Two-mode squeezed states in cavity optomechanics via single-mode reservoir engineering

The generation and verification of a macroscopic, all-mechanical entangled state is a major goal and (at present) outstanding task in the study of mechanical systems in the quantum regime. The canonical continuous-variable entangled state is the two-mode squeezed state. Here we describe how to prepare and detect a highly-pure, all-mechanical two-mode squeezed state in an optomechanical system via coupling to only one (rather than two [1,2]) cavity mode(s). The approach taken may be viewed as a perturbation of a two-mode back-action-evading measurement [3], and generalizes an earlier proposal for single-mode mechanical squeezing [4].\\[4pt] [1] Y.-D. Wang and A. A. Clerk, Phys. Rev. Lett. 110, 253601 (2012).\\[0pt] [2] H. Tan, G. Li, and P. Meystre, Phys. Rev. A 87, 033829 (2013).\\[0pt] [3] M. J. Woolley and A. A. Clerk, Phys. Rev. A 87, 063846 (2013).\\[0pt] [4] A. Kronwald, F. Marquardt, and A. A. Clerk, arXiv:1307.5309.