Quality factors of quartz crystal resonators operating at 4 Kelvins

Quartz crystal resonators can exhibit huge quality factors close to 1 billion at liquid helium temperature. Nevertheless, they must satisfy a set of conditions to meet this high level of resonance. With the help of experimentation, the main identified conditions are considered in this paper, such as the material quality, the energy trapping through the vibration modes and resonator diameters, and the electrode effect.