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Chinese Physics B

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, Xiao‐Chun Duan, Cheng-Gang Shao, Zhong-Kun Hu

Published Mar 1, 2018• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/27/3/030303

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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.
For high-precision atom interferometry gravimeters, the effect of the Raman pulse duration will become an appreciable fraction and need to be taken into account. Its influence has been reported considering a homogeneous Earth’s gravitational field in some previous works. In this paper, by decomposing the time evolution operator into two parts, the free evolution part and the interaction part, we develop an approach to study this effect in a realistic situation where the Earth’s gravitational field is inhomogeneous. A mathematic expression for the interferometer phase shift because of the Raman pulse duration effect is obtained, which shows that the Raman pulse duration should be taken into account when the gravimeter reaches an accuracy of 10−10 g.
Although frequency-shift gravity-gradient compensation is currently the technique with the most potential to test the weak equivalence principle with atom interferometry at high precision, it faces an unavoidable obstacle on how to cancel the coupling between the Raman-pulse-duration effect and the gravity gradient related to the atomic initial kinematics. According to the Einstein equivalence principle, we develop a method to calculate this coupling effect in a space-stretching free-falling frame, based on which an improved frequency-shift gravity-gradient compensation technique is put forward to make high-accuracy weak-equivalence-principle tests with the microscopic particles, such as at the level of ${10}^{\ensuremath{-}14}$, more possible.
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.
We investigate the dependence of the sensitivity of atom interferometer gravimeter on the Raman laser pulse sequence. The sensitivity of atom gravimeter can be adjusted by changing the pulse duration. Under the standard pulse configuration condition, the atom interferometer with four pulses is insensitive to the gravity if only gravity and its first order gradient are taken into account. The three-pulse Raman atom interferometer gravimeter displays best sensitivity. Atom interferometers with more than four Raman pulses show poorer sensitivity.
Abstract With the rapid development of atom interference technology, multi-loop atom interferometers are widely used in the high-precision measurement of various physical constants and testing of various gravity-related effects. However, in ground-based multi-loop atom interference experiments, the systematic error contribution by classical effects is an important factor that affects the experimental measurement accuracy and gravitational effect detection. Based on this, we used the atomic wave-function evolution-phase accumulation method to provide a high-order interference phase of multi-loop atom interferometers in an inhomogeneous gravitational field containing Earth’s rotation. Furthermore, we propose a new scheme that combines optimised frequency-shift compensation technology with an improved pulse sequence to eliminate systematic errors due to the gravity gradient, Earth’s rotation, and their coupling effect with the pulse duration, as well as the coupling effect of laser detuning with the pulse duration. This study lays a theoretical foundation for experiments on multi-loop atom interferometers with higher precision.
We investigated the Raman-pulse-duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate for the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser. This leads to an appreciable phase shift. The magnitude of the phase shift relative to the differential phase shift of the two interferometers is in an order of $\ensuremath{\tau}/T$, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.