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arXiv:2006.08729 · Physical review. D/Physical review. D.

Resolution of the colocation problem in satellite quantum tests of the universality of free fall

Sina Loriani, Christian Schubert, Dennis Schlippert, Wolfgang A. Ertmer, Franck Pereira dos Santos, Ernst Maria Rasel, Naceur Gaaloul, Peter Wolf

Published Dec 18, 2020• 23 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevd.102.124043

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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{10}^{\ensuremath{-}18}10\ensuremath−18 level given an initial differential position (velocity) uncertainty in the order of \ensuremathμm\ensuremath{\mu}\mathrm{m}\ensuremathμm (\ensuremathμm/s\ensuremath{\mu}\mathrm{m}/\mathrm{s}\ensuremathμm/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.
Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead to a drastic loss of contrast. These difficulties can be mitigated by employing wave packets with narrower position and momentum widths, but this is ultimately limited by Heisenberg's uncertainty principle. We present a promising scheme that overcomes these problems by compensating the effects of the gravity gradients and circumvents the fundamental limitations due to Heisenberg's uncertainty principle. Furthermore, it relaxes the experimental requirements on initial colocation by several orders of magnitude.
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 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.
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 search for a fundamental, self-consistent theoretical framework to cover phenomena over all energy scales is possibly the most challenging quest of contemporary physics. Approaches to reconcile quantum mechanics and general relativity entail the modification of their foundations such as the equivalence principle. This corner stone of general relativity is suspected to be violated in various scenarios and is therefore under close scrutiny. Experiments based on the manipulation of cold atoms are excellently suited to challenge its different facets. Freely falling atoms constitute ideal test masses for tests of the universality of free fall in interferometric setups. Moreover, the superposition of internal energy eigenstates provides the notion of a clock, which allows to perform tests of the gravitational redshift. Furthermore, as atom interferometers constitute outstanding phasemeters, they hold the promise to detect gravitational waves, another integral aspect of general relativity. In recent years, atom interferometers have developed into versatile sensors with excellent accuracy and stability, and allow to probe physics at the interface of quantum mechanics and general relativity without classical analog. In this thesis, various aspects regarding tests of general relativity with atom interferometry have been theoretically investigated. This includes the analysis of fundamental effects as well as feasibility studies of experimental configurations. The work is partially focussed on a space-borne mission scenario for a dedicated quantum test of the universality of free fall beyond state-of-the-art by dropping matter waves of different elements. To enable the target accuracy at the level of 10^(−17), a compensation scheme has been developed and discussed, mitigating the detrimental effects of imperfect test mass co-location upon release and relaxing the requirements on the source preparation by several orders of magnitude. In addition, it was demonstrated that the careful design of quantum degenerate sources is indispensable for these experiments, requiring tailored schemes to prepare miscible binary sources. The possibility to test the gravitational redshift with atom interferometers has also been examined in this thesis and connected to the ideas of clock interferometry. With the proof that closed light pulse atom interferometers without transitions between internal internal states are not sensitive to gravitational time dilation, an ongoing scientific debate has been resolved. Instead, certain configurations were shown to implement a quantum version of the special-relativistic twin paradox, for which an experiment has been proposed. Finally, requirements on atomic sources and atom optics for scenarios of gravitational wave detection on ground and in space have been investigated.
To date, no framework combining quantum field theory and general relativity and hence unifying all four fundamental interactions, exists. Violations of the Einstein's equivalence principle (EEP), being the foundation of general relativity, may hold the key to a theory of quantum gravity. The universality of free fall (UFF), which is one of the three pillars of the EEP, has been extensively tested with classical bodies. Quantum tests of the UFF, e.g. by exploiting matter wave interferometry, allow for complementary sets of test masses, orders of magnitude larger test mass coherence lengths and investigation of spin-gravity coupling. We review our recent work towards highly sensitive matter wave tests of the UFF on ground. In this scope, the first quantum test of the UFF utilizing two different chemical elements, Rb-87 and K-39, yielding an Eötvös ratio η Rb,K=(0.3±5.4)×10−7η_{\,\text{Rb,K}}=(0.3\pm 5.4)\times 10^{-7}ηRb,K​=(0.3±5.4)×10−7 has been performed. We assess systematic effects currently limiting the measurement at a level of parts in 10810^8108 and finally present our strategies to improve the current state-of-the-art with a test comparing the free fall of rubidium and ytterbium in a very long baseline atom interferometry setup. Here, a 10 m baseline combined with a precise control of systematic effects will enable a determination of the Eötvös ratio at a level of parts in 101310^{13}1013 and beyond, thus reaching and overcoming the performance limit of the best classical tests.