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arXiv:2005.11624 · Physical Review Letters

Atom-Interferometric Test of the Equivalence Principle at the 10 − 12 Level

Peter Asenbaum, Chris Overstreet, Minjeong Kim, Joseph Curti, Mark A. Kasevich

Published Nov 2, 2020• 330 citations
arXivHTMLPDF

Abstract

We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ 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 $5.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}/\sqrt{\mathrm{Hz}}$.

DOI
10.1103/physrevlett.125.191101

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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 \ensuremathη=[1.6\ifmmode±\else\textpm\fi1.8(stat)\ifmmode±\else\textpm\fi3.4(syst)]\ifmmode×\else\texttimes\fi10\ensuremath−12\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}\ensuremathη=[1.6\ifmmode±\else\textpm\fi1.8(stat)\ifmmode±\else\textpm\fi3.4(syst)]\ifmmode×\else\texttimes\fi10\ensuremath−12, consistent with zero violation of the equivalence principle. With a resolution of up to 1.4\ifmmode×\else\texttimes\fi10\ensuremath−11  g1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{g}1.4\ifmmode×\else\texttimes\fi10\ensuremath−11  g per shot, we demonstrate a sensitivity to \ensuremathη\ensuremath{\eta}\ensuremathη of 5.4\ifmmode×\else\texttimes\fi10\ensuremath−11/Hz5.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}/\sqrt{\mathrm{Hz}}5.4\ifmmode×\else\texttimes\fi10\ensuremath−11/Hz​.
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.
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.
In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of Δg/g≈6×10^{-11} per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in 10^{13}, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.
This article develops an expanded critical–propositional analysis of Lin Zhou and collaborators’ 2015 experiment, “Test of Equivalence Principle at 10−8 Level by a Dual-Species Double-Diffraction Raman Atom Interferometer,” published in Physical Review Letters, in systematic dialogue with the Theory of Objectivity (TO) formulated by Vidamor Cabannas and Denivaldo Silva. Zhou et al. implemented a simultaneous 85Rb– 87Rb atom interferometer employ- ing a four-wave double-diffraction Raman transition scheme and obtained an Eötvös parameter η = (2.8 ± 3.0) × 10−8 , finding no violation of the Weak Equivalence Principle within the sensitivity of the experiment (Zhou et al. 2015). The experiment is especially significant for the Theory of Objectivity because it combines elemental differentiation, fields, frequencies, radiation, phase evolution, relational measurement, information generation, and gravity within a single controlled physical architecture. The analysis distinguishes four epistemological categories that must not be conflated: direct empirical confirmation, indirect empirical corroboration, structural compatibility, and merely analogical correspondence. Zhou et al. do not test the primordial Logical Nothingness proposed by the First Absolute Truth of TO, nor do they directly demonstrate the ontological existence of a unique field belonging to every element, as asserted by the Second Absolute Truth. Likewise, the experiment does not establish that logical existence itself requires the relational observation described by the Fifth Absolute Truth. Nevertheless, the experiment offers significant operational bridges. The two rubidium isotopes remain physically distinguishable while participating in a common gravitational regularity; their interferometric information is produced through relations involving atoms, radiation, frequencies, momentum transfer, phase, and detection; and the measured equality of free-fall acceleration imposes a quantitative constraint on any TO-derived gravitational model in which elemental individuality or proper fields could generate composition-dependent acceleration. Particular attention is given to the TO conception of the transcendent element as knowledge or information generated in atomic relations and associated with atomic radiation. The interferometer provides a concrete physical chain in which interactions are converted into relative phase, populations, radiation-mediated detection, and finally experimentally accessible information. This does not establish the full ontological interpretation proposed by TO, but it supplies an unusually clear operational analogue. The article further articulates Zhou et al. with the foundational TO literature, the 2025–2026 reformulation of its modal and empirical program, and supporting or dialogical literature including Einstein, Heisenberg, Bohm, Prigogine, Penrose, Kuhn, Aspect, Planck, and gravitational-wave observations. A formal bridge is proposed in which a TO-specific field contribution Φi generates a potential differential acceleration δg(Φi). The Zhou result then becomes an empirical restriction on the magnitude of such a contribution. The central conclusion is therefore deliberately limited but scientifically pro- ductive: Zhou et al. do not confirm the Theory of Objectivity as a whole, but their experiment constitutes an important empirical constraint and a viable platform for converting selected TO propositions into quantitatively testable predictions. Keywords: Theory of Objectivity; Weak Equivalence Principle; atom interferometry; rubidium isotopes; gravity; modal ontology; information; Raman transitions; Eötvös parameter; empirical testability.
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 $\ensuremath{\Delta}g/g=(1.2\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.
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.