Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocal effect which is intrinsically distinct from Bell nonlocality and quantum entanglement. In this paper, we investigate in detail the properties of steady-state light-mechanical Gaussian steerable correlations in a generic cavity optomechanical system. When considering the steering between the intracavity field and the mechanical oscillator, we find that under blue-detuned driving, the steady-state steering via optomechanical parametric downconversion is present in only one direction and, moreover, the steering direction is determined merely by the relative dissipation strength of the cavity to the mechanics. Furthermore, when considering the steering between the cavity output field and the mechanical oscillator, we reveal that under red-detuned driving, strong steering can be achieved in the sideband-unresolved regime for a filtered output field with given central frequency and bandwidth. This steering with the output field can also be present in one way by adjusting the driving strength and exists up to the environment temperature $T\approx 10$ K for the parameters close to those in the recent experiments. Finally, we show that the achieved strong light-mechanical correlations can be explored to realize macroscopic EPR steering of two distant optomechanical oscillators in the regime of unresolved sidebands via entanglement swapping.

• Received 9 January 2017

DOI:https://doi.org/10.1103/PhysRevA.95.053842