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arXiv:1406.5998 · Physical Review A

Effective velocity distribution in an atom gravimeter: Effect of the convolution with the response of the detection

Tristan Farah, Pierre Gillot, Bing Cheng, Arnaud Landragin, Sébastien Merlet, Franck Pereira dos Santos

Published Aug 6, 2014• 27 citations
arXivHTMLPDF

Abstract

We present here a detailed study of the influence of the transverse motion of the atoms in a free-fall gravimeter. By implementing Raman selection in the horizontal directions at the beginning of the atoms' free fall, we characterize the effective velocity distribution, i.e., the velocity distribution of the detected atom, as a function of the laser cooling and trapping parameters. In particular, we show that the response of the detection induces a pronounced asymmetry of this effective velocity distribution that depends not only on the imbalance between molasses beams but also on the initial position of the displaced atomic sample. This convolution with the detection has a strong influence on the averaging of the bias due to Coriolis acceleration. The present study allows a fairly good understanding of results previously published in [New J. Phys. 13, 065025 (2011)], where the mean phase shift due to Coriolis acceleration was found to have a sign different from that expected.

DOI
10.1103/physreva.90.023606

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We present here a detailed study of the influence of the transverse motion of the atoms in a free-fall gravimeter. By implementing Raman selection in the horizontal directions at the beginning of the atoms' free fall, we characterize the effective velocity distribution, i.e., the velocity distribution of the detected atom, as a function of the laser cooling and trapping parameters. In particular, we show that the response of the detection induces a pronounced asymmetry of this effective velocity distribution that depends not only on the imbalance between molasses beams but also on the initial position of the displaced atomic sample. This convolution with the detection has a strong influence on the averaging of the bias due to Coriolis acceleration. The present study allows a fairly good understanding of results previously published in [New J. Phys. 13, 065025 (2011)], where the mean phase shift due to Coriolis acceleration was found to have a sign different from that expected.
The cold atom absolute gravimeters are intrinsically sensitive to its orientation due to the Coriolis effect, which should be understood clearly and compensated for field applications. The sensitivity on the orientation for a free-fall atom gravimeter is investigated in this paper. The apparatus is simplified and improved a lot such that fast adjustment and measurement could be carried out within 20 minutes. From the experimental results, it is found that the orientation angle has a dominant influence on the absolute gravity measurement, especially when the horizontal velocity of atoms is non-negligible. Besides, the magnitude and direction of average horizontal velocity of the detected atoms are obtained in this experiment. In particular, the direction of East-West has been measured by the atom gravimeter itself, such that gravity bias arising from Coriolis effect is estimated precisely.
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.
Limits on the long-term stability and accuracy of a second generation cold atom gravimeter are investigated. We demonstrate a measurement protocol based on four interleaved measurement configurations, which allows rejection of most of the systematic effects, but not those related to Coriolis acceleration and wave-front distortions. Both are related to the transverse motion of the atomic cloud. Carrying out measurements with opposite orientations with respect to the Earth's rotation vector direction allows us to separate the effects and correct for the Coriolis shift. Finally, measurements at different atomic temperatures are presented and analyzed. In particular, we show the difficulty of extrapolating these measurements to zero temperature, which is required in order to correct for the bias due to wave-front distortions.
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.