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Applied Optics and Photonics China (AOPC)

Compensation of motion-induced atom-laser misalignment errors in an atom-interferometry gravimeter

Yishu Yang, Yukun Luo, Fufang Xu

Published Dec 13, 2024• 0 citations

Abstract

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.

DOI: 10.1117/12.3045849

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Atom interferometry is an advanced optical manipulation tool of atoms in precision measurement field. Wavefront aberrations of the Raman beam have become one of the major obstacles impeding the improvement of measurement accuracy. Beforehand measurement of laser wavefront is impractical due to the further wavefront deterioration during optical mounting. In this work, we present a general method for evaluating the effective Raman wavefront that atoms experience and the corresponding phase shift of interferometric fringes. The method extracts the effective Zernike polynomial terms and reconstructs the wavefront using optimal estimation theory. The evaluation accuracy and convergence speed are discussed by simulation. The results predict the method adaptability and provide strong support on analytical and numerical reference for wavefront error compensation.

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.

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

T

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.

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.

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.

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.