Systematic errors from scalar slowing-down models in transient SERF magnetometry

Abstract

Reduced Bloch models of spin-exchange-relaxation-free (SERF) magnetometers commonly describe the coupled electron--nuclear spin dynamics using a single nuclear slowing-down factor. We show that this scalar description becomes inaccurate when the polarization magnitude changes appreciably. We derive an effective Bloch equation with separate longitudinal and transverse slowing-down factors, $q_\parallel(P)$ and $q_\perp(P)$, governing changes in polarization magnitude and direction. For $^{87}\mathrm{Rb}$ under representative SERF conditions and undergoing free-induction decay (FID), comparison with master-equation simulations shows that the dynamic scalar model produces a magnetic-field estimation bias of up to $4.2\%$ at high initial polarization, while fixing the slowing-down factor at a reference value increases the error to $10.1\%$. Lowering the polarization suppresses this bias but also reduces the magnetic-field information contained in the FID signal. We further show that the anisotropic response modifies noncollinear optical pumping and introduces an additional nonlinear contribution to the harmonic response under periodic driving. The resulting model retains the simplicity of a three-component Bloch description while improving the quantitative accuracy of transient and driven SERF magnetometry.