Gravitational entanglement with Gaussian states

Is gravity a quantum force? This question was recently addressed by two proposals (see [1] and [2]) which explored the possibility of detecting entanglement as generated by gravity. Successful detection of entanglement due to a gravitational interaction would imply that gravity is fundamentally a quantum force, since only quantum systems can mediate entanglement.
In my talk, I will show how the experimental scheme in [1] can be modeled for Gaussian states in the continuous variable framework using massive optomechanical spheres for two different settings: trapped systems and freely-falling systems. We evaluate the entanglement generated by the Newtonian potential for both cases and propose the use of two specific continuous variable entanglement witnesses to simplify the detection. The approach also allows us to include other central-potential interactions, such as the attractive Casimir effect.

[1] Bose, Sougato, et al. "Spin entanglement witness for quantum gravity." Physical Review Letters 119.24 (2017): 240401.
[2] Marletto, Chiara, and Vlatko Vedral. "Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity." Physical Review Letters 119.24 (2017): 240402.