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Microsystems & Nanoengineering

Tesla-scale magnetic field measurement based on Sideband-overlap Zeeman spectroscopy using a functionalized MEMS vapor cell

Ju Guo, Yintao Ma, Dejiang Lu, Mingzhi Yu, Yanbin Wang, Ping Yang, Qijing Lin, Libo Zhao, Yuehua Chen

Published Jun 5, 2026• 0 citations
Publisher

Abstract

Accurate measurement of strong magnetic fields in the Tesla range remains a persistent challenge due to calibration drift, nonlinearity, and spatial gradient sensitivity. Here, we present a compact magnetometry approach based on sideband-overlap Zeeman spectroscopy, enabled by a functionalized MEMS cesium vapor cell. The vapor cell features a dual-chamber glass–Si–glass structure with integrated microheaters on the optical window. A first-order electro-optic modulator produces optical sidebands aligned with the σ+ and $${{\rm{\sigma }}}^{-}$$ Zeeman-split components of the Cs D1 line under the hyperfine Paschen–Back regime. Magnetic field scanning from zero to Tesla-scale fields enables extraction of the frequency offset between reference and Zeeman-shifted spectra. This frequency shift is directly converted into magnetic field strength using Zeeman spectroscopy in the hyperfine Paschen–Back regime. The method resolves sixteen Zeeman transitions (eight $${{\rm{\sigma }}}^{+}$$ and eight $${{\rm{\sigma }}}^{-}$$ ), allowing measurement of a field strength of 0.6694921 T, with a single-shot resolution of 6.4 μT and a cross-transition repeatability of σB = 8.9 μT (corresponding to 13 ppm at 0.6695 T). In a millimeter-scale sensing volume, the system achieves sub-10 μT repeatability without requiring a uniform bias field. These results indicate that the microfabricated high-field magnetometer can serve as a compact and practical approach for Tesla-range field measurement and pave the way for chip-scale quantum devices.

DOI
10.1038/s41378-026-01272-7

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Accurate measurement of strong magnetic fields in the Tesla range remains a persistent challenge due to calibration drift, nonlinearity, and spatial gradient sensitivity. Here, we present a compact magnetometry approach based on sideband-overlap Zeeman spectroscopy, enabled by a functionalized MEMS cesium vapor cell. The vapor cell features a dual-chamber glass–Si–glass structure with integrated microheaters on the optical window. A first-order electro-optic modulator produces optical sidebands aligned with the σ+ and σ−{{\rm{\sigma }}}^{-}σ− Zeeman-split components of the Cs D1 line under the hyperfine Paschen–Back regime. Magnetic field scanning from zero to Tesla-scale fields enables extraction of the frequency offset between reference and Zeeman-shifted spectra. This frequency shift is directly converted into magnetic field strength using Zeeman spectroscopy in the hyperfine Paschen–Back regime. The method resolves sixteen Zeeman transitions (eight σ+{{\rm{\sigma }}}^{+}σ+ and eight σ−{{\rm{\sigma }}}^{-}σ− ), allowing measurement of a field strength of 0.6694921 T, with a single-shot resolution of 6.4 μT and a cross-transition repeatability of σB = 8.9 μT (corresponding to 13 ppm at 0.6695 T). In a millimeter-scale sensing volume, the system achieves sub-10 μT repeatability without requiring a uniform bias field. These results indicate that the microfabricated high-field magnetometer can serve as a compact and practical approach for Tesla-range field measurement and pave the way for chip-scale quantum devices.
39 K atoms have the smallest ground state ( 2 S 1 / 2 ) hyperfine splitting of all the most naturally abundant alkali isotopes and, consequently, the smallest characteristic magnetic field value B 0 = A 2 S 1 / 2 / μ B ≈ 170 G , where A 2 S 1 / 2 is the ground state’s magnetic dipole interaction constant. In the hyperfine Paschen–Back regime ( B ≫ B 0 , where B is the magnitude of the external magnetic field applied on the atoms), only eight Zeeman transitions are visible in the absorption spectrum of the D 1 line of 39 K , while the probabilities of the remaining 16 Zeeman transitions tend to zero. In the case of 39 K , this behavior is reached already at relatively low magnetic field B > B 0 . For each circular polarization ( σ − , σ + ), four spectrally resolved atomic transitions having sub-Doppler widths are recorded using a sub-microsized vapor cell of thickness L = 120 − 390 n m . We present a method that allows to measure the magnetic field in the range of 0.1 − 10 k G with micrometer spatial resolution, which is relevant in particular for the determination of magnetic fields with large gradients (up to 3 G/µm). The theoretical model describes well the experimental results.
We use a magnetometer probe based on the Zeeman shift of the rubidium resonant optical transition to explore the atomic magnetic response for a wide range of field values. We record optical spectra for fields from a few tesla up to 60 T, the limit of the coil producing the magnetic field. The atomic absorption is detected by the fluorescence emissions from a very small region with a submillimeter size. We investigate a wide range of magnetic interactions from the hyperfine Paschen-Back regime to the fine one and the transitions between them. The magnetic field measurement is based on the rubidium absorption itself. The rubidium spectroscopic constants were previously measured with high precision, except the excited state Land\'e ggg-factor that we derive from the position of the absorption lines in the transition to the fine Paschen-Back regime. Our spectroscopic investigation, even if limited by the Doppler broadening of the absorption lines, measures the field with a 20 ppm uncertainty at the explored high magnetic fields. Its accuracy is limited to 75 ppm by the excited state Land\'e ggg-factor determination.
Micrometric-thin cells (MCs) with alkali vapor atoms have been valuable for research and applications of hyperfine Zeeman splitting and atomic magnetometers under strong magnetic fields. We theoretically and experimentally study the saturated absorption spectra using a 100-μm cesium MC, where the pump and probe beams are linearly polarized with mutually perpendicular polarizations, and the magnetic field is along the pump beam. Because of the distinctive thin chamber of the MC, crossover spectral lines in saturated absorption spectra are largely suppressed leading to clear splittings of hyperfine Zeeman transitions in experiments, and the effect of spatial magnetic field gradient is expected to be reduced. A calculation method is proposed to achieve good agreements between theoretical calculations and experimental results. This method successfully explains the suppression of crossover lines in MCs, as well as the effects of magnetic field direction, propagation and polarization directions of the pump/probe beam on saturated absorption spectrum. The saturated absorption spectrum with suppressed crossover lines is used for laser frequency stabilization, which may provide the potential value of MCs for high spatial resolution strong-field magnetometry with high sensitivity.
We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10 −4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87 Rb is found to be ∼40 kHz °C −1 .
We present a novel high-field optical quantum magnetometer based on saturated absorption spectroscopy on the extreme angular-momentum states of the cesium D2 line. With key features including continuous readout, high sampling rate, and sensitivity and accuracy in the ppm range, it represents a competitive alternative to conventional techniques for measuring magnetic fields of several teslas. The prototype has four small separate field probes, and all support electronics and optics are fitted into a single 19-inch rack to make it compact, mobile, and robust. The field probes are fiber coupled and made from nonmetallic components, allowing them to be easily and safely positioned inside a 7 T MRI scanner. We demonstrate the capabilities of this magnetometer by measuring two different MRI sequences, and we show how it can be used to reveal imperfections in the gradient coil system, to highlight the potential applications in medical MRI. We propose the term EXAAQ (EXtreme Angular-momentum Absorption-spectroscopy Quantum) magnetometry, for this novel method. Published by the American Physical Society 2024
We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10−4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87Rb is found to be ∼40 kHz °C−1.