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arXiv:0910.2412 · New Journal of Physics

How to estimate the differential acceleration in a two-species atom interferometer to test the equivalence principle

Gael P. Varoquaux, Robert A. Nyman, Rémi Geiger, Patrick Cheinet, Arnaud Landragin, Philippe Bouyer

Published Nov 5, 2009• 69 citations
arXivHTMLPDF

Abstract

We propose a scheme for testing the weak equivalence principle (universality of free-fall (UFF)) using an atom-interferometric measurement of the local differential acceleration between two atomic species with a large mass ratio as test masses. An apparatus in free fall can be used to track atomic free-fall trajectories over large distances. We show how the differential acceleration can be extracted from the interferometric signal using Bayesian statistical estimation, even in the case of a large mass and laser wavelength difference. We show that this statistical estimation method does not suffer from acceleration noise of the platform and does not require repeatable experimental conditions. We specialize our discussion to a dual potassium/rubidium interferometer and extend our protocol with other atomic mixtures. Finally, we discuss the performance of the UFF test developed for the free-fall (zero-gravity) airplane in the ICE project ( http://www.ice-space.fr ).

DOI
10.1088/1367-2630/11/11/113010

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We propose a scheme for testing the weak equivalence principle (universality of free-fall (UFF)) using an atom-interferometric measurement of the local differential acceleration between two atomic species with a large mass ratio as test masses. An apparatus in free fall can be used to track atomic free-fall trajectories over large distances. We show how the differential acceleration can be extracted from the interferometric signal using Bayesian statistical estimation, even in the case of a large mass and laser wavelength difference. We show that this statistical estimation method does not suffer from acceleration noise of the platform and does not require repeatable experimental conditions. We specialize our discussion to a dual potassium/rubidium interferometer and extend our protocol with other atomic mixtures. Finally, we discuss the performance of the UFF test developed for the free-fall (zero-gravity) airplane in the ICE project ( http://www.ice-space.fr ).
The atom interferometry test of the Weak Equivalence Principle is based on a differential measurement performed by two atom interferometers simultaneously probing the acceleration experienced by two clouds of two different atomic species. STE-QUEST will make pair wise comparisons between the two isotopes of rubidium while it orbits around the Earth. Testing the universality of free fall at a level of one part in 10-15 implies a measurement of the differential acceleration between the two atomic species at the same level of precision.
Matter-wave interferometers utilizing different isotopes or chemical elements intrinsically have different sensitivities, and the analysis tools available until now are insufficient for accurately estimating the atomic phase difference under many experimental conditions. In this work, we describe and demonstrate two new methods for extracting the differential phase between dual-species atom interferometers for precise tests of the weak equivalence principle (WEP). The first method is a generalized Bayesian analysis, which uses knowledge of the system noise to estimate the differential phase based on a statistical model. The second method utilizes a mechanical accelerometer to reconstruct single-sensor interference fringes based on measurements of the vibration-induced phase. An improved ellipse-fitting algorithm is also implemented as a third method for comparison. These analysis tools are investigated using both numerical simulations and experimental data from simultaneous 87 Rb and 39 K interferometers, and both new techniques are shown to produce bias-free estimates of the differential phase. We also report observations of phase correlations between atom interferometers composed of different chemical species. This correlation enables us to reject common-mode vibration noise by a factor of 730, and to make preliminary tests of the WEP with a sensitivity of 1.6 × 10 − 6 per measurement with an interrogation time of T = 10 ms. We study the level of vibration rejection by varying the temporal overlap between interferometers in a symmetric timing sequence. Finally, we discuss the limitations of the new analysis methods for future applications of differential atom interferometry.
Differential atom interferometry with 87^{87}87Rb and 85^{85}85Rb for testing the UFF in STE-QUEST
In this paper we discuss in detail an experimental scheme to test the universality of free fall (UFF) with a differential 87^{87}87Rb / 85^{85}85Rb atom interferometer applicable for extended free fall of several seconds in the frame of the STE-QUEST mission. This analysis focuses on suppression of noise and error sources which would limit the accuracy of a violation measurement. We show that the choice of atomic species and the correctly matched parameters of the interferometer sequence are of utmost importance to suppress leading order phase shifts. In conclusion we will show the expected performance of 222 parts in 101510^{15}1015 of such an interferometer for a test of the UFF.
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.
We propose an experiment to test the weak equivalence principle (WEP) with a test mass consisting of two entangled atoms of different species. In the proposed experiment, a coherent measurement of the differential gravity acceleration between the two atomic species is considered, by entangling two atom interferometers operating on the two species. The entanglement between the two atoms is heralded at the initial beam splitter of the interferometers through the detection of a single photon emitted by either of the atoms, together with the impossibility of distinguishing which atom emitted the photon. In contrast to current and proposed tests of the WEP, our proposal explores the validity of the WEP in a regime where the two particles involved in the differential gravity acceleration measurement are not classically independent, but entangled. We propose an experimental implementation using ^{85}Rb and ^{87}Rb atoms entangled by a vacuum stimulated rapid adiabatic passage protocol implemented in a high-finesse optical cavity. We show that an accuracy below 10^{-7} on the Eötvös parameter can be achieved.
In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of Δg/g≈6×10^{-11} per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in 10^{13}, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.