Heading errors in all-optical alkali-metal-vapor magnetometers in geomagnetic fields

Alkali-metal atomic magnetometers suffer from heading errors in geomagnetic fields as the measured magnetic field depends on the orientation of the sensor with respect to the field. In addition to the nonlinear Zeeman splitting, the difference between Zeeman resonances in the two hyperfine ground states can also generate heading errors depending on initial spin polarization. We examine heading errors in an all-optical scalar magnetometer that uses free precession of polarized Rb87 atoms by varying the direction and magnitude of the magnetic field at different spin-polarization regimes. In the high-polarization limit where the lower hyperfine ground state F=1 is almost depopulated, we show that heading errors can be corrected with an analytical expression, reducing the errors by up to two orders of magnitude in earth's field. We also verify the linearity of the measured Zeeman precession frequency with the magnetic field. With lower spin polarization, we find that the splitting of the Zeeman resonances for the two hyperfine states causes beating in the precession signals and nonlinearity of the measured precession frequency with the magnetic field. We correct for the frequency shifts by using the unique probe geometry where two orthogonal probe beams measure opposite relative phases between the two hyperfine states during the spin precession.