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We report an efficient mechanism to generate mechanical entanglement in a two-cascaded cavity optomechanical system with optical parametric amplifiers (OPAs) inside the two coupled cavities. We use the especially tuned OPAs to squeeze the hybrid mode composed of two mechanical modes, leading to strong macroscopic entanglement between the two movable mirrors. The squeezing parameter as well as the effective mechanical damping are both modulated by the OPA gains. The optimal degree of mechanical entanglement therefore depends on the balanced process between coherent hybrid mode squeezing and dissipation engineering. The mechanical entanglement is robust to strong cavity decay, going beyond simply resolved sideband regime, and is resistant to reasonable high thermal noise. The scheme provides an alternative way for generating strong macroscopic entanglement in cascaded optomechanical systems.

We propose a scheme to realize the Heisenberg spin chain in a one-dimensional array of cavities connected by optical fibers. The proposed scheme is based on the off-resonant Raman transitions between two ground states of atoms, and is induced by the cavity modes and external fields. Under the interactions between the nearest neighbors (NNs) and the next NNs, the result shows that the atoms, via the exchange of virtual photons, can be effectively equal to a spin-1/2 Heisenberg model under certain conditions. The parameters of the effective Hamiltonian can be controlled by tuning the laser fields.