Enhancement of mechanical squeezing via feedback control

We explore the generation of nonclassical mechanical states by combining continuous position measurement and feedback control. We find that feedback-induced spring softening can greatly enhance position squeezing. Conversely, even with a pure position measurement, we find that spring hardening can enable momentum squeezing. Beyond enhanced squeezing, we show that feedback also mitigates degradation introduced by background mechanical modes. Together, this significantly lowers the barrier to measurement-based preparation of nonclassical mechanical states at room temperature.