Entanglement dynamics of two mesoscopic objects with gravitational interaction

We analyse the entanglement dynamics of two particles interacting through gravity in a setup similar to the recently proposed experiments that aim to test quantum signatures of gravity [S. Bose, A. Mazumdar, G.W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A.A. Geraci, P.F. Barker, M.S. Kim, G. Milburn, Phys. Rev. Lett. 119, 240401 (2017); C. Marletto, V. Vedral, Phys. Rev. Lett. 119, 240402 (2017)]. We consider the open dynamics of the system under decoherence due to the environmental interaction. We show that as long as the coupling between the particles is strong, the system does indeed develop entanglement, confirming the qualitative analysis in the original proposals. We show that the entanglement is also robust against stochastic fluctuations in setting up the system. The optimal interaction duration for the experiment is computed. A condition under which one can prove the entanglement in a device-independent manner is also derived.