Gravity-induced entanglement in optomechanical systems

We investigate the phenomenon of gravity-induced entanglement in optomechanical systems. Assuming photon number conservation and the Newtonian potential expanded up to the quadratic order of the oscillator positions, we exactly solve the dynamics of the optomehcanical systems. Then, we find that the phase difference due to the Newtonian gravity leads to the large entanglement of photons in separated cavities. We clarify the generating mechanism of large gravity-induced entanglements in optomechanical systems in an exact manner. We also determine the characteristic time to generate the maximal entanglement of photons. Finally, by comparing the characteristic time with the decoherence time due to photon leakage, we evaluate the range of the dissipation rate required for testing the gravity-induced entanglement.