Simultaneous measurement of magnetic field and inertia based on hybrid optical pumping

We present a method for simultaneous measurement of magnetic field and inertia by using a hybrid optical pumping of ³⁹K and ⁸⁵Rb atoms. The K atoms are directly pumped by a laser and the two species interact with each other by spin exchange and the average magnetization of each other. A simultaneous-measurement model of magnetic field and inertia is proposed based on the coupled spin ensemble. By solving the K-Rb Bloch equation analytically and numerically, we find that the steady-state response for K, Rb transverse polarizations is linearly dependent on magnetic field and inertial rotation rate. The optimal bias magnetic field, suppression of the disturbance magnetic field in the signal, density ratio of K/Rb, and temperature of the cell are carefully analyzed to make the measurement model precise.