  Nonlinear forces allow motion of a mechanical oscillator to be squeezed below
the zero-point motion. Of existing methods, mechanical parametric amplification
is relatively accessible, but previously thought to be limited to 3dB of
squeezing in the steady state. We consider the effect of applying continuous
weak measurement and feedback to this system. If the parametric drive is
optimally detuned from resonance, correlations between the quadratures of
motion allow unlimited steady-state squeezing. Compared to back-action evasion,
we demonstrate that the measurement strength, temperature and efficiency
requirements for quantum squeezing are significantly relaxed.
