TLS-induced thermal nonlinearity in a micro-mechanical resonator

TL;DR

This paper demonstrates a thermally-driven nonlinear response in a quartz phononic resonator at millikelvin temperatures, caused by coupling to two-level system defects, with implications for mechanical coherence.

Contribution

It provides the first experimental evidence of TLS-induced thermal nonlinearity in a mechanical resonator at cryogenic temperatures, combining theory and experiment.

Findings

Nonlinear response arises from TLS defects coupled to the mechanical mode.

Reactive nonlinearity can cause softening or hardening depending on thermal conditions.

Readout-enhanced relaxation damping from TLSs limits mechanical coherence.

Abstract

We present experimental evidence of a thermally-driven amplitude-frequency nonlinearity in a thin-film quartz phononic crystal resonator at millikelvin temperatures. The nonlinear response arises from the coupling of the mechanical mode to an ensemble of microscopic two-level system defects driven out of equilibrium by a microwave drive. In contrast to the conventional Duffing oscillator, the observed nonlinearity exhibits a mixed reactive-dissipative character. Notably, the reactive effect can manifest as either a softening or hardening of the mechanical resonance, depending on the ratio of thermal to phonon energy. By combining the standard TLS theory with a thermal conductance model, the measured power-dependent response is quantitatively reproduced and readout-enhanced relaxation damping from off-resonant TLSs is identified as the primary mechanism limiting mechanical coherence. Within this framework, we delineate the conditions under which similar systems will realize this nonlinearity.