Polarization-gradient optical pumping in an atomic magnetometer

High-precision Mz/Mx atomic magnetometers have "dead zones", where the magnetic-field information will be lost because the light-atom interaction vanishes at specific field angles. To suppress dead zones, we propose a scheme with polarization-gradient optical pumping field by using counter-propagating lin⊥lin beams. We found through experiments that the lin⊥lin scheme eliminates dead zones in the transverse plane of the probe beam propagation (minimum ∼40% normalized signal) but leaves two noncanonical magic-angle-like directions (≈30^∘ and 150^∘) in the longitudinal plane, which is distinct from the standard tensor magic angle (≈54^∘ and 126^∘). These observations are quantitatively explained using a multipole-based model formulated in terms of an effective, spatially averaged density matrix, which is the first time that the spatial average density matrix has been used for energy state analysis in atomic magnetometers. Under the probing of a linearly polarized light, the measured signal is determined by the field-angle-dependent projection of the atomic longitudinal alignment moment (m_2,0) onto the B₀-defined quantization axis. Compared with other dead-zone elimination schemes, our scheme avoids polarization modulation and multi-cell architectures, showing potential for improving the spatial response range of compact atomic magnetometry.