Development of a Standalone Sample Thermometer Based on Quartz Tuning Forks*

There is a growing demand within the user program across the Maglab and within the cryogenic industry for thermometers capable of simultaneous operation at ultra-low temperatures down to and below 1 mK and in high magnetic fields. To this end we have developed a thermometer design based upon a tuning fork encapsulated in a small volume containing ³He [1] and demonstrated compatibility with these extreme conditions. Here we discuss the next stages in the design of this thermometer.

We present measurements of the viscosity of liquid ³He and the typical mixture of ³He and ⁴He found in a dilution refrigerator as measured by a variety of quartz tuning forks. We present an enhanced hydrodynamic description of the resonator in both cases, based on drawing together existing models in different temperature regimes. The mixture has a significantly lower viscosity, which is advantageous to the sensitivity of the tuning fork measurement. Thus, we discuss the feasibility of using a cell containing a small volume of such mixture as a sample thermometer. We further detail the use of an array of tuning forks as a diagnostic tool for the mixture level, temperature and location of the phase boundary within the mixing chamber of a dilution refrigerator.

[1] A. J. Woods, A. M. Donald, R. Gazizulin, E. Collin, L. Steinke; Developing compact tuning fork thermometers for sub-mK temperatures and high magnetic fields. J. Appl. Phys. 14 January 2023; 133 (2): 024501. https://doi.org/10.1063/5.0132492