Negative non-linear differential dissipation in mechanical quartz resonators

We observe negative non-linear differential dissipation in a low-frequency (32.7 kHz) miniature quartz tuning fork, representing a high-Q piezoelectric resonator, at temperatures below 0.3 K. Similar drive-induced dissipation suppression has previously been reported in superconducting microwave resonators, and high-frequency MEMS devices, associated to coupling with tunneling two-level systems (TTLSs). In the case of low-frequency resonators, the equivalent temperature of the mechanical mode is orders of magnitude lower than the thermodynamic temperature of the device, implying that accessible TTLS states are largely saturated. We demonstrate that the observed temperature and drive dependence of the losses fit well within the framework of an interacting TTLS bath, indicating the presence of a channel for energy transfer between the mechanical mode and thermally activated TTLSs. As a possible coupling mechanism, we suggest microwave phonon modes in the metallic electrodes of the tuning fork.