Optomechanical tests of a Schrodinger-Newton equation for gravitational quantum mechanics

We show that optomechanical systems can test the Schrodinger-Newton equation of gravitational quantum mechanics due to Yang et al. Phys. Rev. Lett. 110, 170401 (2013). This equation is motivated by semiclassical gravity, a widely used theory of interacting gravitational and quantum fields. From the many-body Schrodinger-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 Schrodinger-Newton equation lacks free parameters, these will allow its experimental confirmation or refutation.