Two-Level System Damping in a Quasi-One-Dimensional Optomechanical Resonator

TL;DR

This study investigates how two-level system defects cause damping in a quasi-one-dimensional nanomechanical resonator, providing experimental validation of the standard tunneling model and quantifying defect densities at cryogenic temperatures.

Contribution

The paper introduces an optomechanically-mediated thermal ringdown technique to measure dissipation in nanomechanical modes and confirms the one-dimensional TLS damping model experimentally.

Findings

Quantitative agreement with the standard tunneling model for TLS in 1D.

Extraction of defect density of states and deformation potentials.

Each mechanical mode couples to less than one thermally-active defect at 10 mK.

Abstract

Nanomechanical resonators have demonstrated great potential for use as versatile tools in a number of emerging quantum technologies. For such applications, the performance of these systems is restricted by the decoherence of their fragile quantum states, necessitating a thorough understanding of their dissipative coupling to the surrounding environment. In bulk amorphous solids, these dissipation channels are dominated at low temperatures by parasitic coupling to intrinsic two-level system (TLS) defects, however, there remains a disconnect between theory and experiment on how this damping manifests in dimensionally-reduced nanomechanical resonators. Here, we present an optomechanically-mediated thermal ringdown technique, which we use to perform simultaneous measurements of the dissipation in four mechanical modes of a cryogenically-cooled silicon nanoresonator, with resonant frequencies ranging from 3 - 19 MHz. Analyzing the device's mechanical damping rate at fridge temperatures between 10 mK - 10 K, we demonstrate quantitative agreement with the standard tunneling model for TLS ensembles confined to one dimension. From these fits, we extract the defect density of states ($P_0 \sim$ 1 - 4 $\times$ 10$^{44}$ J$^{-1}$ m$^{-3}$) and deformation potentials ($\gamma \sim$ 1 - 2 eV), showing that each mechanical mode couples on average to less than a single thermally-active defect at 10 mK.