TLS-induced thermal nonlinearity in phononic crystal defect resonators

The dynamics of many low-temperature circuits are strongly affected by their coupling to an ever-present dissipative bath of microscopic two-level systems (TLS), which greatly limits their performance at millikelvin temperature. Developing a full theory of dissipation, nonlinearity and noise induced by this TLS bath is a critical step in mitigating the loss that it introduces. Phononic crystal defect resonators, which are currently being investigated as a platform for circuit quantum acoustodynamics, are also a valuable tool for exploring TLS physics. In these devices, it has been shown that the TLS can be exceptionally long-lived due to the presence of a phononic bandgap, which restricts their relaxation into acoustic degrees of freedom. This facilitates new ways to study the interplay between a TLS ensemble and a mechanical resonator.

We present here experimental evidence of a thermally-induced amplitude-frequency nonlinearity driven by the coupling of the resonator to a TLS bath and develop a model to account for it. In this model, the nonlinearity is both reactive and dissipative and arises from self-heating of the TLS bath, when probing near the mechanical resonance. We show that at millikelvin temperature its effect can be strong down to remarkably low phonon occupancies due to the small thermal conductance of the phononic crystal supports. We compare the predictions of this model with experimental data and discuss implications for piezoelectric thin-film devices.