Topology optimization of high-performance optomechanical resonator

TL;DR

The paper addresses the challenge of designing compact, high-Q optomechanical resonators suitable for room-temperature quantum information tasks by leveraging dissipation-dilution in pre-stressed Si$_3$N$_4$ membranes. It develops a topology-optimization framework to maximize the damping-dilution factor $D_q$ for higher-order eigenmodes, using a density-based 3-field model and FEM for accurate evaluation of $Q$ and mode shapes. The designs achieve high eigenfrequencies and $Qf$ products in a $\sim(700\times700)\mu$m$^2$ footprint with a central pad for optical coupling, and experiments show ringdown-based $Q$ values consistent with predictions after accounting for variation in $Q_0$ across devices. The approach offers a flexible path to target arbitrary modes and potentially reach frequencies up to several MHz with strong opto-mechanical coupling, enabling robust quantum transduction and sensing.

Abstract

High quality mechanical resonators are critical for driving advances in quantum information technologies, precision sensing, and optomechanics. However, achieving compact resonator designs that maintain high performance is a key challenge. In this study, we present a new class of compact resonators optimized to operate at higher-order eigenmodes, achieving both high frequencies and enhanced quality factor-frequency (Qf) products. By employing topology optimization to maximize the damping dilution factor, these resonators achieve minimized edge bending losses and enhanced intrinsic damping. Their high-(Qf) performance and compact form factor position these resonators as promising candidates for applications in quantum information transduction, advanced optomechanical systems, and next-generation sensing technologies.

Figures (3)

• Figure 1: Specifications of numerical model. (a) Dimensions and boundary conditions: The left and upper boundaries are clamped while the other two are set as symmetric conditions. The gray part represents the design domain, while the white regions indicate the non-design domain. (b) Mesh details: The complete mesh (left) and the locally refined mesh near the corner point (right). The locally defined region spans 7$\upmu$m with 100 elements, each with a resolution of 70nm. The coarser mesh has a resolution of 1.75$\upmu$m, resulting in a total mesh size of 296$\times$296 quadrilateral elements.
• Figure 2: Configurations of optimized resonators. (a) Design 2, 3 and 4, showing the normalized targeted eigenmode profiles of out-of-plane displacement plotted on the smoothed optimized designs. (b) Upper: evolution of design 1 from the initial guess to the final optimized design. Black indicates voids, while white represents the Si$_3$N$_4$ layer. In the final optimized structure, small holes were manually filled to facilitate fabrication. Lower: corresponding targeted eigenmodes plotted on elements with physical design variable $\bar{\rho}_e>0.65$.
• Figure 3: (a) Ringdown measured Q and f values. Optical microscope images for design 1-4 are shown on top, where the white regions represent the Si$_3$N$_4$ layer, and black regions indicate voids. Data points correspond to measured values, while the dashed lines represent the numerically calculated Q (horizontal) and f (vertical) using a body-fitted mesh in COMSOL Multiphysics, as listed in Table \ref{['table1']}. (b) Comparison with reported results: Qf (left) and size (right). The black solid lines indicates the contour where Qf$=$6.2$\times$10$^{12}$. The yield represents the number of samples with Qf exceeding this limit out of the total measured samples for each design: 54/58 for Design 1, 48/57 for Design 2, 27/35 for Design 3, and 46/62 for Design 4. The highest measured Qf values of the designs are highlighted with magenta circle bib11 and crosses bib13. Q values of other designs, indicated by magenta diamond bib15, squares bib16 and triangles bib25 are scaled to thickness of 50nm for consistency with design 1-4. (c) A representative power spectrum of Design 1. The inset shows the corresponding ringdown curve over 30s at the targeted mode, with f: 1.248MHz and Q: 29.13$\times10^{6}$.