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arXiv:2410.07720 · Optics Express

Influence of optical aberrations on the accuracy of an atomic gravimeter

Louis Pagot, Sébastien Merlet, Franck Pereira dos Santos

Published Dec 15, 2024• 4 citations
arXivHTMLPDF

Abstract

We present numerical simulations of the impact of laser beam wavefront aberrations in cold atom interferometers. We demonstrate that to reach accuracy at the mrad level, it is insufficient to base simulations on a description of retroreflective optics using only low-order Zernike polynomials, as the results will then depend on the decomposition order and the decomposition technique chosen. Moreover, simulations with high-order Zernike polynomials or equivalently high spatial frequency components require the propagation of aberrations to be taken into account, rather than adding them to the ideally propagated beam. Finally, we examine the impact of the parameters of the atomic source and show that the use of a delta-kicked atomic cloud would efficiently mitigate the impact of this systematic effect.

DOI
10.1364/oe.544378

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We present numerical simulations of the impact of laser beam wavefront aberrations in cold atom interferometers. We demonstrate that to reach accuracy at the mrad level, it is insufficient to base simulations on a description of retroreflective optics using only low-order Zernike polynomials, as the results will then depend on the decomposition order and the decomposition technique chosen. Moreover, simulations with high-order Zernike polynomials or equivalently high spatial frequency components require the propagation of aberrations to be taken into account, rather than adding them to the ideally propagated beam. Finally, we examine the impact of the parameters of the atomic source and show that the use of a delta-kicked atomic cloud would efficiently mitigate the impact of this systematic effect.
One of the main residual limitations of inertial sensors based on atom interferometry stems from laser beam distortions, which cause parasitic phase shifts and non-homogeneous matter-light couplings. Here we present numerical simulations, accompanied by analytical calculations, which quantify the impact of these effects in a cold atom gradiometer. We demonstrate that the propagation of interferometric laser beam aberrations, combined with initial asymmetry and significant time-of-flight expansion of the the two atomic sources, limit the common-mode rejection of phase noise in a differential configuration. The resulting deviations in gravitational acceleration and its gradient are within reach of current experimental devices. Our study allows us to evaluate the surface quality requirements for retroreflective optics in cold-atom gradiometers of various baselines, and can be extended to other sensors based on different interferometer geometries.
Wavefront aberrations are one of the largest uncertainty factors in present atom interferometers. We present a detailed numerical and experimental analysis of this effect based on measured aberrations from optical windows. By placing windows into the Raman beam path of our atomic gravimeter, we verify for the first time the induced bias in very good agreement with theory. Our method can be used to reduce the uncertainty in atomic gravimeters by one order of magnitude resulting in an error of less than 3 × 10−10 g and it is suitable in a wide variety of atom interferometers with thermal or ultra cold atoms. We discuss the limitations of our method, potential improvements and its role in future generation experiments. 1
Summary form only given. Atom interferometry based on cold atoms and light beamsplitters is a mature technique, which allows for the realization of highly sensitive inertial sensors. In the most advanced inertial sensors based on atom interferometry, atomic wavepackets are manipulated by light beamsplitters using two-photon Raman transitions. The interferometer phase shift, which depends on the acceleration and the rotation of the experimental setup with respect to the inertial reference frame defined by the atoms in free fall, is derived from the relative displacement of the atoms with respect to the beamsplitter laser's equiphases. Wavefront aberrations thus induce parasitic phase shifts, which bias the measurement, and which are linked to the residual ballistic motion of the atoms across the laser beam profile during their free fall and cancels out at zero atomic temperature. The wavefront distortions of the lasers beamsplitters is an important limit in the accuracy of atom interferometers and in particular, the dominating contribution in best cold atom gravimeters (CAG) uncertainty budget. This work clears the way towards unprecedented accuracies for absolute gravimetry, below the 1 μGal level. The method proposed can be applied to any atomic sensor based on light beamsplitters, which are inevitably affected by distortions of the lasers wavefronts. The improved control of systematics it provides will have significant impact in high precision measurements with atom interferometry, with important applications to geodesy, fundamental physics tests and to the development of highest grade inertial sensors.
We report on the implementation of ultracold atoms as a source in a state of the art atom gravimeter. We perform gravity measurements with 10 nm s −2 statistical uncertainties in a so-far largely unexplored temperature range for such a high accuracy sensor, down to 50 nK. This allows for an improved characterization of the most limiting systematic effect, related to wavefront aberrations of light beamsplitters. A thorough model of the impact of this effect onto the measurement is developed and a method is proposed to correct for this bias based on the extrapolation of the measurements down to zero temperature. Finally, an uncertainty of 13 nm s −2 is obtained in the evaluation of this systematic effect, which can be improved further by performing measurements at even lower temperatures. Our results clearly demonstrate the benefit brought by ultracold atoms to the metrological study of free falling atom interferometers. By tackling their main limitation, the method presented here allows reaching record-breaking accuracies for inertial sensors based on atom interferometry.