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Characterization of Systematic Errors Due to Intensity Inhomogeneities of Raman Beams in a Cold Atom Absolute Gravimeter

Diego Alejandro Lancheros Naranjo

Published Oct 1, 2025• 0 citations
Publisher

Abstract

Correlations between the internal and external degrees of freedom of neutral atoms enable state-of-the-art accuracy and sensitivity in inertial sensors. This thesis presents the latest developments in the absolute cold-atom gravimeter (CAG) of the LTE, based on momentum-state interferometry using Raman transitions in a freely falling atomic cloud of 87 Rb. We identify intensity inhomogeneities as a primary source of contrast loss in the CAG and highlight the role of non-resonant interactions resulting from the counter propagating geometry of the Raman beams. Following optimization of the optical setup, the interferometer contrast improved by nearly 10%, with local intensity-related features successfully eliminated. Additionally, we identified bias phases arising from intensity variations, predominantly during the mirror pulse. We introduce a dynamical method for evaluating these phase shifts, which generalizes the traditional adiabatic approximation. This method enables us to distinguish between phase shifts caused by two-photon processes and those of other origins. Crucially, it links the population of stray momentum states to the accumulation of nonlinear phase shifts at the interferometers output ports. We report a systematic bias in the measurement of g at the level of 5 × 10−9 g, attributed to intensity inhomogeneities, and a sensitivity of 20 × 10−9 g Hz−1/2.

