  Cavity optomechanical (COM) sensors, enhanced by quantum squeezing or
entanglement, have become powerful tools for measuring ultra-weak forces with
high precision and sensitivity. However, these sensors usually rely on linear
COM couplings, a fundamental limitation when measurements of the mechanical
energy are desired. Very recently, a giant enhancement of the signal-to-noise
ratio was predicted in a quadratic COM system. Here we show that the
performance of such a system can be further improved surpassing the standard
quantum limit by using quantum squeezed light. Our approach is compatible with
available engineering techniques of advanced COM sensors and provides new
opportunities for using COM sensors in tests of fundamental laws of physics and
quantum metrology applications.
