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arXiv:1503.08423 · New Journal of Physics

Correlative methods for dual-species quantum tests of the weak equivalence principle

B. Barrett, Laura Antoni‐Micollier, Laure Chichet, Baptiste Battelier, P-A Gominet, Andréa D Bertoldi, Philippe Bouyer, Arnaud Landragin

Published Aug 27, 2015• 64 citations

Abstract

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.

DOI: 10.1088/1367-2630/17/8/085010

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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.

We present here the performance of a simultaneous dual-species matter-wave accelerometer for measuring the differential acceleration between two different atomic species (

^{87}\mathrm{Rb}

and

^{85}\mathrm{Rb}

). 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 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 $\ensuremath{\Delta}g/g=(1.2\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.

We theoretically investigate the application of the fringe-locking method (FLM) in the dual-species quantum test of the weak equivalence principle (WEP). With the FLM, the measurement is performed invariably at the midfringe, and the extraction of the phase shift for atom interferometers is linearized. For the simultaneous interferometers, this linearization enables a good common-mode rejection of vibration noise, which is usually the main limit for high precision WEP tests of dual-species kind. We note that this method also allows for an unbiased determination of the gravity accelerations difference, which meanwhile is readily to be implemented.

The Weak Equivalence Principle (WEP) is a central pillar of general relativity. Its precise test with quantum systems in space offers a unique window onto new physics. Here we report the first in-orbit quantum test of the WEP. A dual-species (85Rb/87Rb) atom interferometer is realized aboard the China Space Station. Methods of platform motion suppression, fluorescence detection switching, and two-photon detuning switching are developed to eliminate phase noise and improve measurement accuracy. A test uncertainty of 2.8*10-8 is obtained from 280 days of WEP test data, and a test result of (-3.1+/-4.6)*10-7 is achieved after error estimation. This improves prior atom-interferometric WEP tests in microgravity by three orders of magnitude. This work paves the way for space-borne quantum inertial sensors and their application to future fundamental physics in space.

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 ).

Atom interferometry-based sensors have demonstrated remarkable precision, making them attractive for diverse applications compared to traditional sensors. However, practical experiments inevitably encounter noise, which limits precision. We investigate the performance of two commonly used methods, ellipse fitting (EF) and fringe fitting (FF), for differential phase estimation in a dual atom interferometer under various noise conditions. We comprehensively analyze the efficacy of these methods for each type of Gaussian noise, including phase noise, amplitude noise, and offset noise. Using a colored noise model, we investigate the Allan deviation results. Our investigations will offer valuable insights for future quantum sensing based on dual interferometers.