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arXiv:1606.02843 · Physical Review A

Coherent population trapping in a Raman atom interferometer

Bing Cheng, Pierre Gillot, Sébastien Merlet, Franck Pereira dos Santos

Published Jun 17, 2016• 6 citations
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Abstract

We investigate the effect of coherent population trapping (CPT) in an atom interferometer gravimeter based on the use of stimulated Raman transitions. We find that CPT leads to significant phase shifts, on the order of a few mrad, which may compromise the accuracy of inertial measurements. We show that this effect is rejected by the $k$-reversal technique, which consists of averaging inertial measurements performed with two opposite orientations of the Raman wave vector $k$, provided that internal states at the input of the interferometer are kept identical for both configurations.

DOI
10.1103/physreva.93.063621

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We investigate the effect of coherent population trapping (CPT) in an atom interferometer gravimeter based on the use of stimulated Raman transitions. We find that CPT leads to significant phase shifts, on the order of a few mrad, which may compromise the accuracy of inertial measurements. We show that this effect is rejected by the kkk-reversal technique, which consists of averaging inertial measurements performed with two opposite orientations of the Raman wave vector kkk, provided that internal states at the input of the interferometer are kept identical for both configurations.
Raman pulse atom interferometry is an important modality for precision measurements of inertial forces and tests of fundamental physics. Typical Raman atom optics use two coherent laser fields applied at gigahertz-scale detunings from optical resonance, so that spontaneous emission produces a minor or negligible source of decoherence. An additional consequence of spontaneous emission is coherent population trapping (CPT). We show that CPT produces coherences and population differences which induce systematic effects in Raman pulse atom interferometers. We do not believe that CPT has been previously identified as an error mechanism in Raman pulse atom interferometry. We present an experimental characterization of CPT coherences and population differences induced in laser-cooled cesium atoms by application of Raman pulses at detunings near 1 GHz, commensurate with detunings used in several precision measurement experiments. We are not aware of previous demonstrations of CPT-induced population difference. We argue that CPT effects could induce phase shifts of several milliradians in magnitude for typical experimental parameters and stipulate that these errors can be suppressed by propagation direction reversal in Raman interferometer-based precision measurements.
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.
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.
Owing to the use of a symmetrization $\ensuremath{\pi}$ pulse at the middle of their laser sequences, Mach-Zehnder-type atom interferometers are insensitive to clocks shifts and Doppler shifts, if constant, but to changes in these quantities, which makes them accurate and sensitive inertial-force sensors. However, variations of the Raman laser coupling between laser pulses restore a parasitic sensitivity to the Doppler shift. This effect, which sets a limit to the symmetry of the interferometer, is quantitatively evaluated here as a function of the experimental parameters, in the case of an atom gravimeter experiment, and compared to expectations. We show in particular that velocity-distribution asymmetries lead to parasitic phase shifts that can compromise the accuracy and long-term stability of the gravity measurement in the low ${10}^{\ensuremath{-}9}g$ range.
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.
In this paper, we study the dynamics of a trapped atom interferometer with internal state labeling in the presence of interactions. We consider two situations: an atomic clock in which the internal states remain superposed, and an inertial sensor configuration in which they are separated. From the average spin evolution, we deduce the fringe contrast and the phase shift. In the clock configuration, we recover the well-known identical spin rotation effect (ISRE) which can significantly increase the spin coherence time. We also find that the magnitude of the effect depends on the trap geometry in a way that is consistent with our recent experimental results in a clock configuration [M. Dupont-Nivet, R. Demur, C. I. Westbrook, and S. Schwartz, New J. Phys. 20, 043051 (2018)], where ISRE was not observed. In the case of an inertial sensor, we show that despite the spatial separation it is still possible to increase the coherence time by using mean field interactions to counteract asymmetries of the trapping potential.