Study on Feedback Linearization of Atomic Polarizability Based on Bloch Equations

This paper investigates the linearization control methods for Bloch equations. For the first time, we examine the diffeomorphic transformations of the spin-exchange relaxation-free (SERF) atomic magnetometer (AM) from a differential geometry perspective, and design stable and convergent controllers using feedback linearization methods. The Bloch equations of SERF AMs can be rewritten as a class of single-input affine nonlinear systems. For such systems, a differential transformation method using Lie derivatives is employed for their linearization study. For different output scenarios, various control functions are constructed using feedback linearization methods. Simulations validate the effectiveness of these control functions in regulating polarization.