Mechanical squeezing via feedback control

We explore the generation of nonclassical mechanical states by combining continuous measurement and feedback control. We find that feedback-induced spring softening can greatly enhance position squeezing, allowing squeezing despite measurement rates slower than the mechanical frequency. Conversely, even from a pure position measurement, we find that spring hardening can enable momentum squeezing, in a new regime we term the fast feedback regime. We interpret these effects as arising from correlations between the feedback drive and the measurement imprecision noise, which in turn effectively modify the measurement rates for position and momentum. Together, this significantly lowers the barrier to measurement-based preparation of nonclassical mechanical states at room temperature.