Probing Liquid ^4He with Quartz Tuning Forks Using a Novel Multifrequency Lock-in Technique

We report on a novel technique to measure quartz tuning forks, and possibly other vibrating objects, in a quantum fluid using a multifrequency lock-in amplifier. The multifrequency technique allows to measure the resonance curve of a vibrating object much faster than a conventional single frequency lock-in amplifier technique. Forks with resonance frequencies of 12 kHz and 16 kHz were excited and measured electro-mechanically either at a single frequency or at up to 40 different frequencies simultaneously around the same mechanical mode. The response of each fork was identical for both methods and validates the use of the multifrequency lock-in technique to probe properties of liquid helium at low fork velocities. Using both methods we measured the resonance frequency and drag of two 25-\(\upmu \)m-wide quartz tuning forks immersed in liquid \(^4\)He in the temperature range from 4.2 K to 1.5 K at saturated vapour pressure. The damping and shift of resonance frequency experienced by both tuning forks at low velocities are well described by hydrodynamic contributions in the framework of the two-fluid model. The sensitivity of the 25-\(\upmu \)m-wide tuning forks is larger compared to similar 75-\(\upmu \)m-wide forks and in combination with the faster multifrequency lock-in technique could be used to improve thermometry in liquid \(^4\)He. The multifrequency technique could also be used for studies of the onset of non-linear phenomena such as quantum turbulence and cavitation in superfluids.