Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1805.05159 · Physical Review A

Mapping the absolute magnetic field and evaluating the quadratic Zeeman-effect-induced systematic error in an atom interferometer gravimeter

Qingqing Hu, Christian Freier, Bastian Leykauf, Vladimir Schkolnik, Jun Jie Yang, Markus Krutzik, Achim Peters

Published Sep 20, 2017• 38 citations
arXivHTMLPDF

Abstract

Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the $\ensuremath{\mu}\mathrm{Gal}$ regime ($1\ensuremath{\mu}\mathrm{Gal}={10}^{\ensuremath{-}8}\mathrm{m}/{\mathrm{s}}^{2}\ensuremath{\approx}{10}^{\ensuremath{-}9}\mathrm{g}$). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as $2.04\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{Gal}$. The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.

DOI
10.1103/physreva.96.033414

Related papers

Evaluation of the systematic error induced by quadratic Zeeman effect using hyperfine-ground-state-exchange method in a long-baseline dual-species atom interferometer

Yu-Hang Ji, Chuan He, Sitong Yan +7 more

The systematic error induced by inhomogeneous residual magnetic fields through the quadratic Zeeman effect is non-negligible in atom interferometers and must be precisely evaluated. We use a hyperfine-ground-state-exchange (HGSE) method to evaluate the systematic error due to the quadratic Zeeman effect in the long-baseline $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ dual-species atom interferometer. We compare the HGSE method to two alternative evaluation methods used in the past, mapping the absolute magnetic field in the interference region and performing phase measurements at different bias fields, obtaining consistent results with an accuracy at the ${10}^{\ensuremath{-}11}$ level. In addition, we show that, unlike the other methods, the HGSE method can obtain the systematic error induced by the quadratic Zeeman effect in real time in case of slow drifts of either the ambient magnetic field or other systematic effects differential to the two hyperfine ground states. Using the HGSE method to suppress the quadratic Zeeman-effect-induced systematic error in long-baseline atom interferometer-based precision measurements could enable searches for new physics such as testing the equivalence principle.

arXiv:2404.01199•Physical Review A•Jul 16, 2024•1 citation

Increasing the length of free-falling path with homogeneous bias field for compact cold atom interferometers by configuring MOT coils

Huankai Zhang, Yaning Wang, Lingxiao Zhu +5 more

In a cold atom interferometer, a bias magnetic field, usually generated by a solenoid or a set of coils, is used to select specific Raman transitions of atoms in the interference region, and its inhomogeneity leads to a Zeeman-effect-induced error for the measurement. To improve the measurement’s accuracy further, we propose a simple method to compensate for the non-uniformity of the bias field by reversing the direction and tuning the value of the current running through the pair of quadrupole coils used for magneto-optical trap (MOT). To smoothen the field with MOT coils, the current applied should be controlled timely and precisely, which was done with a fast-responding electric circuit we designed and built. We also used Raman spectroscopy to characterize the magnetic field profile without and with our method applied, which shows that the length of the homogeneous field (where the fluctuation of magnetic strength is less than 10%) is expanded from 81.87 mm to 101.64 mm. From our calculations, with the free evolution time T of 30 ms, the quadratic Zeeman-effect-induced phase shift Δϕzeeman can be reduced by 76%, which reduces the quadratic Zeeman-effect-induced error of measured gravity Δgzeeman to a quarter of that without our method applied (from 1.745 mGal to 0.418 mGal). Simulation and experiment prove that this method is effective. This method can also be used in other atom interferometers, especially compact systems.

AIP Advances•Sep 1, 2020•3 citations

Effect of Raman-pulse duration related to the magnetic field gradient in high-precision atom gravimeters

Yuan Sheng Cheng, Yu-Jie Tan, Min-Kang Zhou +3 more

The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effect with a simplified theoretical model of the time-propagation operator. According to the typical parameters, we find that this effect should be taken into account when the gravimeter reaches an accuracy of 10 −10 g, and the larger the pulse duration is, the more obvious the systematic effect will be. Finally, we make a simple discussion on the possibility of testing this effect.

Chinese Physics B•Mar 1, 2018•4 citations

Rapid extraction of the phase shift of the cold-atom interferometer via phase demodulation

Bing Cheng, Zhaoying Wang, Ao-Peng Xu +2 more

Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T . If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T . Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T .

