Precision measurement of electrical charge with optomechanically induced transparency

We propose a potentially practical scheme to precisely measure the charge number of small charged objects by using optomechanically induced transparency (OMIT) in optomechanical systems. In contrast to conventional measurements based on noise backaction on optomechanical systems, our scheme presents an alternative way to detect the charge number exactly, by monitoring small deformation of the mechanical resonator sensitive to the charge number of nearby charged object. The relationship between the charge number and the OMIT window width is investigated and the feasibility of the scheme is justified by numerical simulation with currently available experimental values.