Sources of heading error in optically pumped magnetometers operated at Earth's magnetic field

When optically pumped magnetometers are aimed for the use in Earth's magnetic field, the orientation of the sensor to the field direction is of special importance to achieve accurate measurement result. Measurement errors and inaccuracies related to the heading of the sensor can be an even more severe problem in the case of special operational configurations, such as for example the use of strong off-resonant pumping. We systematically study the main contributions to the heading error in systems that promise high magnetic field resolutions at Earth's magnetic field strengths, namely the non-linear Zeeman splitting and the orientation dependent light shift. The good correspondence of our theoretical analysis to experimental data demonstrates that both of these effects are related to a heading dependent modification of the interaction between the laser light and the dipole moment of the atoms. Also, our results promise a compensation of both effects using a combination of clockwise and counter clockwise circular polarization.