Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Limits to the symmetry of a Mach-Zehnder-type atom interferometer

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

Published Jan 12, 2016• 38 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.93.013609

Related papers

Dependence of sensitivity of atom interferometer gravimeters on the Raman laser pulse sequences

Ren Li-Chun, Zhou Lin, Runbing Li +4 more

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.

Acta Physica Sinica•Jan 1, 2009•4 citations

Influence of chirping the Raman lasers in an atom gravimeter: Phase shifts due to the Raman light shift and to the finite speed of light

Bing Cheng, Pierre Gillot, Sébastien Merlet +1 more

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 $k$. This thus constitutes a limit to the rejection efficiency of the $k$-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.

arXiv:1506.03207•Physical Review A•Dec 9, 2015•28 citations

Exact Semiclassical Phase Shifts for Relativistic Atom Interferometers in Flat Spacetime

Hunter Swan, Jason M. Hogan

Atom interferometry is a sensitive tool for measuring relativistic effects, but there are no known non-trivial exact solutions for relativistic atom interferometer phase shifts. Here we derive relativistically exact expressions within the usual semiclassical approximation for a wide range of experimentally interesting atom interferometer pulse sequences in flat spacetime, including Mach-Zehnder, resonant, and large momentum transfer interferometer geometries. As an example, the leading order phase shift $ω_a g T^2/c$ for a Mach-Zehnder clock atom interferometer is found to become $ω_a \left(1 + \frac{ω_a}{2m}\right)(e^{-gT/c}-1)^2 c/g$ when all relativistic kinematics are included. We calculate exact phase shifts for both clock (single-photon) interferometers and Raman or Bragg (two-photon) interferometers.

arXiv:2607.10042•Jul 10, 2026•0 citations

Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation

Olivier Carraz, Renée Charrière, Malo Cadoret +3 more

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.

arXiv:1205.0690•Physical Review A•Sep 5, 2012•79 citations

Zero-velocity atom interferometry using a retroreflected frequency-chirped laser

Isadora Perrin, Jeanne Bernard, Yannick Bidel +5 more

Atom interferometry using stimulated Raman transitions in a retroreflected configuration is the first choice in high-precision measurements because it provides low phase noise, a high-quality Raman wave front, and a simple experimental setup. However, it cannot be used for atoms at zero velocity because two pairs of Raman lasers are simultaneously resonant. Here we report a method which allows this degeneracy to be lifted by using a frequency chirp on the Raman lasers. Using this technique, we realize a Mach-Zehnder atom interferometer hybridized with a force balanced accelerometer which provides horizontal acceleration measurements with a short-term sensitivity of $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.28em}{0ex}}{\mathrm{m}\phantom{\rule{0.16em}{0ex}}\mathrm{s}}^{\ensuremath{-}2}/\sqrt{\text{Hz}}$. This technique could be used for multiaxis inertial sensors, tiltmeters, or atom interferometry in a microgravity environment.

arXiv:1907.04403•Physical Review A•Nov 21, 2019•24 citations

Raman-pulse-duration effect in gravity gradiometers composed of two atom interferometers

Cheng-Gang Shao, Dekai Mao, Min-Kang Zhou +4 more

We investigated the Raman-pulse-duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate for the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser. This leads to an appreciable phase shift. The magnitude of the phase shift relative to the differential phase shift of the two interferometers is in an order of $\ensuremath{\tau}/T$, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.

arXiv:1503.01199•Physical Review A•Nov 16, 2015•6 citations
Owing to the use of a symmetrization \ensuremathπ\ensuremath{\pi}\ensuremathπ 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−9g{10}^{\ensuremath{-}9}g10\ensuremath−9g range.
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.
Atom interferometry is a sensitive tool for measuring relativistic effects, but there are no known non-trivial exact solutions for relativistic atom interferometer phase shifts. Here we derive relativistically exact expressions within the usual semiclassical approximation for a wide range of experimentally interesting atom interferometer pulse sequences in flat spacetime, including Mach-Zehnder, resonant, and large momentum transfer interferometer geometries. As an example, the leading order phase shift ωagT2/cω_a g T^2/cωa​gT2/c for a Mach-Zehnder clock atom interferometer is found to become ωa(1+ωa2m)(e−gT/c−1)2c/gω_a \left(1 + \frac{ω_a}{2m}\right)(e^{-gT/c}-1)^2 c/gωa​(1+2mωa​​)(e−gT/c−1)2c/g when all relativistic kinematics are included. We calculate exact phase shifts for both clock (single-photon) interferometers and Raman or Bragg (two-photon) interferometers.
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.
Atom interferometry using stimulated Raman transitions in a retroreflected configuration is the first choice in high-precision measurements because it provides low phase noise, a high-quality Raman wave front, and a simple experimental setup. However, it cannot be used for atoms at zero velocity because two pairs of Raman lasers are simultaneously resonant. Here we report a method which allows this degeneracy to be lifted by using a frequency chirp on the Raman lasers. Using this technique, we realize a Mach-Zehnder atom interferometer hybridized with a force balanced accelerometer which provides horizontal acceleration measurements with a short-term sensitivity of $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.28em}{0ex}}{\mathrm{m}\phantom{\rule{0.16em}{0ex}}\mathrm{s}}^{\ensuremath{-}2}/\sqrt{\text{Hz}}$. This technique could be used for multiaxis inertial sensors, tiltmeters, or atom interferometry in a microgravity environment.
We investigated the Raman-pulse-duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate for the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser. This leads to an appreciable phase shift. The magnitude of the phase shift relative to the differential phase shift of the two interferometers is in an order of $\ensuremath{\tau}/T$, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.