Mechanism of the AC-Light-Shift-Induced Phase Shift and a DC Compensation Strategy in Bell-Bloom Magnetometers

The Bell-Bloom magnetometer is promising for mobile applications, but its accuracy is limited by heading errors. A recently identified source of such error is a phase shift in the magnetic resonance, which arises from the superposition of two signals, i.e., the primary resonance from synchronous pumping and a secondary resonance, 90° out-of-phase, driven by the AC light shift of the pump laser. Through Bloch equation modeling and experiment, we uncover a counter-intuitive mechanism: although initiated by the AC light shift, the phase shift's magnitude is determined solely by the pump light's average power (DC component) and is independent of its AC modulation. This occurs because the amplitude ratio of the two resonances depends exclusively on the DC-power-induced atomic polarization. Based on this insight, we propose a novel DC compensation scheme by adding a continuous counter-polarized beam to cancel the net DC pumping. Theoretically, this simultaneously suppresses both the AC-light-shift-induced phase shift and the DC-light-shift-induced frequency shift. The scheme's advantage is its simplified approach to polarization control, avoiding the need for high-speed polarization modulation or major hardware changes as the beams share the same optical path. This makes it highly suitable for demanding mobile applications like aerial magnetic surveying and wearable bio-magnetic sensing in unshielded environments.