  The optomechanical force sensor in non-Markovian environment for a mechanical
oscillator is presented. By performing homodyne detection we obtain an
generally expression for the output signal. It is shown that the weak force
detection is sensitive to the non-Markovian environment. The additional noise
can be obviously reduced comparing to the Markovian condition. Moreover, the
optimal additional noise can be maintained in a rather low level without using
assistant system or squeezing under available experimental condition in
unsolved sideband regime. Our results provides a promising platform for
reducing the additional noise by using engineered non-Markovian reservoir in
ultrasensitive detection.
