Investigating the hyperfine systematic error and relative phase in low spin-polarization alkali FID magnetometers

TL;DR

This study investigates hyperfine systematic errors in low spin-polarization alkali FID magnetometers, revealing their dependence on spin polarization and proposing mitigation techniques that significantly improve magnetic field measurement accuracy.

Contribution

The paper introduces double-frequency fitting and synchronous-pulse pumping methods to reduce hyperfine systematic errors in alkali FID magnetometers, achieving up to sevenfold accuracy improvements.

Findings

Systematic errors cause up to 3.5 nT inaccuracies at low polarization.

Mitigation techniques reduce errors to below 1.5 nT.

Simulations and experiments show sevenfold accuracy enhancement.

Abstract

Alkali-metal optically-pumped magnetometers are prone to inaccuracies arising from the overlap of the average F = I + 1/2 and F = I - 1/2 ground-state Zeeman resonances. We employ density-matrix simulations and experiments to investigate how this hyperfine systematic error varies with spin polarization in a $^{87}$Rb free-induction-decay (FID) magnetometer. At low spin polarizations, ($P \leq 0.5$), this effect causes single-frequency magnetic-field extraction techniques to exhibit inaccuracies up to approximately 3.5 nT. Density-matrix simulations reveal that this bias can be traced to the relative amplitude and phase between the F = I $\pm$ 1/2 hyperfine ground-state manifolds in the FID spin precession signal. We show that this systematic error can be mitigated using either a double-frequency fitting model that accounts for the relative amplitude and phase or synchronous-pulse pumping, that minimizes the F = 1 contribution to the FID signal. Theoretical simulations predict accuracies within 0.5 nT for both techniques across a wide range of spin polarizations, suggesting a sevenfold enhancement over single-frequency extraction methods. Our experiments validate this, showcasing a variation in the extracted field below 1 nT, a 3.5-fold improvement compared to single-frequency extraction methods. Furthermore, the mitigation techniques demonstrate agreement of the extracted magnetic field within 1.5 nT.