Zero-field atomic magnetometer unaffected by longitudinal magnetic field interference

Zero-field atomic magnetometers are susceptible to cross-axis coupling caused by longitudinal magnetic fields aligned with the pump beam direction, which degrades measurement accuracy on the sensitive axes. Herein, we propose a zero-field dual-axis atomic magnetometer with immunity to longitudinal magnetic field interference. Accounting for the zero-offset error, we establish the analytical model for dual-axis magnetic field measurement using the concept of generalized inverse matrix. We implement a closed-loop control method that stabilizes the first- and second-harmonic response signals at the double zero-offset points, actively rendering the magnetometer to an operating state invariant to longitudinal magnetic field fluctuations. Furthermore, to evaluate the performance, we also introduce the closed-loop suppression ratio as an indicator for control fidelity and the relative coupling suppression ratio (RCSR) to quantify effectiveness in coupling suppression. This method significantly enhances robustness against both quasi-static and dynamic longitudinal magnetic field variations and effectively suppresses cross-axis coupling. The closed-loop magnetometer achieves sensitivities of 7 fT/Hz^1/2 and 17 fT/Hz^1/2 along the x-axis and y-axis, respectively, exhibiting minimal degradation compared to normal open-loop performance. The proposed approach demonstrates strong resistance to complex longitudinal magnetic field fluctuations while maintaining high sensitivity and wide dynamic range, which offers great potential for precision multi-axis quantum sensing applications.