Enhancing photon entanglement in a three-mode optomechanical system via imperfect phonon measurements

By considering a 3-mode optomechanical system formed by two cavities interacting with a common mechanical mode, we demonstrate that phonon-counting measurements lead to a significant enhancement of entanglement in the output of the two cavities. This conclusion still holds for an inefficient detector, but the dependence on system parameters changes qualitatively from the ideal limit of perfect projective measurements. We find non-trivial optimal points for the entanglement as functions of detector efficiency, measurement outcome, and optical drive strengths. We characterize both the highest achievable entanglement as well as a ‘typical’ value,obtained at the most likely measurement outcome. Numerical results are well understood within an approximate analytical approach based on perturbation theory around the ideal detector limit.