  We theoretically investigate the weak force-sensing based on coherent quantum
noise cancellation (CQNC) scheme in a hybrid cavity optomechanical system
containing a trapped ensemble of ultracold atoms and an optical parametric
amplifier (OPA). In our proposed system the back action noise can be completely
eliminated at all frequencies as well as through the proper choice of the OPA
parameters noise spectral density can be also reduced at lower frequencies.
This leads to the significant enhancement in the weak force sensing and also
surpasses the standard quantum limit (SQL) even for small input power at lower
detection frequency. Our study can be used for the realization of force sensor
based on hybrid cavity optomechanical systems and for coherent quantum control
in macroscopic systems.
