We propose a superconducting circuit comprising a dc-SQUID with mechanically compliant arm embedded in a coplanar microwave cavity that realizes an optomechanical system with a degenerate or non-degenerate parametric interaction generated via the dynamical Casimir effect. For experimentally feasible parameters, this setup is capable of reaching the single-photon, ultra-strong coupling regime, while simultaneously possessing a parametric coupling strength approaching the renormalized cavity frequency. This opens up the possibility of observing the interplay between these two fundamental nonlinearities at the single-photon level.
@article{arxiv.1507.00115,
title = {Ultra-Strong Optomechanics Incorporating the Dynamical Casimir Effect},
author = {P. D. Nation and J. Suh and M. P. Blencowe},
journal= {arXiv preprint arXiv:1507.00115},
year = {2016}
}