Generalized dissipation dilution in strained mechanical resonators

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.

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• Strained crystalline nanomechanical resonators with ultralow dissipation
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• Nanomechanical Dissipation and Strain Engineering
• Fractal-like mechanical resonators with soft-clamped fundamental mode
• Engineering the dissipation of crystalline micromechanical resonators
• Nanomechanical resonators with ultra-high-$Q$ perimeter modes
• High-Strength Amorphous Silicon Carbide for Nanomechanics
• Centimeter-scale nanomechanical resonators with low dissipation
• Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators
• Modelling and observation of nonlinear damping in dissipation-diluted nanomechanical resonators
• Direct laser-written optomechanical membranes in fiber Fabry-Perot cavities
• High-Q trampoline resonators from strained crystalline InGaP for integrated free-space optomechanics
• Silicon-nitride nanosensors toward room temperature quantum optomechanics
• Tuning dissipation dilution in 2D material resonators by MEMS-induced tension
• Nanomechanical crystalline AlN resonators with high quality factors for quantum optoelectromechanics
• Universal length dependence of tensile stress in nanomechanical string resonators
• Low-Dissipation Nanomechanical Devices from Monocrystalline Silicon Carbide
• Broadband Dichromatic Variational Measurement
• Mode-Dependent Scaling of Nonlinearity and Linear Dynamic Range in a NEMS Resonator
• Integration of High-Tc Superconductors with High Q Factor Oxide Mechanical Resonators
• Thickness dependence of the mechanical properties of piezoelectric high-$Q_m$ nanomechanical resonators made from aluminium nitride
• Nano-beam clamping revisited
• On-Chip Frequency Noise Cancellation in Nanomechanical Resonators using Cavity Optomechanics
• High-$Q$ membrane resonators using ultra-high-stress crystalline TiN films
• Soft-clamped silicon nitride string resonators at millikelvin temperatures
• Optomechanical Accelerometer Search for Ultralight Dark Matter
• Membrane phononic crystals for high-Qm mechanical defect modes in piezoelectric aluminum nitride