We propose a scheme for generation of the stationary continuous-variable entanglement and Einstein-Podolsky-Rosen (EPR) steering between an optical cavity mode and a nanomechanical resonator (NMR) mode. The cavity and the NMR are commonly coupled with two separated quantum dots (QDs), where the two QDs are driven simultaneously by a strong laser field. By adjusting the frequency of the strong laser field, the two QDs are nearly trapped on different dressed states, which is helpful to generate the entanglement between the cavity mode and the NMR mode. Due to the combined resonant interaction of...
