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arXiv:1506.06535 · Physical Review A

Characterization of a simultaneous dual-species atom interferometer for a quantum test of the weak equivalence principle

Alexis Bonnin, Nassim Zahzam, Yannick Bidel, Alexandre Bresson

Published Aug 18, 2015• 51 citations
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Abstract

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.

DOI
10.1103/physreva.92.023626

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•Jul 14, 2018•0 citations
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×\else\texttimes\fi10\ensuremath−7g/Hz1.23\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}g/\sqrt{\mathrm{Hz}}1.23\ifmmode×\else\texttimes\fi10\ensuremath−7g/Hz​ limited by the detection noise and a resolution of 2\ifmmode×\else\texttimes\fi10\ensuremath−9g2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}g2\ifmmode×\else\texttimes\fi10\ensuremath−9g 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×\else\texttimes\fi10\ensuremath−3g3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}g3\ifmmode×\else\texttimes\fi10\ensuremath−3g, 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 \ensuremathη\ensuremath∼10\ensuremath−9\ensuremath{\eta}\ensuremath{\sim}{10}^{\ensuremath{-}9}\ensuremathη\ensuremath∼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{}^{87}87Rb and 85{}^{85}85Rb). 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 $\ensuremath{\Delta}g/g=(1.2\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.
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 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.
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 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 ).
Quantum technology based on cold-atom interferometers is showing great promise for fields such as inertial sensing and fundamental physics. However, the best precision achievable on Earth is limited by the free-fall time of the atoms, and their full potential can only be realized in Space where interrogation times of many seconds will lead to unprecedented sensitivity. Various mission scenarios are presently being pursued, which plan to implement matter-waves inertial sensors to detect gravitational waves, to measure the Earth gravity field or to test fundamental physics such as the Equivalence Principle.We developed a cold atom sensor experiment adapted to microgravity platforms, especially the ZERO-G plane. To achieve a test of the Universality of Free Fall, we realize the first onboard operation of simultaneous ^{87}Rb - ^{39}K interferometers in the weightlessness environment produced during parabolic flight. The large vibration levels (10 ^{-2} g/Hz ^{1/2}), acceleration range and rotation rates (5 deg/s) during flight present significant technical challenges for atom interferometers. By hybridizing each atomic sensor with a common mechanical accelerometer, we achieve a sensitivity of 3.4 10 ^{-5} g per shot-more than 1600 times below the ambient vibration level onboard the aircraft. We demonstrate the capability of our dual-quantum sensor by measuring the Eötvös parameter with systematic-limited uncertainties of 3.0 10 ^{-4} during micro-gravity. This constitutes the first quantum test of the equivalence principle in a free falling vehicle. Our results can be extended to the trajectory of a satellite for future Space missions. We also achieved a simultaneous ^{87}Rb- ^{39}K interferometer on ground with a long term stability on the differential acceleration measurement around 5 10 ^{-8}g, limited by the fall of the atom clouds. To increase the interrogation time and the sensitivity, a ZERO-G simulator has been installed in our laboratory and allows our experiment to be in free fall during 500 ms every 12 seconds, to achieve highly repeatable measurements in microgravity. We expect to increase our short-term sensitivity by two orders of magnitude, and consequently reach a long-term measurement of the Eötvös parameter at the level of 10 ^{-11}.To benefit from the free fall of the experiment completely, it is necessary to produce atoms clouds with a reduced velocity dispersion. To reach this goal, we put ^{87}Rb atoms in an optical dipole trap supplied by a compact fiber laser compliant with onboard applications and decrease the optical power on a very controlled way to obtain evaporative cooling. Preliminary results of ultra-fast evaporative cooling (less than a few seconds) onboard the ZERO-G plane allowed us to reach a regime of temperature compliant with an interrogation time of the order of one second. This method and technology will be tested on the ZERO-G simulator as well.