Achieving steady-state entanglement of remote micromechanical oscillators by cascaded cavity coupling

In this paper, we propose a scheme for generating steady-state entanglement of remote micromechanical oscillators in unidirectionally coupled cavities. For the system of two mechanical oscillators, we show that when two cavity modes in each cavity are driven at red-and blue-detuned sidebands, respectively, a stationary two-mode squeezed vacuum state of the two mechanical oscillators can be generated by the cascaded cavity coupling. The degree of squeezing is controllable by adjusting the relative strength of the pump lasers. Our calculations also show that the achieved mechanical entanglement is robust against thermal fluctuations. For the case of multiple mechanical oscillators, we find that steady-state genuine multipartite entanglement can also be built up among the remote mechanical oscillators. The present scheme does not require nonclassical light input or conditional quantum measurements, and it can be realized with current experimental technology. DOI: 10.1103/PhysRevA.87.022318