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.
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.
The Einstein equivalence principle (EEP) links the universality of free fall, local Lorentz invariance, and local position invariance to the geometric description of gravity. In quantum systems, however, internal energy is represented by an operator and may occupy coherent superpositions; consequently, equality of classical mass parameters is not sufficient to establish equivalence at the operator level. This work develops a compact operator-level Quantum Equivalence Principle (QEP) residual and performs a literature-based experimental cross-validation using independent high-precision experiments. The theoretical basis follows the operator formulation of Zych and Brukner and its relativistic extension by Das, Fridman, and Lambiase. The quantum weak equivalence sector is tested using the 87Rb Bragg atom-interferometry experiment of Rosi et al., which compared two hyperfine internal-energy eigenstates and a coherent superposition, finding Eotvos ratios consistent with zero and constraining the off-diagonal quantum-WEP parameter to 5 x 10^-8. A classical diagonal WEP benchmark is supplied by the final MICROSCOPE result, eta(Ti,Pt) = [-1.5 +/- 2.3(stat) +/- 1.5(syst)] x 10^-15. The local Lorentz-invariance sector is cross-checked using fast 7Li+ optical clocks, which verified relativistic time dilation at 2 x 10^-10 accuracy, while the local-position-invariance sector is cross-checked using millimetre-scale 87Sr optical-clock gravitational-redshift measurements with fractional-frequency uncertainty 7.6 x 10^-21. Finally, published 2025 gravitational-wave QEP bounds are evaluated, with GW190814 providing the intervals [-0.59,0.54], [-0.40,0.37], and [-0.19,0.17] for WEP-, LLI-, and LPI-associated mass-energy differences, respectively. No statistically significant violation is identified in any analyzed sector. The combined evidence supports operator-level QEP consistency over laboratory quantum superpositions, relativistic clock kinematics, gravitational redshift, precision free fall, and strong-field gravitational-wave phenomenology, while also isolating the remaining experimental gap: direct off-diagonal tests of quantum LLI and quantum LPI.
The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.
We propose an experiment to test the weak equivalence principle (WEP) with a test mass consisting of two entangled atoms of different species. In the proposed experiment, a coherent measurement of the differential gravity acceleration between the two atomic species is considered, by entangling two atom interferometers operating on the two species. The entanglement between the two atoms is heralded at the initial beam splitter of the interferometers through the detection of a single photon emitted by either of the atoms, together with the impossibility of distinguishing which atom emitted the photon. In contrast to current and proposed tests of the WEP, our proposal explores the validity of the WEP in a regime where the two particles involved in the differential gravity acceleration measurement are not classically independent, but entangled. We propose an experimental implementation using ^{85}Rb and ^{87}Rb atoms entangled by a vacuum stimulated rapid adiabatic passage protocol implemented in a high-finesse optical cavity. We show that an accuracy below 10^{-7} on the Eötvös parameter can be achieved.
The Weak Equivalence Principle (WEP) is a central pillar of general relativity. Its precise test with quantum systems in space offers a unique window onto new physics. Here we report the first in-orbit quantum test of the WEP. A dual-species (85Rb/87Rb) atom interferometer is realized aboard the China Space Station. Methods of platform motion suppression, fluorescence detection switching, and two-photon detuning switching are developed to eliminate phase noise and improve measurement accuracy. A test uncertainty of 2.8*10-8 is obtained from 280 days of WEP test data, and a test result of (-3.1+/-4.6)*10-7 is achieved after error estimation. This improves prior atom-interferometric WEP tests in microgravity by three orders of magnitude. This work paves the way for space-borne quantum inertial sensors and their application to future fundamental physics in space.
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 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 108 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 1013 and beyond, thus reaching and overcoming the performance limit of the best classical tests.
We propose tests of the weak equivalence principle (WEP) using a torsion balance, in which superposition of energy eigenstates are created in a controllable way for the test masses. After general considerations on the significance of tests of the WEP using quantum states and the need for considering inertial and gravitational masses as operators, we develop a model to derive the matrix elements of the free-fall operator, showing that the variance of the acceleration operator, in addition to its mean, enables estimation of violations of the WEP due to quantum coherence in a way that is robust with respect to shot-to-shot fluctuations. Building on this analysis, we demonstrate how the validity of the WEP may be tested in a torsion balance setup, by accessing the mean and variance of a torque operator we introduce and quantize. Due to the long acquisition times of the signal as compared to the timescale on which coherent superposition states may survive, we further propose a dynamical setting, where the torsion balance is subject to a time-dependent gravitational field, and measurements of angular acceleration encode possible violations of the WEP.