Abstract We propose an experimental test of the quantum equivalence principle introduced by Zych and Brukner (arXiv: 1502.00971 ), which generalises the Einstein equivalence principle to superpositions of internal energy states. We consider a harmonically trapped spin ‐ 1 2 atom in the presence of both gravity and an external magnetic field and show that when the external magnetic field is suddenly switched off, various violations of the equivalence principle would manifest as otherwise forbidden transitions. Performing such an experiment would put bounds on the various phenomenological violating parameters. We further demonstrate that the classical weak equivalence principle can be tested by suddenly putting the apparatus into free fall, effectively ‘switching off’ gravity.
Abstract We propose an experimental test of the quantum equivalence principle introduced by Zych and Brukner (arXiv: 1502.00971 ), which generalises the Einstein equivalence principle to superpositions of internal energy states. We consider a harmonically trapped spin ‐ 1 2 atom in the presence of both gravity and an external magnetic field and show that when the external magnetic field is suddenly switched off, various violations of the equivalence principle would manifest as otherwise forbidden transitions. Performing such an experiment would put bounds on the various phenomenological violating parameters. We further demonstrate that the classical weak equivalence principle can be tested by suddenly putting the apparatus into free fall, effectively ‘switching off’ gravity.
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.
Recently, we have started to investigate behavior of a composite quantum body in an external gravitational field in the framework of General Relativity [see, for a review, A. G. Lebed, Mod. Phys. Lett. A, {\bf 35}, 2030010 (2020)]. As the simplest example, we have considered a hydrogen atom in a weak gravitational field. Our results are the following. The Einstein's Equivalence Principle survives for the most of macroscopic ensembles of the atoms, containing the stationary quantum states. On the other hand, we have demonstrated that this principle is sometimes broken. In particular, it is broken for the so-called Gravitational demons, which are the coherent macroscopic ensembles of two or more stationary quantum states in the hydrogen atoms. In the above cited paper we have considered the Gedanken experiment, where the gravitational field is suddenly switched on in a free from gravitation space. In the current paper we consider the much more realistic from experimental point of view Gedanken experiment and come to the same conclusion about violations of the Einstein's Equivalence Principle for the Gravitational demons.
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.
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.
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.
The weak equivalence principle (WEP), that is, the universality of free fall, states that all point-like neutral particles in a gravitational field fall in the same way. This is the basis of the geometrization of the gravitational interaction. Together with further requirements on the behavior of point particles, light propagation and clocks one can show that gravity is modeled by a Riemannian geometry. Since in the quantum domain all objects are extended, it is not clear whether the notion of a WEP in the quantum domain makes sense at all. We show that for matter wave interferometry the notion of WEP still can be given a meaning. We give a short overview over schemes which allows a violation of the WEP and emphasize that there are also schemes which show that there might be violations of the WEP in the quantum regime which are not present classically. This makes a test of the WEP with quantum matter necessary. We also give a brief outline of the efforts made for testing the WEP with interferometry with cold atoms in the Bremen drop tower carried out by the QUANTUS and PRIMUS collaboration.