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arXiv:1904.07096 · Physical Review A

Joint mass-and-energy test of the equivalence principle at the 10−10 level using atoms with specified mass and internal energy

Lin Zhou, Chuan He, Sitong Yan, Xi Chen, Dong-Feng Gao, Wei-Tao Duan, Yu-Hang Ji, Rundong Xu, Biao Tang, Chao Zhou, Sachin Barthwal, Qi Ming Wang, Zhuo Hou, Zongyuan Xiong, Yuan‐Zhong Zhang, Min Liu, Wei-Tou Ni, Jin Wang, Mingsheng Zhan

Published Aug 26, 2021• 35 citations
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Abstract

We use rubidium atoms with specified mass and internal energy to carry out a joint mass-energy test of the equivalence principle (EP). We improve the four-wave double-diffraction Raman transition method (4WDR) we proposed before to select atoms with a certain mass and angular momentum state, and form a dual-species atom interferometer. By using the extended 4WDR to $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ atoms with different angular momenta, we measure their differential gravitational acceleration, and we determine the value of the E\"otv\"os parameter, $\ensuremath{\eta}$, which measures the strength of the violation of EP. The E\"otv\"os parameters of the four paired combinations $^{85}\mathrm{Rb}|F=2\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=1\ensuremath{\rangle}$, $^{85}\mathrm{Rb}|F=2\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=2\ensuremath{\rangle}$, $^{85}\mathrm{Rb}|F=3\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=1\ensuremath{\rangle}$, and $^{85}\mathrm{Rb}|F=3\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=2\ensuremath{\rangle}$ were measured to be ${\ensuremath{\eta}}_{1}=(1.5\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, ${\ensuremath{\eta}}_{2}=(\ensuremath{-}0.6\ifmmode\pm\else\textpm\fi{}3.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, ${\ensuremath{\eta}}_{3}=(\ensuremath{-}2.5\ifmmode\pm\else\textpm\fi{}4.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and ${\ensuremath{\eta}}_{4}=(\ensuremath{-}2.7\ifmmode\pm\else\textpm\fi{}3.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, respectively. The violation parameter of mass is constrained to ${\ensuremath{\eta}}_{0}=(\ensuremath{-}0.8\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and that of internal energy to ${\ensuremath{\eta}}_{E}=(0.0\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ per reduced energy ratio $a$ ($a=h{\ensuremath{\nu}}_{0}/{m}_{i}^{85}{c}^{2}$, and ${\ensuremath{\nu}}_{0}=1$ GHz). This work opens a door for joint tests of two attributes beyond the traditional pure mass or energy tests of EP with quantum systems.

