Macroscopic Mechanical Entanglement Stability in Two Distant Dissipative Optomechanical Systems

A theoretical scheme for the stable entanglement generation of two remote mechanical modes is introduced. Two identical optomechanical systems, each constituting a single-mode optical field as well as a qubit and a moveable mirror driven by an external pump field, are considered. To make the model more realistic, atomic, photonic, and phononic dissipations are considered. The time-dependent state of each subsystem is obtained, analytically. Then, by an appropriate Bell-state measurement (BSM) on the state of the whole system (first approach), the entanglement of two mechanical modes is created. As a second parallel approach, appropriate atomic measurement is applied after the BSM. According to these numerical simulations via concurrence, the noteworthy features are as follows. There exists optimum value of photon-phonon coupling strength for obtaining the steady-state entanglement; by choosing appropriate values of dissipation, photon-phonon coupling, and pump amplitude, a significant degree and stable entanglement between the two mechanical modes are accessible. The present scheme opens new practical perspectives in constructing stable entanglement between two remote mechanical modes and can be helpful to realize quantum memories for quantum information processing and establishing long-distance quantum communication networks.