We consider the physics of an optomechanical cavity subject to coherent two-phonon driving, i.e. degenerate parametric amplification of the mechanical mode. We show that in such a system, the cavity mode can effectively "inherit" parametric driving from the mechanics, yielding phase-sensitive amplification and squeezing of optical signals reflected from the cavity. We also demonstrate how such a system can be used to perform single-quadrature detection of a near-resonant narrow-band force applied to the mechanics with extremely low added noise from the optics. The system also exhibits strong differences from a conventional degenerate parametric amplifier: in particular, the cavity spectral function can become negative, indicating a negative effective photon temperature.
@article{arxiv.1605.09275,
title = {Optomechanics with two-phonon driving},
author = {B. A. Levitan and A. Metelmann and A. A. Clerk},
journal= {arXiv preprint arXiv:1605.09275},
year = {2016}
}