Ultra-coherent nanomechanical resonators via soft clamping and dissipation dilution (1608.00937v1)

Abstract: The small mass and high coherence of nanomechanical resonators render them the ultimate force probe, with applications ranging from biosensing and magnetic resonance force microscopy, to quantum optomechanics. A notorious challenge in these experiments is thermomechanical noise related to dissipation through internal or external loss channels. Here, we introduce a novel approach to defining nanomechanical modes, which simultaneously provides strong spatial confinement, full isolation from the substrate, and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localises the mode, without imposing the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables mechanical $Q>10^{8}$ at $ 1 \,\mathrm{MHz}$, yielding the highest mechanical $Qf$-products ($>10^{14}\,\mathrm{Hz}$) yet reported at room temperature. The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to $4{.}2$ Kelvin predicts $\sim$quanta/ms heating rates, similar to trapped ions.

• The paper introduces a novel resonator design that uses a phononic bandgap structure to localize modes and exponentially reduce dissipation.
• The paper achieves mechanical quality factors exceeding 10⁸ at a 1 MHz resonance frequency with Qf products above 10¹⁴ Hz, outperforming conventional limits.
• The paper employs laser interferometry and high-fidelity simulations to validate its design’s potential for quantum optomechanics, biosensing, and precise force measurements.

Overview of Ultra-Coherent Nanomechanical Resonators via Soft Clamping and Dissipation Dilution

The paper "Ultra-coherent nanomechanical resonators via soft clamping and dissipation dilution" authored by Y. Tsaturyan, A. Barg, E.S. Polzik, and A. Schliesser presents a detailed paper on the design and performance of nanomechanical resonators. These devices are proposed as high-sensitivity tools with potential applications in areas such as biosensing, magnetic resonance force microscopy, and quantum optomechanics. This work provides a novel approach towards enhancing the mechanical quality factor, $Q$, and the $Qf$-product, a key metric of coherence in nanomechanical systems.

Key Contributions and Findings

The authors introduce an innovative design for nanomechanical resonators that leverages a phononic bandgap structure. This effectively localizes mechanical modes without imposing rigid clamping conditions, thereby reducing dissipation exponentially. Through this mechanism, they achieve dissipation dilution by five orders of magnitude. The mechanical quality factor surpasses $Q > 10^8$ at a resonance frequency of 1 MHz, with $Qf$-products in excess of $10^{14} \, \mathrm{Hz}$ at room temperature. This substantial increase in $Qf$-product is attributed to a synergy between soft clamping and dissipation dilution.

Methodology and Techniques

• Phononic Bandgap Structure: The design incorporates a phononic crystal with a specific bandgap to isolate and confine vibrational modes effectively. This suppresses radiation loss significantly and enhances coherence.
• Fabrication: The resonators are developed from silicon nitride films under high tensile stress, influencing both the mechanical properties and the stress distribution of the phononic crystal structure.
• Measurement: Mechanical characteristics such as frequency and quality factor are determined utilizing laser interferometry, which confirms the localization of modes and their enhanced $Qf$-products.

Numerical and Analytical Insights

The experimental results showed the ability to exceed $10^{14} \, \mathrm{Hz}$ in $Qf$-products consistently, surpassing typical limitations like Akhiezer damping in material resonators at room temperature. A $Q \propto a^2/h$ scaling is observed, where $a$ represents the lattice constant and $h$ the thickness, confirming that soft clamping reduces curvature-induced losses. High fidelity simulations corroborate the observed data, aligning closely with empirical findings and supporting the extrapolations made for cryogenic applications.

Practical Implications and Future Directions

The enhanced coherence and low mass of these resonators position them as promising candidates for sensing technologies that demand minimal thermomechanical noise. Their potential application in quantum optomechanics is significant as they meet the $Q \cdot f > 6 \times 10^{12}\,\mathrm{Hz}$ criterion for coherent quantum functionalities at room temperature. They may further benefit force sensitivity applications, including magnetic resonance force microscopy and mass detection, where a root mean square sensitivity in the aN/√Hz range is desirable.

For future developments, the versatility of the phononic clamping concept could extend to other materials and dimensional regimes. One-dimensional resonators and nanotube structures, optimized by similar phononic crystal approaches, hold potential for even greater performance enhancements. Additionally, arrays and coupled defect modes within phononic structures present intriguing prospects for multimode interactions in quantum systems.

In conclusion, this paper provides substantial advancements in nanomechanical resonator technology through the innovative application of phononic engineering and soft clamping. The results present a clear trajectory toward devices with unprecedented coherence, greatly expanding both the fundamental understanding and practical applications in high-precision measurement and quantum technologies.