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 ${}^{87}\mathrm{Rb}$ 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.

中文翻译：

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地磁场中全光碱金属蒸气磁强计的航向误差

碱金属原子磁力计在地磁场中存在航向误差，因为测量的磁场取决于传感器相对于磁场的方向。除了非线性塞曼分裂之外，两个超精细基态中塞曼共振之间的差异也会根据初始自旋极化产生航向误差。我们检查了使用极化自由进动的全光学标量磁力计的航向误差${}^{87}铷$通过在不同的自旋极化状态下改变磁场的方向和大小来改变原子。在低超精细基态的高极化极限$F=1$人口几乎减少，我们表明航向误差可以通过解析表达式进行校正，将地球磁场中的误差减少多达两个数量级。我们还验证了测量的塞曼进动频率与磁场的线性关系。对于较低的自旋极化，我们发现两个超精细状态的塞曼共振分裂导致进动信号的跳动以及测量的进动频率与磁场的非线性。我们通过使用独特的探针几何结构来校正频移，其中两个正交探测光束在自旋进动期间测量两个超精细状态之间的相反相对相位。