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arXiv:2204.05071 · Physical Review Letters

Heading-Error-Free Optical Atomic Magnetometry in the Earth-Field Range

Rui Zhang, Dimitra Kanta, Arne Wickenbrock, Hong Mei Guo, Dmitry Budker

Published Apr 12, 2023• 31 citations
arXivHTMLPDF

Abstract

We demonstrate an alignment-based $^{87}\mathrm{Rb}$ 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 $9\text{ }\text{ }\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at $5\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}$ and remains at tens of $\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at $50\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}$ at room temperature.

DOI
10.1103/physrevlett.130.153601

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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  \ensuremathμT5\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}5  \ensuremathμT and remains at tens of fT/Hz\mathrm{fT}/\sqrt{\mathrm{Hz}}fT/Hz​ at 50  \ensuremathμT50\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{T}50  \ensuremathμT at room temperature.
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.
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.
A prototype magnetometer for anti-submarine warfare applications is being developed based on nonlinear magneto-optical rotation (NMOR) in atomic vapors. NMOR is an atomic spectroscopy technique that exploits coherences among magnetic sublevels of atoms such as cesium or rubidium to measure magnetic fields with high precision. NMOR uses stroboscopic optical pumping via frequency or amplitude modulation of a linearly polarized laser beam to create the alignment. An anti-relaxation coating on the walls of the atomic vapor cell can result in a long lifetime of 1 s or more for the coherence and enables precise measurement of the precession frequency. With proper feedback, the magnetometer can self-oscillate, resulting in accurate tracking and fast time response. The NMOR magnetic resonance spectrum of 87Rb has been measured as a function of heading in Earth's field. Optical pumping of alignment within the F=2 hyperfine manifold generates three resonances separated by the nonlinear Zeeman splitting. The spectra show a high degree of symmetry, consisting of a central peak and two side peaks of nearly equal intensity. As the heading changes, the ratio of the central peak to the average of the two side peaks changes. The amplitudes of the side peaks remain nearly equal. An analysis of the forced oscillation spectra indicates that, away from dead zones, heading error in self-oscillating mode should be less than 1 nT. A broader background is also observed in the spectra. While this background can be removed when fitting resonance spectra, understanding it will be important to achieving the small heading error in self-oscillating mode that is implied by the spectral measurements. Progress in miniaturizing the magnetometer is also reported. The new design is less than 10 cm across and includes fiber coupling of light to and from the magnetometer head. Initial tests show that the prototype has achieved a narrow spectral width and a strong polarization rotation signal.
Nonlinear Zeeman (NLZ) shifts arising from magnetic-field mixing of the two hyperfine ground states in alkali-metal atoms lead to splitting of magnetic-resonance lines. This is a major source of sensitivity degradation and the so-called ``heading errors'' of alkali-metal-vapor atomic magnetometers operating in the geophysical field range $(B\ensuremath{\approx}0.2--0.7\phantom{\rule{0.3em}{0ex}}\mathrm{G})$. Here, it is shown theoretically and experimentally that NLZ shifts can be effectively canceled by light shifts caused by a laser field of appropriate intensity, polarization, and frequency, a technique that can be readily applied in practical situations.
We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high-frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. Based on experimentally measured signal-to-noise ratio, we demonstrate a sensitivity of 100pG∕Hz100\phantom{\rule{0.3em}{0ex}}\mathrm{pG}∕\sqrt{\mathrm{Hz}}100pG∕Hz​ (rms) in a $3.5\text{\ensuremath{-}}\mathrm{cm}$-diameter paraffin coated cell. Assuming detection at the photon shot-noise limit, we project a sensitivity as low as 25pG∕Hz25\phantom{\rule{0.3em}{0ex}}\mathrm{pG}∕\sqrt{\mathrm{Hz}}25pG∕Hz​ (rms).
Optical magnetometers measure magnetic fields with extremely high precision and without cryogenics. However, at geomagnetic fields, important for applications from landmine removal to archaeology, they suffer from nonlinear Zeeman splitting, leading to systematic dependence on sensor orientation. We present experimental results on a method of eliminating this systematic error, using the hexadecapole atomic polarization moment. In particular, we demonstrate selective production of the atomic hexadecapole moment at Earth’s magnetic field and verify its immunity to nonlinear Zeeman splitting. This technique promises to eliminate directional errors in all-optical atomic magnetometers, potentially improving their measurement accuracy by several orders of magnitude.