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arXiv:1708.05262 · Physical Review Letters

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

Guzhi Bao, Arne Wickenbrock, Simon Rochester, Weiping Zhang, Dmitry Budker

Published Jan 17, 2018• 69 citations
arXivHTMLPDF

Abstract

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 ∼100 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.

DOI
10.1103/physrevlett.120.033202

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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 ∼100 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.
The nonlinear Zeeman effect can induce splittings and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. We demonstrate a scheme to suppress the nonlinear Zeeman effect all optically based on spin locking. Spin locking is achieved with an effective oscillating magnetic field provided by the AC Stark-shift of an intensity-modulated and polarization-modulated laser beam. This results in the collapse of the multi-component asymmetric magnetic-resonance line with about 100 Hz width in the Earth-field range into a peak with a central component width of 25Hz. 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 and decreasing its width. Advantage of an all-optical approach is the absence of cross-talk between nearby sensors when these are used in a gradiometric or in an array arrangement.
The nonlinear Zeeman effect can induce splittings and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. We demonstrate an all-optical scheme, based on spin locking, to suppress the nonlinear Zeeman effect. This scheme achieves spin locking via an effective oscillating magnetic field in the form of AC Stark shifts induced by an intensity- and polarization-modulated laser beam. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ width in the Earth-field range into a peak with a central component width of 25 Hz. 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 and decreasing its width. An advantage of the all-optical approach is the absence of crosstalk between nearby sensors when they are used in a gradiometric or array arrangement.
Heading errors of atomic magnetometers refer to the dependence of measurement results on the sensor orientation with respect to the external magnetic field. There are three main sources of such errors: the light shift effect, the linear nuclear-spin Zeeman effect, and the nonlinear Zeeman effect. In this work, we suppress the first two effects by using the Bell-Bloom optical pumping method and probe the atomic signals while the pumping beam is off, and focus on the heading error induced by nonlinear Zeeman effect while the sensor operates in the geomagnetic field range. We demonstrate several schemes to suppress this remaining heading error within 1 nT using a single magnetometer or a comagnetometer. In the magnetometer system, two schemes are developed to average out the horizontal atomic polarization in space or in time, respectively. In the comagnetometer system, we combine the simultaneously measured Larmor frequencies of two different alkali atoms to either suppress the heading error or extract the orientation of the pumping beam relative to the bias field.
We demonstrate an alignment-based 87Rb^{87}\mathrm{Rb}87Rb magnetometer that is immune to nonlinear Zeeman (NLZ) splitting, addressing an important problem in alkali-metal atomic magnetometry. In our scheme, there is a single magnetic resonance peak and well-separated hyperfine transition frequencies, making the magnetometer insensitive or even immune to NLZ-related heading errors. It is shown that the magnetometer can be implemented for practical measurements in geomagnetic environments, and the photon-shot-noise-limited sensitivity reaches 9  fT/Hz9\text{ }\text{ }\mathrm{fT}/\sqrt{\mathrm{Hz}}9  fT/Hz​ at $5\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}$ and remains at tens of fT/Hz\mathrm{fT}/\sqrt{\mathrm{Hz}}fT/Hz​ at $50\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}$ at room temperature.
Precession frequencies measured by optically pumped scalar magnetometers are dependent on the relative angle between the sensor and the external magnetic field. This dependence is known to be induced mainly by the nonlinear Zeeman effect and the orientation-dependent light shift, resulting in the so-called heading errors if the magnetic field orientation is not well known or is not stable. In this work, we find that the linear nuclear Zeeman effect has also a significant impact on the heading errors. It not only shifts the precession frequency but causes asymmetry: the heading error for sensors orienting in the upper-half plane with respect to the external field is different from the case when the sensors work in the lower-half plane. This heading error also depends on the relative direction of the probe laser to the driving magnetic field. With a left-handed circularly-polarized pump laser, when the probe laser is parallel to the driving field, the angular dependence of the precession frequency is smaller when the sensor is in the upper plane. Otherwise, when they are perpendicular to each other, the heading error is smaller when the sensor is in the lower plane. Furthermore, to suppress the heading error, we propose to utilize a small magnetic field along the propagation direction of the pump laser. By tuning the magnitude of this auxiliary field, the heading-error curve is flattened around different angles, which can increase the accuracy in practice when the magnetometer works around a certain orientation angle.
Abstract Heading error is a major limitation for resonance-based atomic magnetometers operating in the geomagnetic-field range, where the magnetic-field direction often changes with respect to the sensor. Here, we investigate the physical origin of heading error in a single-beam amplitude-modulated nonlinear magneto-optical rotation magnetometer based on the hyperfine alignment resonances of the 87 Rb D1 line in a buffer-gas vapor cell. Unlike orientation-based magnetometers, where nonlinear Zeeman effects usually constitute a major source of heading error, the F = 2 alignment resonance spectrum maintains a stable center frequency under different magnetic-field orientations when the individual resonance components are unresolved. In practical single-beam measurements, the observed heading error is associated with an orientation-dependent residual spectral background, which breaks the apparent symmetry of the alignment-resonance profile and biases the extracted center frequency. To suppress this background-induced bias, we propose a multi-point frequency extraction method that retrieves the resonance center from distorted single-beam spectra. In unshielded geomagnetic-field measurements, the equal-weight pooled peak-to-peak heading-error estimate for the F = 2 manifold is reduced to 0.32 nT, with a one-sided 95% upper coverage limit of 0.90 nT. Separately, an estimated photon-shot-noise-limited sensitivity of about 23 fT / Hz 1 / 2 is obtained. These results provide a compact route to low-heading-error and high-sensitivity atomic magnetometry for practical geomagnetic-field quantum sensing.