Optomechanically induced transparency in the presence of an external time-harmonic-driving force

We propose a potentially valuable scheme to measure the properties of an external time-harmonic-driving force with frequency ω via investigating its interaction with the combination of a pump field and a probe field in a generic optomechanical system. We show that the spectra of both the cavity field and output field in the configuration of optomechanically induced transparency are greatly modified by such an external force, leading to many interesting linear and non-linear effects, such as the asymmetric structure of absorption in the frequency domain and the antisymmetry breaking of dispersion near ω = ωm. Furthermore, we find that our scheme can be used to measure the initial phase of the external force. More importantly, this setup may eliminate the negative impact of thermal noise on the measurement of the weak external force in virtue of the process of interference between the probe field and the external force. Finally, we show that our configuration can be employed to improve the measurement resolution of the radiation force produced by a weak ultrasonic wave.