  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.
