Phase projection errors in rf-driven optically pumped magnetometers

TL;DR

This paper analyzes phase projection errors in rf-driven optically pumped magnetometers, revealing fundamental limitations in response time and accuracy, especially under dynamic magnetic field conditions, with implications for geomagnetic surveying and mobile applications.

Contribution

It provides an analytical solution to the phase response in scalar rf-driven OPMs and demonstrates how magnetic field tilts cause transient phase errors affecting magnetometer performance.

Findings

Transient phase response depends on magnetic field tilt.

Alignment of rf field reduces static phase dependence.

Fundamental limits identified for response time and accuracy.

Abstract

We investigate the phase relationship between the oscillating (rf) excitation field and the detected (light) power modulation in scalar rf-driven optically pumped magnetometers (OPMs), in particular in the $M_x$ configuration. While the static dependence of the demodulation phase on the direction of the external static magnetic field vector can be largely mitigated by aligning the oscillating rf field along the light propagation direction, we demonstrate that a dynamic (transient) phase response arises under magnetic field tilts. We analytically solve the corresponding modified Bloch equation and confirm agreement with experimental observations obtained using an $M_x$ magnetometer incorporating a paraffin-coated Cs vapor cell. The results reveal fundamental limitations of $M_x$ magnetometers regarding response time and accuracy, in particular when employed with active electronic feedback, such as a phase-locked loop. Therefore, this work is highly relevant to important magnetometry applications where the direction of the quasi-static magnetic field of interest is unknown \textit{a priori} or varies over time, or in measurements requiring a large detection bandwidth. Such conditions are encountered in applications such as geomagnetic surveying, particularly with mobile platforms.