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arXiv:2001.07478 · Physical Review A

Impact of direct-digital-synthesizer finite resolution on atom gravimeters

Romain Karcher, Franck Pereira dos Santos, Sébastien Merlet

Published Apr 28, 2020• 13 citations
arXivHTMLPDF

Abstract

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 $g$ 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.

DOI
10.1103/physreva.101.043622

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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.
One major systematic error for free-fall atom gravimeters is the effect of two-photon light shift (LS2). In the process of evaluating LS2, the results can be affected by the residual frequency error of direct digital synthesizers due to necessary experimental parameter changes. In this paper, the impact of the coupling effect between the frequency error and LS2 has been investigated and analyzed, along with the related physical mechanisms. The parameters of the frequency error sequence, such as the time step of δt and the time delay of Δt, significantly affect the bias and uncertainty of LS2. Notably, when these parameters are significantly altered or misaligned, the impact can reach several tens of µGal. Conversely, when they remain within the optimal ranges, the impact can be minimal. Specifically, when δt is less than or equal to 10 µs, the impact on the LS2 bias is less than 0.3 µGal, with the contribution to the total uncertainty of the gravity value being approximately 0.1 µGal. Furthermore, after correcting the phase shift introduced by the frequency error, the evaluation results have a similar improvement effect on the whole. Compared to the LS2 theoretical value, the residual is generally on the order of µGal. Through the comprehensive analysis and optimization, as well as related experiments, this cross-effect is managed and decoupled, leading to accurate LS2 evaluation results. This improvement ensures a better accuracy in the obtained absolute gravity values. The analysis methods discussed can provide an effective strategy for enhancing the performance of atom gravimeters.
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.
The use of a Raman laser generated by modulation for a light-pulse atom interferometer allows for a laser system that is compact and robust. However, the additional laser frequencies generated can perturb the atom interferometer. In this article, we present a precise calculation of the phase shift induced by the additional laser frequencies. The model is validated by comparison with experimental measurements on an atom gravimeter. The uncertainty of the phase-shift determination limits the accuracy of our compact gravimeter to $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\text{m}/{\text{s}}^{2}$. We show that it is possible to reduce this inaccuracy considerably with a better control of experimental parameters or with particular interferometer configurations.
The technology of electro-optic modulation is one of the several methods of generating the Raman beams. The experimental system based on this method is simple and much easier to implement, and the environmental adaptability is strong as well. However, this kind of modulation technology will produce additional laser lines, which may affect the measurement accuracy of cold atom gravimeter. Based on a homemade transportable cold atom gravimeter, the influence of Raman sideband effect on the accuracy of cold atom gravimeter is investigated in this paper. We analyze in detail the relationship between Raman sideband effect and some experimental parameters, such as the height of Raman retro-reflection mirror, the time of free fall of the atoms, the detuning of Raman laser, etc. It is found that those parameters have a dominant influence on the measured gravity resulting from Raman sideband effect. Besides, it is also found that the gravity measurements will be sensitive again to some experimental parameters in the case of Raman sideband effect while these parameters are usually insensitive in case of laser system without sideband effect. Finally, we investigate the relationship between Raman sideband effect and Raman detuning, and presente a method of evaluating the gravity induced by Raman sideband effect. The experimental results in this paper can provide a reference for reducing the influence of Raman sideband effect on the accuracy evaluation of cold atomic gravimeter.
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.