Frequency-dependent drag from quantum turbulence produced by quartz tuning forks in superfluidHe4

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-μm-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 = ω/2π 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 ≈ √ 0.7κ ω where κ is the circulation quantum. The drag from quantum turbulence shows a small frequency dependence when plotted against the scaled velocity v/v c .

A Quasiparticle Detector for Imaging Quantum Turbulence in Superfluid $$^3$$ 3 He-B

“…The wafer also holds other forks which have been used for different experiments in superfluid 4 He. There are several single forks which have fundamental resonant frequencies in the range 6-32 kHz and an additional array with forks having resonant frequencies in the range 20-160 kHz.…”

“…There are several single forks which have fundamental resonant frequencies in the range 6-32 kHz and an additional array with forks having resonant frequencies in the range 20-160 kHz. These were used to study frequency dependent properties in superfluid 4 He such as sound emission [15] and turbulent drag [4]. Each array is attached to the frame of the wafer by two small tabs at one end next to the contact pads.…”

“…Quartz tuning forks have very high quality factors, of order 10 5 , making them sufficiently sensitive to study the mechanical properties of helium fluids at low temperatures. They have found many applications in superfluids research including measurements of viscosity [5][6][7], quantum turbulence in 4 He [8][9][10], cavitation [11], Andreev scattering in 3 He-B [12,13] and acoustic modes [14][15][16]. Here we describe their use as sensitive probes of ballistic quasiparticles in superfluid 3 He-B.…”

“…The response of a fork can be easily calibrated to measure the prong velocity [3,4]. Quartz tuning forks have very high quality factors, of order 10 5 , making them sufficiently sensitive to study the mechanical properties of helium fluids at low temperatures.…”

“…There have been a number of developments in recent years to visualise turbulence in superfluid 4 He. At relatively high temperatures hydrogen particles have been used as tracers to visualise the flow [18][19][20].…”