Suppression of the Nonlinear Zeeman Effect and Heading Error in Earth-Field-Range Alkali-Vapor Magnetometers

The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. This is a major source of “heading error” for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear Zeeman effect and heading error based on spin locking. In an all-optical synchronously pumped magnetometer with separate pump and probe beams, we apply a radio-frequency field which is in phase with the precessing magnetization. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with $\sim 100\mathrm{Hz}$ width in the Earth-field range into a single peak with a width of 22 Hz, whose position is largely independent of the orientation of the sensor within a range of orientation angles. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude, decreasing its width, and removing the important and limiting heading-error systematic.

Figure 1

(a) Hyperfine structure of the Cs ground state manifolds in an external magnetic field. In this work, we are concerned with fields that correspond to $\sim {10}^{-4}$ of the shown range, where the NLZ effect is a small perturbation. (b) Optical-rotation signal amplitude (see Fig. 2) from the lock-in amplifier for a fixed pump-modulation frequency of 216 560 Hz and a sweep of the magnetic field (given in Larmor frequency of the magnetic resonance neglecting NLZ shifts). The central field is $B\approx 62\mu \mathrm{T}$. The data are fit with eight Lorentzian peaks arising due to the NLZ effect. (c) The same data collected with a 20° tilt of the sensor and a pump-modulation frequency of 230 475 Hz.

Figure 2

Experimental setup. AOM, acousto-optic modulator used to pulse the pump beam; HWP, half-wave plate; PBS, polarizing beam splitter; PD, balanced photodetector; LIA, lock-in amplifier; LO, local oscillator. Atoms are contained in a vapor cell positioned in the center of the magnetic shield and are pumped and probed by laser beams under a static (along $\widehat{z}$) and an oscillating magnetic field (along $\widehat{y}$). A partial view of the magnetic shield is shown in the figure.

Figure 3

Normalized magnetic-resonance data for a pump-modulation frequency of 324 840 Hz as a function of the leading magnetic field along the $\widehat{z}$ axis with (red, right vertical scale) and without (black, left vertical scale) an applied spin-locking rf field.

Figure 4

(a) Optical-rotation signal amplitude for a fixed pump-modulation frequency of 223 700 Hz while scanning the magnetic field (expressed in Larmor frequency). The red curve shows the effect of a heading error for a 10° misalignment of the magnetic-field axis to the direction of the probe beam (the $\widehat{x}$ axis). A tilt in the field seems to shift the center of the resonance to higher frequencies and causes a visible asymmetry in the line shape. We fit the signal with eight Lorentzian peaks. The center of the resonance is found by averaging the eight individual center frequencies. The black curve shows the magnetic resonance for the same misaligned magnetic field with an applied 1 nT spin-locking field. The resonance is symmetric with the correct central frequency. (b) Observed shift of the magnetic resonance due to a heading error as a function of the misalignment angle for different amplitudes of the spin-locking field. Without this, the heading error is about $1.1\mathrm{Hz}/\mathrm{degree}$, and it reduces for increasing spin-locking field amplitudes.