A proposed method to measure weak magnetic field based on a hybrid optomechanical system

Optomechanical systems have long been considered in the field of precision measurement. In this work, measurement of weak magnetic field in a hybrid optomechanical system is discussed. In contrast to conventional measurements based on detecting the change of magnetic flux, our scheme presents an alternative way to measure the magnetic field with a precision of 0.1 nT. We show that the effective cavity resonance frequency will be revised due to the electromagnetic interactions. Therefore, a resonance valley in the transmission spectrum of the probe field will shift in the presence of the magnetic field, and the width of an asymmetric transparency in the optomechanically induced transparency (OMIT) shows a strong dependence on the magnetic field strength. Our results may have potential application for achieving high precision measurement of the magnetic field.