  Squeezing is a resource that enables precision enhancements in quantum
metrology and can be used as a basis for the generation of entanglement by
linear optics. While strong squeezing is challenging to generate in optical
fields, here we present simple periodic modulation protocols in optomechanical
systems that can generate large squeezing of their mechanical degrees of
freedom for realistic system parameters. We then proceed to show how such
protocols can serve to improve the measurement precision of weak forces and
enhance the generation of entanglement between test masses that are subject to
any kind of weak interaction. Moreover, these protocols can be reverted to
reduce the amount of injected energy, while preserving the generated
entanglement and making it more resilient to noise. We present the principle at
work, discuss its application in a variety of physical settings, including
levitated and tethered mechanical harmonic oscillators, and present example
applications to Casimir and gravitational forces.
