Quantum-state steering in optomechanical devices

We show that optomechanical systems in the quantum regime can be used to demonstrate EPR-type quantum entanglement between the optical field and the mechanical oscillator, via quantum-state steering. Namely, the conditional quantum state of the mechanical oscillator can be steered into different quantum states depending the choice made on which quadrature of the out-going field is to be measured via homodyne detection. More specifically, if quantum radiation pressure force dominates over thermal force, the oscillator's quantum state is steerable with a photodetection efficiency as low as 50%, approaching the ideal limit shown by Wiseman and Gambetta [Phys. Rev. Lett. {\bf 108}, 220402 (2012)]. We also show that requirement for steerability is the same as those for achieving sub-Heisenberg state tomography using the same experimental setup.