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arXiv:1503.01199 · Physical Review A

Raman-pulse-duration effect in gravity gradiometers composed of two atom interferometers

Cheng-Gang Shao, Dekai Mao, Min-Kang Zhou, Yu-Jie Tan, Lele Chen, Jun Luo, Zhong-Kun Hu

Published Nov 16, 2015• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.92.053613

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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 \ensuremathτ/T\ensuremath{\tau}/T\ensuremathτ/T, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.
Gravity gradients represent a major obstacle in high-precision measurements by atom interferometry. Controlling their effects to the required stability and accuracy imposes very stringent requirements on the relative positioning of freely falling atomic clouds, as in the case of precise tests of Einstein's equivalence principle. We demonstrate a new method to exactly compensate the effects introduced by gravity gradients in a Raman-pulse atom interferometer. By shifting the frequency of the Raman lasers during the central π pulse, it is possible to cancel the initial position- and velocity-dependent phase shift produced by gravity gradients. We apply this technique to simultaneous interferometers positioned along the vertical direction and demonstrate a new method for measuring local gravity gradients that does not require precise knowledge of the relative position between the atomic clouds. Based on this method, we also propose an improved scheme to determine the Newtonian gravitational constant G towards the 10 ppm relative uncertainty.
Light-pulse atom gravimetry has emerged as a powerful technique for precisely measuring absolute gravitational acceleration. Raman lasers are commonly used in this technique to coherently manipulate the atomic wave packet, of which the effective frequency is chirped continuously to compensate for the Doppler shift. In this study we investigate an additional phase shift in the Raman lasers that arises due to the frequency chirp. We directly measure this phase shift by recording the beat signal of the Raman lasers with a high-speed oscilloscope, providing an independent evaluation of the resultant error in atom gravimeters caused by this phase shift. Concurrently, we detect the influence of the additional phase shift on gravity measurements using our atom gravimeter, and the results are in good agreement with the independent evaluation. Notably, there may still be a residual error at the microgal level when performing differential measurements by reversing the direction of the effective wave vector of the Raman lasers. We propose that this residual error can in principle be eliminated by selecting the same chirp frequency range for both directions in the differential measurement.
We present here an analysis of the influence of the frequency dependence of the Raman laser light shifts on the phase of a Raman-type atom gravimeter. Frequency chirps are applied to the Raman lasers in order to compensate gravity and ensure the resonance of the Raman pulses during the interferometer. We show that the change in the Raman light shift when this chirp is applied only to one of the two Raman lasers is enough to bias the gravity measurement by a fraction of $\ensuremath{\mu}\mathrm{Gal}$ ($1\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{Gal}\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\mathrm{m}/{\mathrm{s}}^{2}$). We also show that this effect is not compensated when averaging over the two directions of the Raman wave vector kkk. This thus constitutes a limit to the rejection efficiency of the kkk-reversal technique. Our analysis allows us to separate this effect from the effect of the finite speed of light, which we find in perfect agreement with expected values. This study highlights the benefit of chirping symmetrically the two Raman lasers.
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.
We here present a high sensitivity gravity-gradiometer based on atom interferometry. In our apparatus, two clouds of laser-cooled rubidium atoms are launched in fountain configuration and interrogated by a Raman interferometry sequence to probe the gradient of gravity field. We recently implemented a high-flux atomic source and a newly designed Raman lasers system in the instrument set-up. We discuss the applications towards a precise determination of the Newtonian gravitational constant G. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement precision below the 100 ppm level.