Probing gravitational interaction between milligram optomechanical oscillators operating in the quantum regime

Understanding the intersection of gravity and quantum mechanics remains a fundamental challenge in physics. While quantum control of mechanical systems has advanced significantly, most experiments are limited to smaller masses. This study proposes an experimental platform to probe gravitational interactions between two milligram-scale oscillators, aiming to bridge the gap between macroscopic gravitational measurements and quantum-limited optomechanical sensing.

The setup utilizes two microfabricated silicon oscillators: a 'Source' driven at resonance to generate a time-dependent gravitational field, and a 'Probe' acting as a sensitive detector. The oscillators are designed with a mass of approximately 23 mg and resonance frequencies near 20 kHz. To achieve the necessary sensitivity, the Probe is integrated into a high-finesse optical cavity and operated at ultra-cryogenic temperatures (20 mK) to minimize thermal noise. The experiment employs a 'membrane-in-the-middle' configuration, where a thin silicon nitride membrane facilitates optical readout without significantly compromising the mechanical quality factor of the oscillators.

• Mechanical Isolation: The system incorporates a multi-stage suspension chain and nodal mounting to minimize mechanical cross-talk and energy dissipation, targeting a mechanical quality factor of 50 million.
• Electrostatic Shielding: A bifunctional element featuring a gold-coated surface is placed between the oscillators to suppress non-gravitational electrostatic coupling.
• Signal Amplification: By modulating the Source at the Probe's resonance frequency, the gravitational signal is resonantly amplified, allowing it to emerge from the background noise.

This experiment represents a concrete step toward testing gravity in a regime where quantum effects become relevant. By successfully scaling up the mass of optomechanical systems while maintaining high-sensitivity readout, this platform provides a realistic pathway to investigate whether gravity can be treated as a quantum field or if it requires a different theoretical framework when interacting with quantum-coherent mechanical systems.