in a Bose–Einstein Condensate
Abstract Turbulent drag of an oscillating microsphere that is levitating in superfluid 4^44 4 He at mK temperatures, is unstable slightly above a critical velocity amplitude vcv_cvc​ v c . The lifetime τ\tauτ τ of the turbulent state is determined by the number n of vortices shed per half-period. It is found that this number is identical to the superfluid Reynolds number. The possibility of moving a levitating sphere through superfluid 3^33 3 He at microkelvin temperatures is considered. A laser beam moving through a Bose–Einstein condensate (BEC) (as observed by other authors) also produces vortices in the BEC. In particular, in either case, a linear dependence of the shedding frequency fvf_vfv​ f v on Δv=v−vc\Delta v = v - v_cΔv=v−vc​ Δ v = v - v c is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above vcv_cvc​ v c for the onset of turbulent flow: fv=a Δvf_v = a \,\Delta vfv​=aΔv f v = a Δ v , where the coefficient a is proportional to the oscillation frequency ω\omegaω ω above some characteristic frequency ωk\omega _kωk​ ω k and assumes a finite value for steady motion ω→0\omega \rightarrow 0ω→0 ω → 0 . A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.
Abstract Since we still lack a theory of classical turbulence, attention has focused on the conceptually simpler turbulence in quantum fluids. Reaching a better understanding of the quantum case may provide additional insight into the classical counterpart. That said, we have hitherto lacked detectors capable of the real-time, non-invasive probing of the wide range of length scales involved in quantum turbulence. Here we demonstrate the real-time detection of quantum vortices by a nanoscale resonant beam in superfluid 4 He at 10 mK. Essentially, we trap a single vortex along the length of a nanobeam and observe the transitions as a vortex is either trapped or released, detected through the shift in the beam resonant frequency. By exciting a tuning fork, we control the ambient vortex density and follow its influence on the vortex capture and release rates demonstrating that these devices are capable of probing turbulence on the micron scale.