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arXiv:0809.0149 · Physical Review A

Off-resonant Raman transition impact in an atom interferometer

A. Gauguet, T. E. Mehlstäubler, Thomas Lévèque, Julien Le Gouët, Walid Chaibi, B. Canuel, Andr  Clairon, Franck Pereira dos Santos, Arnaud Landragin

Published Oct 29, 2008• 103 citations
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Abstract

We study the influence of off-resonant two-photon transitions on high-precision measurements with atom interferometers based on stimulated Raman transitions. These resonances induce a two-photon light shift on the resonant Raman condition. The impact of this effect is investigated in two highly sensitive experiments using a gravimeter and a gyroscope-accelerometer. We show that it can lead to significant systematic phase shifts, which have to be taken into account in order to achieve the best performances in terms of accuracy and stability.

DOI
10.1103/physreva.78.043615

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We study the influence of off-resonant two-photon transitions on high-precision measurements with atom interferometers based on stimulated Raman transitions. These resonances induce a two-photon light shift on the resonant Raman condition. The impact of this effect is investigated in two highly sensitive experiments using a gravimeter and a gyroscope-accelerometer. We show that it can lead to significant systematic phase shifts, which have to be taken into account in order to achieve the best performances in terms of accuracy and stability.
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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.
We investigate the dependence of the sensitivity of atom interferometer gravimeter on the Raman laser pulse sequence. The sensitivity of atom gravimeter can be adjusted by changing the pulse duration. Under the standard pulse configuration condition, the atom interferometer with four pulses is insensitive to the gravity if only gravity and its first order gradient are taken into account. The three-pulse Raman atom interferometer gravimeter displays best sensitivity. Atom interferometers with more than four Raman pulses show poorer sensitivity.
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.
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 use of a Raman laser generated by modulation for a light-pulse atom interferometer allows for a laser system that is compact and robust. However, the additional laser frequencies generated can perturb the atom interferometer. In this article, we present a precise calculation of the phase shift induced by the additional laser frequencies. The model is validated by comparison with experimental measurements on an atom gravimeter. The uncertainty of the phase-shift determination limits the accuracy of our compact gravimeter to $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.28em}{0ex}}\text{m}/{\text{s}}^{2}$. We show that it is possible to reduce this inaccuracy considerably with a better control of experimental parameters or with particular interferometer configurations.