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arXiv:1312.5963

Differential atom interferometry with $^{87}$Rb and $^{85}$Rb for testing the UFF in STE-QUEST

Christian Schubert, Hartwig, J, Henning Ahlers, K Posso-Trujillo, Naceur Gaaloul, Ulrich Velte, Arnaud Landragin, Andréa D Bertoldi, Baptiste Battelier, Philippe Bouyer, Fiodor Sorrentino, Guglielmo Maria Tino, Markus Krutzik, Achim Peters, Sven Herrmann, Cláus Lämmerzahl, L. Cacciapouti, Emanuele Rocco, Kai Bongs, Wolfgang A. Ertmer, Ernst Maria Rasel

Published Dec 20, 2013• 17 citations
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Abstract

In this paper we discuss in detail an experimental scheme to test the universality of free fall (UFF) with a differential $^{87}$Rb / $^{85}$Rb 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 $2$ parts in $10^{15}$ of such an interferometer for a test of the UFF.

DOI
10.48550/arxiv.1312.5963

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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.
The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The STE-QUEST satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the Universality of Free Fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose-Einstein condensates of Rb85 and Rb87. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the Eötvös parameter of at least 2x10E-15. In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources.
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.
A major challenge common to all Galilean drop tests of the universality of free fall (UFF) is the required control over the initial kinematics of the two test masses upon release due to coupling to gravity gradients and rotations. In this work, we consider a space-borne test of the UFF based on atom interferometry and show that this detrimental effect can be mitigated at the ${10}^{\ensuremath{-}18}$ level given an initial differential position (velocity) uncertainty in the order of $\ensuremath{\mu}\mathrm{m}$ ($\ensuremath{\mu}\mathrm{m}/\mathrm{s}$) of the test masses. This corresponds to a relaxation of the source control by several orders of magnitude with respect to comparable mission scenarios, such as the STE-QUEST mission proposal reported in [D. N. Aguilera et al., Classical Quantum Gravity 31, 115010 (2014)]. Our twofold mitigation strategy extends a compensation mechanism that is already established in terrestrial experiments to satellite missions with varying gravity gradients and exploits the spectral distribution of the systematics. We assess the experimental feasibility and find that the moderate parameters of the proposed scheme are in line with technological capabilities. The described attenuation of the gravity-gradient-induced uncertainty removes one major obstacle in quantum tests of the UFF and allows us to consider mission scenarios with target accuracies beyond the state of the art.
The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The spacetime explorer and quantum equivalence principle space test satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the universality of free fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose-Einstein condensates of 85Rb and 87Rb. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the Eötvös parameter of at least 2 × 10-15. In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources.
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 ).
Testing the Universality of Free Fall at 10−10{10^{ - 10}}10−10 level by Comparing the Atoms in Different Hyperfine States with Bragg Diffraction
We have performed a precision atomic interferometry experiment on testing the universality of free fall (UFF) considering atoms' spin degree of freedom. Our experiment employs the Bragg atom interferometer with 87^{87}87Rb atoms either in hyperfine state $\left| {F = 1,{m_F} = 0} \right\rangle $ or $\left| {F = 2,{m_F} = 0} \right\rangle ,andthewavepacketsinthesetwostatesarediffractedinonepairofBraggbeamsalternatively,whichcanhelpsuppressthecommon−modesystematicerrors.WehaveobtainedanE, and the wave packets in these two states are diffracted in one pair of Bragg beams alternatively, which can help suppress the common-mode systematic errors. We have obtained an E,andthewavepacketsinthesetwostatesarediffractedinonepairofBraggbeamsalternatively,whichcanhelpsuppressthecommon−modesystematicerrors.WehaveobtainedanE\rm{\ddot{o}}tvtvtv\rm{\ddot{o}}$s ratio η=(0.9±2.7)×10−10η= \left( { 0.9 \pm 2.7} \right) \times {10^{ - 10}}η=(0.9±2.7)×10−10, and set a new record on the precision with a nearly 5 times improvement. Our experiment gives stronger restrictions on the possible UFF breaking mechanism.