  We investigate the quantum signature of gravity in optomechanical systems
under quantum control. We analyze the gravity-induced entanglement and
squeezing in mechanical mirrors in a steady state. The behaviors and the
conditions for generating the gravity-induced entanglement and squeezing are
identified in the Fourier modes of the mechanical mirrors. The condition of
generating the entanglement between the mirrors found in the present paper is
more severe than that of the gravity-induced entanglement between output
lights. The gravity-induced entanglement in optomechanical systems is an
important milestone towards verifying the quantum nature of gravity, which
should be verified in the future.