DOI
10.1103/physreva.104.022822

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We use rubidium atoms with specified mass and internal energy to carry out a joint mass-energy test of the equivalence principle (EP). We improve the four-wave double-diffraction Raman transition method (4WDR) we proposed before to select atoms with a certain mass and angular momentum state, and form a dual-species atom interferometer. By using the extended 4WDR to 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb atoms with different angular momenta, we measure their differential gravitational acceleration, and we determine the value of the E"otv"os parameter, \ensuremathη\ensuremath{\eta}\ensuremathη, which measures the strength of the violation of EP. The E"otv"os parameters of the four paired combinations 85Rb∣F=2\ensuremath⟩\ensuremath-87Rb∣F=1\ensuremath⟩^{85}\mathrm{Rb}|F=2\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=1\ensuremath{\rangle}85Rb∣F=2\ensuremath⟩\ensuremath-87Rb∣F=1\ensuremath⟩, 85Rb∣F=2\ensuremath⟩\ensuremath-87Rb∣F=2\ensuremath⟩^{85}\mathrm{Rb}|F=2\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=2\ensuremath{\rangle}85Rb∣F=2\ensuremath⟩\ensuremath-87Rb∣F=2\ensuremath⟩, 85Rb∣F=3\ensuremath⟩\ensuremath-87Rb∣F=1\ensuremath⟩^{85}\mathrm{Rb}|F=3\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=1\ensuremath{\rangle}85Rb∣F=3\ensuremath⟩\ensuremath-87Rb∣F=1\ensuremath⟩, and 85Rb∣F=3\ensuremath⟩\ensuremath-87Rb∣F=2\ensuremath⟩^{85}\mathrm{Rb}|F=3\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=2\ensuremath{\rangle}85Rb∣F=3\ensuremath⟩\ensuremath-87Rb∣F=2\ensuremath⟩ were measured to be \ensuremathη1=(1.5\ifmmode±\else\textpm\fi3.2)\ifmmode×\else\texttimes\fi10\ensuremath−10{\ensuremath{\eta}}_{1}=(1.5\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ensuremathη1​=(1.5\ifmmode±\else\textpm\fi3.2)\ifmmode×\else\texttimes\fi10\ensuremath−10, \ensuremathη2=(\ensuremath−0.6\ifmmode±\else\textpm\fi3.7)\ifmmode×\else\texttimes\fi10\ensuremath−10{\ensuremath{\eta}}_{2}=(\ensuremath{-}0.6\ifmmode\pm\else\textpm\fi{}3.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ensuremathη2​=(\ensuremath−0.6\ifmmode±\else\textpm\fi3.7)\ifmmode×\else\texttimes\fi10\ensuremath−10, \ensuremathη3=(\ensuremath−2.5\ifmmode±\else\textpm\fi4.1)\ifmmode×\else\texttimes\fi10\ensuremath−10{\ensuremath{\eta}}_{3}=(\ensuremath{-}2.5\ifmmode\pm\else\textpm\fi{}4.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ensuremathη3​=(\ensuremath−2.5\ifmmode±\else\textpm\fi4.1)\ifmmode×\else\texttimes\fi10\ensuremath−10, and \ensuremathη4=(\ensuremath−2.7\ifmmode±\else\textpm\fi3.6)\ifmmode×\else\texttimes\fi10\ensuremath−10{\ensuremath{\eta}}_{4}=(\ensuremath{-}2.7\ifmmode\pm\else\textpm\fi{}3.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ensuremathη4​=(\ensuremath−2.7\ifmmode±\else\textpm\fi3.6)\ifmmode×\else\texttimes\fi10\ensuremath−10, respectively. The violation parameter of mass is constrained to \ensuremathη0=(\ensuremath−0.8\ifmmode±\else\textpm\fi1.4)\ifmmode×\else\texttimes\fi10\ensuremath−10{\ensuremath{\eta}}_{0}=(\ensuremath{-}0.8\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ensuremathη0​=(\ensuremath−0.8\ifmmode±\else\textpm\fi1.4)\ifmmode×\else\texttimes\fi10\ensuremath−10, and that of internal energy to \ensuremathηE=(0.0\ifmmode±\else\textpm\fi0.4)\ifmmode×\else\texttimes\fi10\ensuremath−10{\ensuremath{\eta}}_{E}=(0.0\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ensuremathηE​=(0.0\ifmmode±\else\textpm\fi0.4)\ifmmode×\else\texttimes\fi10\ensuremath−10 per reduced energy ratio aaa (a=h\ensuremathν0/mi85c2a=h{\ensuremath{\nu}}_{0}/{m}_{i}^{85}{c}^{2}a=h\ensuremathν0​/mi85​c2, and \ensuremathν0=1{\ensuremath{\nu}}_{0}=1\ensuremathν0​=1 GHz). This work opens a door for joint tests of two attributes beyond the traditional pure mass or energy tests of EP with quantum systems.
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 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 $5.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}/\sqrt{\mathrm{Hz}}$.
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 equivalence principle (EP) is a basic assumption of the general relativity. The quantum test of the equivalence principle with atoms is an important way to examine the applicable scope of the current physical framework so as to discover new physics. Recently, we extended the traditional pure mass or energy tests of the equivalence principle to the joint test of mass–energy by atom interferometry (Zhou et al.,Phys.Rev.A 104,022822). The violation parameter of mass is constrained to η0 = (−0.8 ± 1.4) × 10–10 and that of internal energy to ηE = (0.0 ± 0.4) × 10–10 per reduced energy ratio. Here, we first briefly outline the joint test idea and experimental results, and then, we analyze and discuss how to improve the test accuracy. Finally, we report the latest experimental progress toward a high-precision mass–energy test of the equivalence principle. We realize atom interference fringes of 2T = 2.6 s in the 10-m long-baseline atom interferometer. This free evolution time T, to the best of our knowledge, is the longest duration realized in the laboratory, and the corresponding resolution of gravity measurement is 4.5 × 10−11 g per shot.
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 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.