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New Journal of Physics

Testing the weak equivalence principle with positronium by Rydberg-atom interferometry

L R McCaul, D. B. Cassidy, S. D. Hogan

Published Aug 22, 2025• 2 citations
Publisher

Abstract

Abstract We describe an experimental scheme wherein phase shifts induced by the gravitational field of the Earth on atoms in superpositions of Rydberg states with large static electric dipole moments can be observed by matter-wave interferometry. Such measurements, performed using positronium (Ps) atoms would constitute a test of the weak equivalence principle for a purely leptonic matter-antimatter system. Using realistic experimental parameters, obtained from measured data, we estimate that this approach could make it possible to measure the gravitational acceleration of Ps with a precision on the order of 10%.

DOI
10.1088/1367-2630/adfe87

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Abstract We describe an experimental scheme wherein phase shifts induced by the gravitational field of the Earth on atoms in superpositions of Rydberg states with large static electric dipole moments can be observed by matter-wave interferometry. Such measurements, performed using positronium (Ps) atoms would constitute a test of the weak equivalence principle for a purely leptonic matter-antimatter system. Using realistic experimental parameters, obtained from measured data, we estimate that this approach could make it possible to measure the gravitational acceleration of Ps with a precision on the order of 10%.
Matter-wave interference has been observed for a wide range of objects: from electrons to neutrons and complex molecules. On the other hand, a double-slit-like experiment has never been carried out with positrons (the anti-particle of the electron) or with any other system containing antimatter. This thesis provides the theoretical foundations and experimental results of a Talbot-Lau interferometer specifically designed for this goal. Future applications include the measurement of the gravitational acceleration of positronium, to provide a test of the weak equivalence principle on a matter-antimatter symmetric, purely leptonic system.
Matter-wave interferometry has been performed with helium atoms in high Rydberg states. In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼320 nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field.
Matter-wave interferometry has been performed with helium atoms in high Rydberg states. In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼320 nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field.
We consider some of the obstacles that will have to be overcome in order to perform a direct measurement of the gravitational free-fall of positronium atoms. Foremost among these are the production of positronium atoms in a cryogenic environment, efficient excitation of these atoms to suitably long-lived Rydberg states, and their subsequent control via the interaction of their large electric dipole moments with inhomogeneous electric fields. Recent developments in all of these areas can be directly applied to a positronium free-fall gravity measurement, making such an endeavour both timely and feasible.
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.
In this paper we consider the feasibility of observing the gravitational quantum states of positronium. The proposed scheme employs the flow-throw technique used for the first observation of this effect with neutrons. Collimation and Stark deceleration of Rydberg positronium atoms allow to select the required velocity class. If this experiment could be realized with positronium it would lead to a determination of g for this matter-antimatter system at the few % level. As discussed in this contribution, most of the required techniques are currently available but important milestones have to be demonstrated experimentally before such an experiment could become reality. Those are: the efficient focusing of a bunched positron beam, Stark deceleration of Rydberg positronium and its subsequent excitation into states with large angular momentum. We provide an estimate of the efficiencies we expect for these steps and assuming those could be confirmed we calculate the signal rate.