Polarization-dynamics model of triaxial modulation in spin-exchange-relaxation-free atomic magnetometers

Triaxial spin-exchange-relaxation-free (SERF) atomic magnetometers (AMs), as opposed to the single-axis configuration, provide more comprehensive magnetic field information on biomagnetic measurements, effectively improving their capabilities for magnetic source reconstruction. Typically, the triaxial AM is considered to be three independent orthogonal single-axis AMs, but the interaction of the triaxial modulation is ignored. This study established a polarization-dynamics model under triaxial modulation, providing a theoretical model for triaxial AMs. On the basis of perturbation iteration theory, the modulation field along the cross-axis is regarded as a perturbation term. Subsequently, we established the polarization-dynamics model by summing the steady-state and multiorder perturbations of the triaxial polarization projections. Based on the proposed model, we discovered an optimal modulation coefficient formula for the triaxial SERF AM, replacing the constant optimal coefficient used when treating it as three independent single-axis AMs. The proposed optimal modulation coefficient exhibited a 12% improvement in response relative to the conventional coefficient. We also constructed a triaxial-modulation SERF AM to verify the proposed polarization-dynamics model under different triaxial-modulation parameters. The proposed polarization-dynamics model is beneficial for further investigation of triaxial SERF AMs and contributes to the improvement of their sensitivity.