  In this work we theoretically investigate a hybrid system of two
optomechanically coupled resonators, which exhibits induced transparency. This
is realized by coupling an optical ring resonator to a toroid. In the
semiclassical analyses, the system displays bistabilities, isolated branches
(isolas) and self-sustained oscillation dynamics. Furthermore, we find that the
induced transparency transparency window sensitively relies on the mechanical
motion. Based on this fact, we show that the described system can be used as a
weak force detector and the optimal sensitivity can beat the standard quantum
limit without using feedback control or squeezing under available experimental
conditions.
