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Space Science Reviews

Atom-Based Test of the Equivalence Principle

Sebastian Fray, Martin Weitz

Published Jul 24, 2009• 11 citations
Publisher

Abstract

We describe a test of the equivalence principle with quantum probe particles based on atom interferometry. For the measurement, a light pulse atom interferometer based on the diffraction of atoms from effective absorption gratings of light has been developed. A differential measurement of the Earth’s gravitational acceleration g for the two rubidium isotopes 85 Rb and 87 Rb has been performed, yielding a difference Δ g / g =(1.2±1.7)×10 −7 . In addition, the dependence of the free fall on the relative orientation of the electron to the nuclear spin was studied by using atoms in two different hyperfine states. The determined difference in the gravitational acceleration is Δ g / g =(0.4±1.2)×10 −7 . Within their experimental accuracy, both measurements are consistent with a free atomic fall that is independent from internal composition and spin orientation.

DOI
10.1007/s11214-009-9566-x

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We describe a test of the equivalence principle with quantum probe particles based on atom interferometry. For the measurement, a light pulse atom interferometer based on the diffraction of atoms from effective absorption gratings of light has been developed. A differential measurement of the Earth’s gravitational acceleration g for the two rubidium isotopes 85 Rb and 87 Rb has been performed, yielding a difference Δ g / g =(1.2±1.7)×10 −7 . In addition, the dependence of the free fall on the relative orientation of the electron to the nuclear spin was studied by using atoms in two different hyperfine states. The determined difference in the gravitational acceleration is Δ g / g =(0.4±1.2)×10 −7 . Within their experimental accuracy, both measurements are consistent with a free atomic fall that is independent from internal composition and spin orientation.
We have developed a matter wave interferometer based on the diffraction of atoms from effective absorption gratings of light. In a setup with cold rubidium atoms in an atomic fountain the interferometer has been used to carry out tests of the equivalence principle on an atomic basis. The gravitational acceleration of the two isotopes 85Rb^{85}\mathrm{R}\mathrm{b}85Rb and 87Rb^{87}\mathrm{R}\mathrm{b}87Rb was compared, yielding a difference $\ensuremath{\Delta}\mathbf{g}/\mathbf{g}=(1.2\ifmmode\pm\else\textpm\fi{}1.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. We also perform a differential free fall measurement of atoms in two different hyperfine states, and obtained a result of $\ensuremath{\Delta}\mathbf{g}/\mathbf{g}=(0.4\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.
We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an E\"otv\"os parameter of $\ensuremath{\eta}=[1.6\ifmmode\pm\else\textpm\fi{}1.8(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}3.4(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$, consistent with zero violation of the equivalence principle. With a resolution of up to $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{g}$ per shot, we demonstrate a sensitivity to $\ensuremath{\eta}$ of $5.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}/\sqrt{\mathrm{Hz}}$.
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.
We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between 85Rb and 87Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an Eötvös parameter of [1.6 +/- 1.8 (stat) +/- 3.4 (syst)] x 10^-12, consistent with zero violation of the equivalence principle. With a resolution of up to 1.4 x 10^-11 g per shot, we demonstrate the highest sensitivity to the Eötvös parameter of any laboratory experiment.
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.
Abstract The Einstein equivalence principle (EEP) has a central role in the understanding of gravity and space–time. In its weak form, or weak equivalence principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms: a Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superposition. The use of the superposition state allows testing genuine quantum aspects of EEP with no classical analogue, which have remained completely unexplored so far. In addition, we measure the Eötvös ratio of atoms in two hyperfine levels with relative uncertainty in the low 10−9, improving previous results by almost two orders of magnitude.