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arXiv:2305.00263 · Physical Review A

Stroboscopic microwave spectroscopy of Voigt-based optically pumped magnetometers

H. M. Florez, Tadas Pyragius, T. Fernholz

Published Oct 1, 2024• 0 citations
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Abstract

We present the results of stroboscopic microwave spectroscopy of a radio-frequency-dressed optically pumped magnetometer. The interaction between radio-frequency-dressed atoms and a synchronously pulsed microwave field followed by Voigt-effect-based optical probing allows us to perform a proper ground-state interrogation for dressed state and assess the efficiency of the state preparation process. This work shows that through the stroboscopic technique the microwave spectrum is simplified when compared to the continuous counterpart. This is a necessary step towards investigating vector magnetometers in unshielded environments, where the influence of the nonlinear Zeeman effect, a source of heading errors, would otherwise be spectrally unresolved in dressed states. To theoretically describe the system, we solve the dynamical equation of the density matrix employing Floquet expansion. Our theoretical results are in good agreement with experimental measurements over a wide range of parameters and pumping conditions.

DOI
10.1103/physreva.110.043102

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We present the results of stroboscopic microwave spectroscopy of a radio-frequency-dressed optically pumped magnetometer. The interaction between radio-frequency-dressed atoms and a synchronously pulsed microwave field followed by Voigt-effect-based optical probing allows us to perform a proper ground-state interrogation for dressed state and assess the efficiency of the state preparation process. This work shows that through the stroboscopic technique the microwave spectrum is simplified when compared to the continuous counterpart. This is a necessary step towards investigating vector magnetometers in unshielded environments, where the influence of the nonlinear Zeeman effect, a source of heading errors, would otherwise be spectrally unresolved in dressed states. To theoretically describe the system, we solve the dynamical equation of the density matrix employing Floquet expansion. Our theoretical results are in good agreement with experimental measurements over a wide range of parameters and pumping conditions.
We present a theoretical description of the Voigt and Faraday effect based optically pumped magnetometers using the Floquet expansion. Our analysis describes the spin-operator dynamics of the first- $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{F}(t)$ and second-order ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{F}}^{2}(t)$ moments and takes into account different pumping profiles and decoherence effects. We find that the theoretical results are consistent with previous experimental demonstrations over a wide range of fields and pumping conditions. Finally, the theoretical analysis presented here is generalized and can be extended to different magnetometry schemes with arbitrary pumping profiles and multiple radio-frequency fields.
Magnetism plays a fundamental role in nature existing in almost every conceivable domain of the physical world ranging from stars and planets to our brains and hearts. Some magnetic phenomena are easy to observe and measure, whilst others are small and subtle making them almost impossible to detect. Developments in precision magnetometry, utilising the quantum nature of atoms has given access to the world of small and subtle enabling the understanding of such signals as well as pushing the boundaries of knowledge of the fundamental forces of nature. In this thesis we describe theoretical and experimental methods to dispersively detect all three vector components of an external magnetic field using radio-frequency dressed alkali atoms based on the Voigt effect. To achieve this, we measure the linear birefringence of the radio frequency dressed atomic medium via polarization homodyning. This gives rise to modulated polarization signals at the first and second harmonic of the dressing frequency. The vector components of the external magnetic field are mapped onto the quadratures of these harmonics. Our scheme requires only one frequency of modulation and has a simple single axis beam geometry making it advantageous for miniature magnetic field sensors. Furthermore, we extend our Voigt effect scheme to dressed microwave spectroscopy and show that it can be used to infer the prepared state populations paving the way towards partial quantum state tomography.
We describe a method to dispersively detect all three vector components of an external magnetic field using alkali-metal atoms based on the Voigt effect. Our method relies on measuring the linear birefringence of the radio-frequency dressed atomic medium via polarization homodyning. This gives rise to modulated polarization signals at the first and second harmonic of the dressing frequency. The vector components of the external magnetic field are mapped onto the quadratures of these harmonics. We find that our scheme can be utilized in both cold and hot atomic gases to detect such external fields in shielded and unshielded environments. In the shielded hot vapor case we achieve field sensitivities in the pT/Hz\mathrm{pT}/\sqrt{\mathrm{Hz}}pT/Hz​ range for all three vector components, using pump-probe cycles with 125-Hz repetition rate, and limited by the short coherence time of the cell. Finally, our scheme has a simple single axis beam geometry, making it advantageous for miniature magnetic-field sensors.
We study the hyperfine spectrum of atoms of 87Rb^{87}\mathrm{Rb}87Rb dressed by a radio-frequency field and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap, and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant sidebands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum using a semiclassical model in the low-field limit and the rotating-wave approximation for alkali-metal-like species, in general, and 87Rb^{87}\mathrm{Rb}87Rb atoms, in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.
Optically pumped magnetometers usually rely on optical pumping using circularly or linearly polarized light. We study here zero-field magnetometers pumped with elliptically polarized light, preparing both atomic orientation and alignment with complementary geometries. We start by extending the three-step approach for elliptically polarized pumping. This allows us to study the Hanle effect in elliptical polarization by comparing the analytical absorption signals with experiments made on 4He^{4}\mathrm{He}4He metastable state. We then study parametric resonance magnetometers based on elliptical polarization by using the dressed-atom formalism with one and two radio-frequency fields. The results show good agreement with the experimental measurements and interesting perspectives for magnetometry where symmetry breaking by pumping light is mitigated.
Robust calibration of vector optically pumped magnetometers (OPMs) is a nontrivial task, but increasingly important for applications requiring high-accuracy such as magnetic navigation, geophysics research, and space exploration. Here, we showcase a vector OPM that utilizes Rabi oscillations driven between the hyperfine manifolds of 87 Rb to measure the direction of a DC magnetic field against the polarization ellipse structure of a microwave field. By relying solely on atomic measurements—free-induction decay (FID) signals and Rabi measurements across multiple atomic transitions—this sensor can detect drift in the microwave vector reference and compensate for systematic shifts caused by off-resonant driving, nonlinear Zeeman (NLZ) effects, and buffer gas collisions. To facilitate deadzone-free operation, we also introduce a Rabi measurement that utilizes dressed-state resonances that appear during simultaneous Larmor precession and Rabi driving (SPaR). These measurements, performed within a microfabricated vapor cell platform, achieve an average vector accuracy of 0.46 mrad and vector sensitivities down to 11µrad/Hz for geomagnetic field strengths near 50 µT. This performance surpasses the challenging 1-deg (17 mrad) accuracy threshold of several contemporary OPM methods utilizing atomic vapors with an electromagnetic vector reference.