Quartz Tuning Fork as a Parametric Resonator in High Magnetic Fields
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Quartz Tuning Fork as a Parametric Resonator in High Magnetic Fields Marcel Človečko1 · Kamil Goliaš2 · Peter Skyba1 Received: 15 July 2019 / Accepted: 16 February 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We present the measurements of a parametrically excited quartz tuning fork in vacuum at very low temperatures ( ∼ 20 mK) and magnetic field of 1.5 Tesla. We show that if a quartz tuning fork is exposed to a high static magnetic field, the motion of the tuning fork in this field modifies its potential energy forming a time-dependent term oscillating at twice of its fundamental frequency. This phenomenon gives an opportunity to study and use the quartz tuning forks as the parametric resonators. Here, we present the technique of the parametric excitation of the quartz tuning forks, and we discuss the results of the measurements. Keywords Quartz tuning fork · Parametric resonator · High magnetic fields
1 Introduction In the field of low temperature physics, the quartz tuning forks (QTFs) have proven to be a vital experimental tool used in the study of quantum liquids and solids, quantum turbulence, etc. [1–10]. Due to their obvious advantages (low cost, simplicity of measurement, extremely fine displacement), these resonators are widely used in scanning probe techniques like AFM, STM, etc. [11–13] as well. In a latter case, the measurements are carried out in vacuum at low temperatures and in high magnetic fields. Therefore, it is important to know the influence of such conditions, namely high magnetic fields, on the resonant characteristics of the quartz tuning forks. Our previous works showed that a tuning fork constant 𝛼f does not depend on the applied magnetic field [14], and that quartz tuning forks, in principle, have potential to be used as thermometers in millikelvin temperature regime and high magnetic fields * Marcel Človečko [email protected] 1
Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
2
Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia
13
Vol.:(0123456789)
Journal of Low Temperature Physics
[15]. In the following, we show that a quartz tuning fork being exposed to high magnetic fields exhibit the property of a parametric resonator, i.e., such quartz tuning fork can be excited parametrically.
2 Idea of an Experiment The recently observed temperature dependence of the quartz tuning forks resonance frequencies in zero magnetic field has been interpreted using a phenomenological model based on the presence of the van der Waals interactions, which emerges on cooling and increases the stiffness of the potential energy [15, 16] ) ( Q2 x2 , Vpot ≈ k + (1) 𝛼(T) where the first term is related to the potential energy associated with elastic deformation of the lattice with k being the spring constant. The second term expresses the contribution of the van der Waals interaction with 𝛼(T) being the po
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