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Physical Review A

Evaluation of a frequency-dependent phase shift in chirped Raman lasers for atom gravimeters

Yaoyao Xu, Qingsong Wang, Jiafeng Cui, Hua-Qing Luo, Qin Luo, Xiao-Bing Deng, Min-Kang Zhou, Xiao‐Chun Duan, Zhong-Kun Hu

Published Dec 19, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.110.062816

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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.
We report on the study of the impact of the finite resolution of the chirp rate applied on the frequency difference between the Raman lasers beamsplitters onto the phase of a free fall atom gravimeter. This chirp induces a phase shift that compensates the one due to gravity acceleration, allowing for its precise determination in terms of frequencies. In practice, it is most often generated by a direct digital synthesizer (DDS). Besides the effect of eventual rounding errors, we evaluate here the bias on the ggg measurement due to the finite time and frequency resolution of the chirp generated by the DDS, and show that it can compromise the measurement accuracy. However, this effect can be mitigated by an adequate choice of the DDS chirp parameters resulting from a trade-off between interferometer phase resolution and induced bias.
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.
As the existence of the gravity gradient, the output of gravimeters is actually the gravitational acceleration at the reference instrumental height. Precise knowledge of the reference height is indispensable in the utilization of gravity measurements, especially for absolute gravimeters. Here, we present an interferometric method to measure the distance between the atomic cloud and a reflecting mirror directly, which consequently determines the reference height of our atom gravimeter. This interferometric method is based on a frequency jump of Raman lasers applied at the π pulse of the atom interferometer, which induces an additional phase shift proportional to the interested distance. An uncertainty of 2 mm is achieved here for the distance measurement, and the effect of the gravity gradient on absolute gravity measurements can thus be constrained within 1 μGal. This work provides a concrete-object-based measurement of the reference height for atom gravimeters.
The sensitive axis of an atom gravimeter is defined by the direction of the Raman lasers. Any tilt of the Raman lasers with respect to the vertical direction introduces systematic errors in gravity measurements. In this work, we report a determination of the tilt of Raman lasers, where the fringe of the atom interferometer is scanned by varying the tilt, rather than the phase, of the Raman lasers. Unlike the periodic cosine fringes typically used in atom interferometers, the fringe obtained by changing the tilt, referred to as the tilt-scanned fringe, is aperiodic in tilt and exhibits a shift due to the presence of a nonzero tilt. The tilt-scanned fringe is highly sensitive to the tilt-caused shift, enabling convenient and precise determination of the Raman laser tilt in atom gravimeters. We demonstrate that one tilt-scanned fringe, corresponding to a tilt measurement sampling time of 13 s, can determine the tilt with a typical precision of about $30\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{rad}$ in our developed atom gravimeter. The short-term sensitivity and measurement accuracy of the tilt-scanned fringe method were evaluated, demonstrating performance comparable to conventional tilt determination techniques. We expect this method to offer a convenient solution for Raman laser alignment in atom gravimeters and enhance the efficiency of absolute gravity surveys.
The additional sidebands (ASBs) in a Raman laser will have a significant effect on the performance of atom gravimeters (AGs) based on phase-modulated Raman lasers. We propose a method of modulating the sideband-to-carrier ratio in Raman lasers to determine the magic time intervals where the phase shift induced by the ASB effect is minimized, and this method is demonstrated by experiments. Among these magic time intervals, some noise-immunity points are predicted. Based on the prediction and the result of the ASB effect changing with the interval time T between adjacent Raman pulses, an optimal magic time interval is selected. Therefore, the uncertainty to the gravity measurement induced by the ASB effect when the AG works at the magic time interval is reduced to 0.5 μGal. Furthermore, the ASB effect and its zero-phase points in four-pulse atom interferometers are also discussed. This work provides a clear way to eliminate the phase shift induced by the ASB effect in high-precision AGs employing phase-modulated Raman lasers.