DOI
10.70675/240d0828z0a4cz4e53z9d29zda2a119867fc

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Correlations between the internal and external degrees of freedom of neutral atoms enable state-of-the-art accuracy and sensitivity in inertial sensors. This thesis presents the latest developments in the absolute cold-atom gravimeter (CAG) of the LTE, based on momentum-state interferometry using Raman transitions in a freely falling atomic cloud of 87 Rb. We identify intensity inhomogeneities as a primary source of contrast loss in the CAG and highlight the role of non-resonant interactions resulting from the counter propagating geometry of the Raman beams. Following optimization of the optical setup, the interferometer contrast improved by nearly 10%, with local intensity-related features successfully eliminated. Additionally, we identified bias phases arising from intensity variations, predominantly during the mirror pulse. We introduce a dynamical method for evaluating these phase shifts, which generalizes the traditional adiabatic approximation. This method enables us to distinguish between phase shifts caused by two-photon processes and those of other origins. Crucially, it links the population of stray momentum states to the accumulation of nonlinear phase shifts at the interferometers output ports. We report a systematic bias in the measurement of g at the level of 5 × 10−9 g, attributed to intensity inhomogeneities, and a sensitivity of 20 × 10−9 g Hz−1/2.
Les corrélations entre les degrés de liberté internes et externes des atomes neutres permettent d'atteindre une précision et une sensibilité de pointe dans les capteurs inertiels. Cette thèse présente les derniers développements réalisés sur le gravimètre absolu à atomes froids (CAG) du LTE, basé sur l'interférométrie d’états de moment via des transitions Raman dans un nuage d'atomes de 87 Rb en chute libre. Nous identifions les inhomogénéités d'intensité comme la principale source de perte de contraste dans le CAG, et mettons en évidence le rôle des interactions non résonantes induites par la géométrie contre-propagative des faisceaux Raman. Après optimisation du dispositif optique, le contraste de l'interféromètre s'est amélioré de près de 10 %, et les structures locales liées au champ ont été éliminées. Par ailleurs, nous avons identifié des phases de biais provenant des variations d'intensité laser, principalement pendant l'impulsion miroir. Nous introduisons une méthode dynamique pour évaluer ces déphasages, qui constitue une généralisation de l'approximation adiabatique classique. Cette approche permet de distinguer les déphasages causés par des processus à deux photons de ceux ayant une autre origine. Elle relie notamment la population d'états de moment indésirables à l'accumulation de phases non linéaires aux sorties de l'interféromètre. Nous rapportons un biais systématique dans la mesure de g de l'ordre de 5 × 10−9 g, attribué aux inhomogénéités d'intensité, ainsi qu'une sensibilité de 20 × 10−9 g Hz−1/2.
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.
Caractérisation des erreurs systématiques dues aux inhomogénéités d'intensité des faisceaux Raman dans un gravimètre absolu à atomes froids Les corrélations entre les degrés de liberté internes et externes des atomes neutres permettent d'atteindre une précision et une sensibilité de pointe dans les capteurs inertiels. Cette thèse présente les derniers développements réalisés sur le gravimètre absolu à atomes froids (CAG) du LTE, basé sur l'interférométrie d’états de moment via des transitions Raman dans un nuage d'atomes de 87 Rb en chute libre. Nous identifions les inhomogénéités d'intensité comme la principale source de perte de contraste dans le CAG, et mettons en évidence le rôle des interactions non résonantes induites par la géométrie contre-propagative des faisceaux Raman. Après optimisation du dispositif optique, le contraste de l'interféromètre s'est amélioré de près de 10 %, et les structures locales liées au champ ont été éliminées. Par ailleurs, nous avons identifié des phases de biais provenant des variations d'intensité laser, principalement pendant l'impulsion miroir. Nous introduisons une méthode dynamique pour évaluer ces déphasages, qui constitue une généralisation de l'approximation adiabatique classique. Cette approche permet de distinguer les déphasages causés par des processus à deux photons de ceux ayant une autre origine. Elle relie notamment la population d'états de moment indésirables à l'accumulation de phases non linéaires aux sorties de l'interféromètre. Nous rapportons un biais systématique dans la mesure de g de l'ordre de 5 × 10−9 g, attribué aux inhomogénéités d'intensité, ainsi qu'une sensibilité de 20 × 10−9 g Hz−1/2.
Cold atom free-fall interferometers now realize state-of-the-art precision inertial sensors, opening perspectives towards embedded devices for applications and fundamental physics tests on earth and in space. The acceleration of gravity can be measured in a stimulated Raman transition interferometer where the acceleration under gravity of a cloud of freely falling atoms is sensed by three Raman pulses allowing to split, reflect and interfere atomic wave packets [1]. The gravimeter developped at SYRTE allows to measure the acceleration of gravity at state-of-the-art performances compared to the best classical absolute gravimeters, with a sensitivity of 2×10−8g over 1s and an exactitude of 5×10−9 g [2]. This exactitude is currently limited by wavefront aberrations of the lasers, sampled by residual transverse trajectories of the molasse-cooled cloud over the free fall. Unbalanced transverse trajectories will also bias the measurement due to Coriolis effect [3]. We will investigate the use of a colder atom source to reduce these systematic effects, by implementing Bose-Einstein condensation of the initial cloud, allowing both better position control and better focusing of our source.
Atomic gravimeter based on atom interferometry has become a hotspot of quantum optics applications in recent years and shown rapid progress in static-scene measurements. Improving the adaptability on dynamic scenes is an important development direction, which calls for in-depth research on various errors caused by carrier motions. This work focuses on the error evaluation and compensation of motion-induced misalignment between the Raman laser beam and the atomic trajectory. A theoretical analysis framework is formed to investigate the atom-laser misalignment errors by considering both the inhomogeneous Raman laser intensity and wavefront phase distributions in a dynamic perspective. The influence on fringe contrast and phase shift in an atom-interferometry gravimeter is discussed. Quantitative study has been done with different motion types, motion rates as well as random motion noises. The results show oscillational decay trends of fringe contrast with the motion amplitude and the increased significance of rotationally antisymmetric Zernike terms in dynamical Raman wavefront phase shift evaluation. Strong correlations can be found between the misalignment errors and the experimental parameters. A compensation method is proposed accordingly via quickly adjusting the Raman intensity or pulse duration and comprehensive Raman wavefront characterization. Both amplitude and phase corrections are achieved. The analytical approach and results provide a practical solution for further advances of atom-interferometry under harsh motional conditions.
The mechanism of light-shift-related uncertainty in an atom-interferometry gravimeter is investigated systematically, which arises from the inhomogeneous intensity of Raman beams and the Gaussian distribution of an atomic cloud. Experiments using atom interferometry are performed to verify this systematic error by directly modulating the integration time TTT and the intensity ratio of Raman laser beams. Using our method, the uncertainty of gravity measurements contributed by the single-photon light shift in an atom gravimeter can be corrected to a $\mathrm{sub}\ensuremath{-}\ensuremath{\mu}\mathrm{Gal}\phantom{\rule{0.28em}{0ex}}(1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{Gal}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\mathrm{m}/{\mathrm{s}}^{2})$ level.