Generalized dissipation dilution in strained mechanical resonators

TL;DR

This paper develops a comprehensive theory explaining how tensile stress and geometric nonlinearity enhance the quality factors of mechanical resonators, applicable to various geometries and optimized through shape engineering.

Contribution

It introduces a generalized dissipation dilution theory for arbitrary resonator shapes, clarifies the physical origin, and explores optimization strategies for high-Q nanomechanical resonators.

Findings

Dissipation dilution is due to tension and geometric nonlinearity.

Shape modifications like soft clamping enhance quality factors.

Analytical limits for dissipation dilution are derived.

Abstract

Mechanical resonators with high quality factors are of relevance in precision experiments, ranging from gravitational wave detection and force sensing to quantum optomechanics. Beams and membranes are well known to exhibit flexural modes with enhanced quality factors when subjected to tensile stress. The mechanism for this enhancement has been a subject of debate, but is typically attributed to elastic energy being "diluted" by a lossless potential. Here we clarify the origin of the lossless potential to be the combination of tension and geometric nonlinearity of strain. We present a general theory of dissipation dilution that is applicable to arbitrary resonator geometries and discuss why this effect is particularly strong for flexural modes of nanomechanical structures with high aspect ratios. Applying the theory to a non-uniform doubly clamped beam, we show analytically how dissipation dilution can be enhanced by modifying the beam shape to implement "soft clamping", thin clamping and geometric strain engineering, and derive the ultimate limit for dissipation dilution.