Optomechanical tests of a Schr\"odinger-Newton equation for gravitational quantum mechanics

TL;DR

This paper proposes using optomechanical systems to experimentally test the Schrödinger-Newton equation, which models gravitational effects in quantum mechanics, by detecting a unique spectral signature in the system's output.

Contribution

It demonstrates that optomechanical setups can directly test the Schrödinger-Newton equation, providing a parameter-free experimental signature for validation or refutation.

Findings

Predicted a double-peaked spectral signature in optomechanical systems.

Showed the Schrödinger-Newton equation has no free parameters, enabling definitive tests.

Proposed feasible experimental approach for gravitational quantum mechanics.

Abstract

We show that optomechanical systems can test the Schr\"{o}dinger-Newton equation of gravitational quantum mechanics due to Yang et al. This equation is motivated by semiclassical gravity, a widely used theory of interacting gravitational and quantum fields. From the many-body Schr\"{o}dinger-Newton equation follows an approximate equation for the center-of-mass dynamics of macroscopic objects. This predicts a distinctive double-peaked signature in the output optical quadrature power spectral density of certain optomechanical systems. Since the Schr\"{o}dinger-Newton equation lacks free parameters, these will allow its experimental confirmation or refutation.