We adapted the intermodulation approach and have observed that at low oscillation velocities the tuning forks only respond at the excitation frequencies. One such technique excites the fundamental mechanical mode of a resonator using two frequencies and detects intermodulation (mixing) products created by strong non-linear interactions of the system. Atomic force microscopy community also has developed multifrequency techniques for scanning the surface of a sample using a cantilever. For example, the strong non-linearities between the different mechanical resonance modes of an oscillator are utilised to study nano-electromechanical structures. Furthermore, the presence of strong non-linear interactions in a system brings new opportunities to probe such systems using various modes of multifrequency excitation and detection. The single frequency lock-in technique is also used to capture the resonance properties in non-linear systems and has successfully characterised Duffing-like oscillators. While this technique is well established for linear systems, mapping out the complete resonant curve can be quite slow. The miniaturisation of the forks was driven by a desire to probe local properties of helium and to boost the fork’s sensitivity to temperature.Ĭonventional measurements of the resonant properties of an oscillating object use a continual sweep of the excitation frequency using a signal generator and detection of the object’s response using a lock-in amplifier. Here we present the temperature dependence of damping experienced by two forks manufactured on a \(25\,\upmu \)m thick wafer. Previously, to investigate the frequency dependence of acoustic emission and the critical velocity for the generation of turbulence in superfluid \(^4\)He, we had manufactured custom-designed tuning forks on a 75-micron quartz wafer Footnote 1 and used the length of the forks to control resonance frequencies. The majority of tuning forks studied so far in quantum fluids research have been common off-the-shelf electronic components and depending on the manufacturer had different physical dimensions, length, width and thickness, even though the resonance frequencies are the same. The popularity of quartz tuning forks is driven by their availability, high quality factor and ease of use. Quartz tuning forks were relatively recently introduced for probing quantum liquids and were quickly adopted for low temperature thermometry, the generation and detection of quantum turbulence and studies of acoustic emission and cavitation. The multifrequency technique could also be used for studies of the onset of non-linear phenomena such as quantum turbulence and cavitation in superfluids. 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 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. 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 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. 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 multifrequency technique allows to measure the resonance curve of a vibrating object much faster than a conventional single frequency lock-in amplifier 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.
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