Ground state cooling and high-fidelity quantum transduction via parametrically-driven bad-cavity optomechanics

In optomechanical systems, the beam-splitter interaction underlies the utility of many applications, but the two-mode-squeezing interaction creates unwanted excitations and is usually detrimental. In this work, we propose a simple but powerful method based on cavity parametric driving to suppress the unwanted excitation that does not require working with a deeply sideband-resolved cavity. Our approach is based on a simple observation: as both the optomechanical two-mode-squeezing interaction and the cavity parametric drive induce squeezing transformations of the relevant photonic bath modes, they can be made to cancel one another. We illustrate how our method can cool a mechanical oscillator below the quantum back-action limit, and significantly suppress the output noise of a sideband-unresolved optomechanical transducer.