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Physical Review A

Observing the effect of wave-front aberrations in an atom interferometer by modulating the diameter of Raman beams

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

Published Apr 11, 2016• 45 citations
Publisher

Abstract

The effect of wavefront aberrations is one of the most important systematic errors in atom interferometers and limits the accuracy of precision atom gravimeters. A detailed theoretical analysis of this effect is presented, and a theoretical method for observing this effect is proposed and demonstrated in experiment. In addition, with this method, the surface quality of the optical elements in the Raman system was measured with a rms resolution of $0.01\ensuremath{\lambda}$.

DOI
10.1103/physreva.93.043610

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The effect of wavefront aberrations is one of the most important systematic errors in atom interferometers and limits the accuracy of precision atom gravimeters. A detailed theoretical analysis of this effect is presented, and a theoretical method for observing this effect is proposed and demonstrated in experiment. In addition, with this method, the surface quality of the optical elements in the Raman system was measured with a rms resolution of 0.01\ensuremathλ0.01\ensuremath{\lambda}0.01\ensuremathλ.
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
Wavefront aberrations have significant impacts on the accuracy and long-term stability of cold-atom interferometers. This research presents an in situ method for directly measuring the phase shift induced by the wavefront of the Raman beam using the atom interferometer itself. To validate the feasibility of this approach, experiments involving the insertion of a glass plate with a known surface figure into the Raman beam path have been carried out. The phase introduced by the glass plate is measured experimentally by the atom interferometer and calculated theoretically based on the wavefront obtained from the wavefront sensor, and we find good agreement of the experimental results with the theoretical calculations. The method not only allows for the assessment of systematic errors in an atom interferometer, but also provides the capability to retroactively compute the wavefront of Raman beams based on the measured phase shift. The wavefront distribution of the glass plate is inversed from the phase measured by the atom interferometer. This inversed wavefront distribution is consistent with the surface of the glass plate measured by the wavefront sensor, which confirms the effectiveness of the method. This work provides a valuable approach to evaluate the systematic errors in atom interferometers that are sensitive to wavefront aberrations. Furthermore, it offers a novel method to measure the wavefront using atoms.
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.
The wave-front aberration of Raman beams induces phase noise in atom interferometers and thus limits the performance of atom interferometers. We theoretically analyze the wave-front-aberration phase noise in weak-equivalence-principle tests using dual-species atom interferometers, and propose an expansion-rate-selection method to suppress the wave-front-aberration phase noise in both isotopic and nonisotopic atom interferometers. The suppression ratio is about 10 at the expense of half the number of atoms. The simulation based on appropriate experimental parameters shows that the wave-front aberration caused standard deviations to the E\"otv\"os coefficient in weak-equivalence-principle tests using $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ are $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ and $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$. Better results can be obtained by improving the wave-front quality and utilizing atom cloud with lower temperature. The analysis and suppression of wave-front-aberration phase noise will be useful for the design of high-precision atom interferometer--based weak-equivalence-principle tests both on ground and in space.
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.