Lithographically Defined Si$_3$N$_4$ Torsional Pendulum

TL;DR

This work introduces a wafer-scale, lithographically defined Si3N4 torsional pendulum with a monolithic ribbon suspension designed for ultra-low dissipation and flexible 2-D geometries. The authors demonstrate a centimeter-scale pendulum with a torsional mode around $f_n\approx0.162$ Hz and an intrinsic quality factor $Q\approx1.2\times10^4$, along with high-Q swing modes, and show optical actuation and measurement-based feedback cooling in vacuum. A three-mode mechanical model captures the pendulum and torsional dynamics and predicts frequencies that agree with the data, validating the design approach. The results suggest a scalable path toward ultra-coherent, ultra-low-frequency torsional systems capable of probing weak gravitational effects and gravity-related quantum coherence, with future prospects for mass loading and geometry optimization to enhance dissipation dilution.

Abstract

Torsion pendulums provide an opportunity to trap large masses in a potential weak enough to explore two-body gravitation. Cooled to, and then released from a ground state, weak quantum effects, including those from gravity, might reveal themselves in the evolving decoherence of a torsion pendulum, if its baseline dissipation were sufficiently dilute for quantum coherent oscillation. Monolithic ribbon-like, or multi-filar suspension geometries provide a key to such dilution in torsion, but are challenging to make. As a solution, we introduce a lithographically defined silicon nitride (Si$_3$N$_4$) ribbon suspension in a wafer-scale approach to pendulum fabrication that is conducive to such 2-D geometries, making extreme aspect ratios, and even multi-filar designs, a possibility. A monofilar, monolithic, centimeter scale torsion pendulum is fabricated and released in a first proof of concept. Mounted in vacuum, it is optically excited and cooled using measurement based feedback. Though only 37 mg, the device displays a fundamental frequency of 162 mHz and an undiluted Q of 12000, demonstrating a foundational step towards ultra-coherent, ultra-low frequency torsion pendulums.

Figures (7)

• Figure 1: Outline of the fabrication process: a) Si$_3$N$_4$ is deposited on both sides of a doubly polished Si wafer. b) A SiO$_2$ etch mask deposited on the backside of the wafer. c) Photoresist is spin coated and patterned using a mask-less aligner to define the suspension (topside only), frame, and test mass. d) The exposed areas are removed in a plasma etch. e) A deep silicon etch is used to remove most of the Si wafer. f) KOH is used to etch the remaining Si and release the pendulum; a final step, not shown, removes the breakout tabs and frame.
• Figure 2: Photograph and schematic of the torsional pendulum. a) The bob of the torsional pendulum is an 8 mm $\times$ 5 mm $\times$0.4 mm Si wafer. At the top of the fiber is a piece of Si cut from the same wafer as the bob and used to mount the pendulum inside the vacuum chamber. b) A representation of the fiber and the bob of the torsional pendulum with their respective dimensions.
• Figure 3: Schematic of the experiment. The pendulum, in vacuum, is about 300 mm from the optical set up. The detection laser (red) is directed to the pendulum bob via a mirror and the bob's motion is recorded with a quadrant photodiode.
• Figure 4: Ring-down of the torsional and pendulum modes and their respective fits with extracted quality factors.
• Figure 5: a) LSD of the displacement and thermal noise models. The dashed blue line is the thermal model assuming the damping is due to loss in the material, while the black dotted line is a thermal model assuming the damping is viscous damping. b) The same LSD zoomed into the pendulum modes.