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Physical Review A

Effect of the Gaussian distribution of both atomic cloud and laser intensity in an atom gravimeter

Min-Kang Zhou, Lele Chen, Qin Luo, Ke Zhang, Xiao‐Chun Duan, Zhong-Kun Hu

Published May 19, 2016• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.93.053615

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arXiv:1506.03207•Physical Review A•Dec 9, 2015•28 citations
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 sub\ensuremath−\ensuremathμGal(1\ensuremathμGal=1\ifmmode×\else\texttimes\fi10\ensuremath−8m/s2)\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})sub\ensuremath−\ensuremathμGal(1\ensuremathμGal=1\ifmmode×\else\texttimes\fi10\ensuremath−8m/s2) level.
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.
There is a continuous interest in shrinking the dimensions of portable atomic gravimeters. This inevitably ends up truncating the Gaussian wings of the excitation laser beams whose effect has not been properly quantified yet. The diffraction pattern created from this aperture creates ripples in the wavefront in both the phase and the intensity. We calculate the shift in the measured value of an atomic gravimeter introduced by the phase variations in the wavefront. Fortunately, this shift has a Gaussian decay with the aperture size. For extended clouds, we observe a reduction of the effect thanks to an averaging over transverse positions with different values of the shift. Surprisingly, we found that the intensity variations also introduce an important correction to the photon recoil, which contributes at about the same level as the previous shift in the measurement of the gravitational acceleration. Our results should help decide how small an apparatus can be to guarantee a particular accuracy.
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.
Gravity gradients represent a major obstacle in high-precision measurements by atom interferometry. Controlling their effects to the required stability and accuracy imposes very stringent requirements on the relative positioning of freely falling atomic clouds, as in the case of precise tests of Einstein's equivalence principle. We demonstrate a new method to exactly compensate the effects introduced by gravity gradients in a Raman-pulse atom interferometer. By shifting the frequency of the Raman lasers during the central π pulse, it is possible to cancel the initial position- and velocity-dependent phase shift produced by gravity gradients. We apply this technique to simultaneous interferometers positioned along the vertical direction and demonstrate a new method for measuring local gravity gradients that does not require precise knowledge of the relative position between the atomic clouds. Based on this method, we also propose an improved scheme to determine the Newtonian gravitational constant G towards the 10 ppm relative uncertainty.
Accurately measuring the three-dimensional position of an atomic cloud is essential for improving the precision of atom interferometers. In the work presented here, the three-dimensional position of an atomic cloud in an atom interferometer is measured with only one laser beam, generated by a phase modulator. The vertical position is determined from the change in the additional-sideband effect with the time interval TTT between adjacent Raman pulses in the atom interferometer. Based on this method, the vertical position of the atomic cloud is measured with an uncertainty of 0.2 mm; therefore, the uncertainty in a gravity measurement contributed by the gravity gradient is not limited by the uncertainty in the measurement of the vertical position at the level of $0.1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{Gal}$. Furthermore, a method of measuring Rabi oscillations at different horizontal positions to determine the horizontal position of the atomic cloud is proposed and is demonstrated experimentally. With this method, the horizontal position can be determined with an uncertainty of less than 0.1 mm, and the horizontal velocity of the atomic cloud can also be deduced. The methods demonstrated in this paper are helpful for evaluating systematic errors in atom interferometers, and also useful in precision measurements based on an atomic fountain.
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.