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arXiv:2404.01199 · Physical Review A

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, Junjie Jiang, Jia-Qi Lei, Lu Zhou, Lin Zhou, Xi Chen, Jin Wang, Mingsheng Zhan

Published Jul 16, 2024• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.110.013317

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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 85Rb\ensuremath-87Rb^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}85Rb\ensuremath-87Rb 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{10}^{\ensuremath{-}11}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.
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.
In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of Δg/g≈6×10^{-11} per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in 10^{13}, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.
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.
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
We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an E\"otv\"os parameter of $\ensuremath{\eta}=[1.6\ifmmode\pm\else\textpm\fi{}1.8(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}3.4(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$, consistent with zero violation of the equivalence principle. With a resolution of up to $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{g}$ per shot, we demonstrate a sensitivity to $\ensuremath{\eta}$ of $5.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}/\sqrt{\mathrm{Hz}}$.