Precision measurement of electrical charge by tunable double optomechanically induced transparency with quantized fields

We present a scheme for precision measurement of electrical charge using tunable double optomechanically induced transparency (OMIT) with quantized squeezed fields in a hybrid Coulomb-coupled optomechanical system. We show that the double OMIT windows are linearly tuned by the charge number and robust against temperature, cavity decay and squeezed photon number. By monitoring the interval between the two transparency dips in the homodyne spectrum, high-precision charge detection can be achieved with strong noise immunity. This work provides a reliable optical method for micro-nano charge sensing and promotes the application of quantized field assisted OMIT in quantum metrology.