Enhanced Gravitational Entanglement in Modulated Optomechanics

The role of entanglement in determining the non-classicality of a given interaction has gained significant traction over the last few years. In particular, as the basis for new experimental proposals to test the quantum nature of the gravitational field. Here we show that the rate of gravity mediated entanglement between two otherwise isolated optomechanical systems can be significantly increased by modulating the optomechanical coupling. This is most pronounced for low mass, high frequency systems - convenient for reaching the quantum regime - and can lead to improvements of several orders of magnitude, as well as a broadening of the measurement window. Nevertheless, significant obstacles still remain. In particular, we find that modulations increase decoherence effects at the same rate as the entanglement improvements. This adds to the growing evidence that the constraint on noise (acting on the position d.o.f) depends only on the particle mass, separation, and temperature of the environment and cannot be improved by novel quantum control. Finally, we highlight the close connection between the observation of quantum correlations and the limits of measurement precision derived via the Cram\'er-Rao Bound. An immediate consequence is that probing superpositions of the gravitational field places similar demands on detector sensitivity as entanglement verification.