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arXiv:1307.2734 · Physical Review A

Simultaneous dual-species matter-wave accelerometer

Alexis Bonnin, Nassim Zahzam, Yannick Bidel, Alexandre Bresson

Published Oct 11, 2013• 175 citations
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Abstract

We report the realization of a matter-wave interferometer based on Raman transitions which simultaneously interrogates two different atomic species (${}^{87}$Rb and ${}^{85}$Rb). The simultaneous aspect of our experiment presents encouraging preliminary results for future dual-species atom interferometry projects and seems very promising by taking advantage of a differential acceleration measurement. Indeed, the resolution of our differential accelerometer remains lower than $3.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{g}$ even with vibration levels up to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{g}$ thanks to common-mode vibration noise rejection. An atom-based test of the weak equivalence principle has also been carried out leading to a differential free fall measurement between both isotopes of $\ensuremath{\Delta}g/g=(1.2\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.

DOI
10.1103/physreva.88.043615

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We present here the performance of a simultaneous dual-species matter-wave accelerometer for measuring the differential acceleration between two different atomic species (87Rb^{87}\mathrm{Rb}87Rb and 85Rb^{85}\mathrm{Rb}85Rb). We study the expression and the extraction of the differential phase from the interferometer output. The differential accelerometer reaches a short-term sensitivity of $1.23\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}g/\sqrt{\mathrm{Hz}}$ limited by the detection noise and a resolution of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}g$ after 11 000 s, a very high sensitivity using a dual-species atom interferometer. Thanks to the simultaneous measurement, such resolution levels can still be achieved even with vibration levels up to $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}g$, corresponding to a common-mode vibration noise rejection ratio of 94 dB (rejection factor of 50 000). These results prove the ability of such atom sensors for realizing a quantum-based test of the weak equivalence principle at a level of $\ensuremath{\eta}\ensuremath{\sim}{10}^{\ensuremath{-}9}$ even with high vibration levels and a compact sensor.
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We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an E\"otv\"os parameter of $\ensuremath{\eta}=[1.6\ifmmode\pm\else\textpm\fi{}1.8(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}3.4(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$, consistent with zero violation of the equivalence principle. With a resolution of up to $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{g}$ per shot, we demonstrate a sensitivity to $\ensuremath{\eta}$ of $5.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}/\sqrt{\mathrm{Hz}}$.
We report an improved test of the weak equivalence principle by using a simultaneous $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ dual-species atom interferometer. We propose and implement a four-wave double-diffraction Raman transition scheme for the interferometer, and demonstrate its ability in suppressing common-mode phase noise of Raman lasers after their frequencies and intensity ratios are optimized. The statistical uncertainty of the experimental data for E\"otv\"os parameter $\ensuremath{\eta}$ is $0.8\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$ at 3200 s. With various systematic errors corrected, the final value is $\ensuremath{\eta}=(2.8\ifmmode\pm\else\textpm\fi{}3.0)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$. The major uncertainty is attributed to the Coriolis effect.
We have developed a matter wave interferometer based on the diffraction of atoms from effective absorption gratings of light. In a setup with cold rubidium atoms in an atomic fountain the interferometer has been used to carry out tests of the equivalence principle on an atomic basis. The gravitational acceleration of the two isotopes 85Rb^{85}\mathrm{R}\mathrm{b}85Rb and 87Rb^{87}\mathrm{R}\mathrm{b}87Rb was compared, yielding a difference $\ensuremath{\Delta}\mathbf{g}/\mathbf{g}=(1.2\ifmmode\pm\else\textpm\fi{}1.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. We also perform a differential free fall measurement of atoms in two different hyperfine states, and obtained a result of $\ensuremath{\Delta}\mathbf{g}/\mathbf{g}=(0.4\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.
Optical clocks and atom interferometers provide complementary ways to measure time, motion and gravity. Combining these capabilities requires matter-wave beam splitters that manipulate different clock states in the same way, so that optical internal energy becomes a controlled degree of freedom rather than a source of systematic phase shifts. Here we realized a dual matter-wave interferometer operating simultaneously on the two states of the 88^{88}88Sr optical clock transition, 1S0^1S_01S0​ and 3P0^3P_03P0​. The interferometer is driven by Bragg pulses at the 813 nm magic wavelength, for which the two clock states experience the same optical coupling strength. This realizes a common matter-wave beam splitter for atoms whose internal energies differ by an optical excitation. With a sensitivity of 30 mrad, our measurement is consistent with a zero differential phase shift between the two clock-state Mach-Zehnder interferometers, translating to an absence of state-dependent acceleration in free fall at the level of 10−510^{-5}10−5. We further used the same interferometer to measure state-dependent optical dipole forces and determine a tune-out wavelength of the metastable 3P0^3P_03P0​ state to be 478.95(8) nm. These results establish magic-wavelength clock-state interferometry as a platform for differential force sensing, excited-state polarizability metrology and future quantum-clock tests of gravity.