Optical and mechanical squeezing with coherent feedback control beyond the resolved-sideband regime

The noise reduction in squeezed states makes them a powerful nonclassical resource in quantum technologies, especially in quantum sensing, and an essential step for the ongoing development of non-Gaussian states. In particular, optical and mechanical squeezing can both be generated when light interacts with a mechanical oscillator. Here we use a linear optical system as a controller and use coherent optical feedback to enhance squeezing in the unresolved-sideband regime of optomechanics. Feedback control is generally profitable for cooling, manipulating, and stabilizing the dynamics of mechanical oscillators; coherent feedback is then notable for its ability to steer a quantum system toward the highest squeezing without measurement, avoiding backaction. We thoroughly maximize optical and conditional mechanical squeezing feasible with state-of-the-art experimental setups and derive the optimal conditions under which quantum squeezing is generated in the system.