Generating EPR-type entanglement of degenerate optomechanical parametric oscillators

Abstract

Einstein–Podolski–Rosen (EPR) entanglement states are achievable by combining two single-mode position and momentum squeezed states at a 50:50 beam splitter (BS). To generate the EPR mechanical entanglement, we consider the system consisted of two parametric optomechanical resonators, where two mechanical oscillators are linearly coupled. The linear coupling forms the symmetric and antisymmetric combinations of two mechanical modes, parallel to a 50:50 BS mixing. In the weak optomechanical coupling regime and via applying the opposite phases of parametric interactions, the symmetric and antisymmetric mechanical modes can be position and momentum squeezed, respectively. Therefore, two original mechanical modes are EPR entangled. Moreover, the mechanical thermal noise can decrease the entanglement. But with the parametric interaction enhanced optomechanical cooling, the influence of thermal noise on entanglement can be significantly suppressed, and the mechanical entanglement can be generated under a relatively high temperature. We also discuss the critical thermal occupation where the entanglement disappears, which is proportional to the optomechanical cooperativity parameter.

Keywords:

• Mechanical EPR entanglement
• parametric optomechanical resonators
• mechanical squeezing

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61505014], [grant number 11504031]; the Yangtze Youth Talents Fund, and the Yangtze Funds for Youth Teams of Science and Technology Innovation [grant number 2015cqt03].