Chinese Physics B•Nov 1, 2015•5 citations

Rapid extraction of the phase shift of the cold-atom interferometer via phase demodulation

Bing Cheng, 王兆英, 许翱鹏 +2 more

Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T. If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T. Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T.更多还原

中国物理B：英文版•Jan 1, 2015•0 citations

Precisely mapping the magnetic field gradient in vacuum with an atom interferometer

Min-Kang Zhou, Zhong-Kun Hu, Xiao‐Chun Duan +3 more

The magnetic field gradient has been measured with an atom interferometer using the magnetic sublevels of $^{87}\mathrm{Rb}$ atoms. The Doppler-insensitive measurement effectively eliminates the contribution from gravity and background vibration noise, and the differential measurement also can reject some systematic errors. A resolution of $300$ pT/mm has been demonstrated with a $90$-s integration time and a spatial resolution of $1.4$ mm. The gradiometer was then used to measure the magnetic field gradient in an ultrahigh-vacuum environment. The technique will also be very useful to subtract the systematic error arising from the magnetic field inhomogeneity in precision atom-interferometry experiments, such as gravity measurement.

Physical Review A•Dec 10, 2010•61 citations
Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the \ensuremathμGal\ensuremath{\mu}\mathrm{Gal}\ensuremathμGal regime (1\ensuremathμGal=10\ensuremath−8m/s2\ensuremath≈10\ensuremath−9g1\ensuremath{\mu}\mathrm{Gal}={10}^{\ensuremath{-}8}\mathrm{m}/{\mathrm{s}}^{2}\ensuremath{\approx}{10}^{\ensuremath{-}9}\mathrm{g}1\ensuremathμGal=10\ensuremath−8m/s2\ensuremath≈10\ensuremath−9g). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as 2.04\ensuremathμGal2.04\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{Gal}2.04\ensuremathμGal. The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.
The systematic error induced by inhomogeneous residual magnetic fields through the quadratic Zeeman effect is non-negligible in atom interferometers and must be precisely evaluated. We use a hyperfine-ground-state-exchange (HGSE) method to evaluate the systematic error due to the quadratic Zeeman effect in the long-baseline $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ dual-species atom interferometer. We compare the HGSE method to two alternative evaluation methods used in the past, mapping the absolute magnetic field in the interference region and performing phase measurements at different bias fields, obtaining consistent results with an accuracy at the ${10}^{\ensuremath{-}11}$ level. In addition, we show that, unlike the other methods, the HGSE method can obtain the systematic error induced by the quadratic Zeeman effect in real time in case of slow drifts of either the ambient magnetic field or other systematic effects differential to the two hyperfine ground states. Using the HGSE method to suppress the quadratic Zeeman-effect-induced systematic error in long-baseline atom interferometer-based precision measurements could enable searches for new physics such as testing the equivalence principle.
In a cold atom interferometer, a bias magnetic field, usually generated by a solenoid or a set of coils, is used to select specific Raman transitions of atoms in the interference region, and its inhomogeneity leads to a Zeeman-effect-induced error for the measurement. To improve the measurement’s accuracy further, we propose a simple method to compensate for the non-uniformity of the bias field by reversing the direction and tuning the value of the current running through the pair of quadrupole coils used for magneto-optical trap (MOT). To smoothen the field with MOT coils, the current applied should be controlled timely and precisely, which was done with a fast-responding electric circuit we designed and built. We also used Raman spectroscopy to characterize the magnetic field profile without and with our method applied, which shows that the length of the homogeneous field (where the fluctuation of magnetic strength is less than 10%) is expanded from 81.87 mm to 101.64 mm. From our calculations, with the free evolution time T of 30 ms, the quadratic Zeeman-effect-induced phase shift Δϕzeeman can be reduced by 76%, which reduces the quadratic Zeeman-effect-induced error of measured gravity Δgzeeman to a quarter of that without our method applied (from 1.745 mGal to 0.418 mGal). Simulation and experiment prove that this method is effective. This method can also be used in other atom interferometers, especially compact systems.
The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effect with a simplified theoretical model of the time-propagation operator. According to the typical parameters, we find that this effect should be taken into account when the gravimeter reaches an accuracy of 10 −10 g, and the larger the pulse duration is, the more obvious the systematic effect will be. Finally, we make a simple discussion on the possibility of testing this effect.
Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T . If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T . Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T .
Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T. If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T. Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T.更多还原
The magnetic field gradient has been measured with an atom interferometer using the magnetic sublevels of 87Rb^{87}\mathrm{Rb}87Rb atoms. The Doppler-insensitive measurement effectively eliminates the contribution from gravity and background vibration noise, and the differential measurement also can reject some systematic errors. A resolution of 300300300 pT/mm has been demonstrated with a 909090-s integration time and a spatial resolution of 1.41.41.4 mm. The gradiometer was then used to measure the magnetic field gradient in an ultrahigh-vacuum environment. The technique will also be very useful to subtract the systematic error arising from the magnetic field inhomogeneity in precision atom-interferometry experiments, such as gravity measurement.