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Physical Review A

Gravitational quantum states of Antihydrogen

A. Yu. Voronin, Piotr Froelich, Валерий Викторович Несвижевский

Published Mar 8, 2011• 54 citations
Publisher

Abstract

We present a theoretical study of the motion of the antihydrogen atom ($\overline{\mathrm{H}}$) in the gravitational field of Earth above a material surface. We predict that the $\overline{\mathrm{H}}$ atom, falling in the gravitational field of Earth above a material surface, would settle into long-lived quantum states. We point out a method of measuring the difference in the energy of $\overline{\mathrm{H}}$ in such states. The method allows for spectroscopy of gravitational levels based on atom-interferometric principles. We analyze the general feasibility of performing experiments of this kind. We point out that such experiments provide a method of measuring the gravitational force ($\mathit{Mg}$) acting on $\overline{\mathrm{H}}$ and that they might be of interest in the context of testing the weak equivalence principle for antimatter.

DOI
10.1103/physreva.83.032903

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We present a theoretical study of the motion of the antihydrogen atom (H‾\overline{\mathrm{H}}H) in the gravitational field of Earth above a material surface. We predict that the H‾\overline{\mathrm{H}}H atom, falling in the gravitational field of Earth above a material surface, would settle into long-lived quantum states. We point out a method of measuring the difference in the energy of H‾\overline{\mathrm{H}}H in such states. The method allows for spectroscopy of gravitational levels based on atom-interferometric principles. We analyze the general feasibility of performing experiments of this kind. We point out that such experiments provide a method of measuring the gravitational force (Mg\mathit{Mg}Mg) acting on H‾\overline{\mathrm{H}}H and that they might be of interest in the context of testing the weak equivalence principle for antimatter.
We present a theoretical study of the motion of the antihydrogen atom (Hˉ\bar{H}Hˉ) in the Earth's gravitational field above a material surface. We predict that Hˉ\bar{H}Hˉ atom, falling in the Earth's gravitational field above a material surface, would settle in long-living quantum states. We point out a method of measuring the difference in energy of Hˉ\bar{H}Hˉ in such states that allow us to apply spectroscopy of gravitational levels based on atom-interferometric principles. We analyze a general feasibility to perform experiments of this kind. We point out that such experiments provide a method of measuring the gravitational force (MgMgMg) acting on Hˉ\bar{H}Hˉ and they might be of interest in a context of testing the Weak Equivalence Principle for antimatter.
Abstract We propose an approach to measuring gravitational mass of antihydrogen ( ) based on interferometry of time distribution of free-fall events of antiatoms. Our method consists of preparing a coherent superposition of quantum states of localized near a material surface in the gravitational field of the Earth, and then observing the time distribution of annihilation events after the free-fall of the initially prepared superposition from a given height to a detector plate. We show that the time distribution of interest is mapped to a precisely predictable velocity distribution of the initial wave packet. This approach is combined with production of a coherent superposition of gravitational states by inducing a resonant transition using an oscillating gradient magnetic field. We show that the relative accuracy of measuring the atom gravitational mass can be achieved with this approach is 10 −4 , with 10 3 antiatoms settled in lowest gravitational states.
Different experiments are ongoing to measure the effect of gravity on cold neutral antimatter atoms such as positronium, muonium, and antihydrogen. Among those, the project GBAR at CERN aims to measure precisely the gravitational fall of ultracold antihydrogen atoms. In the ultracold regime, the interaction of antihydrogen atoms with a surface is governed by the phenomenon of quantum reflection which results in bouncing of antihydrogen atoms on matter surfaces. This allows the application of a filtering scheme to increase the precision of the free fall measurement. In the ultimate limit of smallest vertical velocities, antihydrogen atoms are settled in gravitational quantum states in close analogy to ultracold neutrons (UCNs). Positronium is another neutral system involving antimatter for which free fall under gravity is currently being investigated at UCL. Building on the experimental techniques under development for the free fall measurement, gravitational quantum states could also be observed in positronium. In this contribution, we report on the status of the ongoing experiments and discuss the prospects of observing gravitational quantum states of antimatter and their implications.
Different experiments are ongoing to measure the effect of gravity on cold neutral antimatter atoms such as positronium, muonium and antihydrogen. Among those, the project GBAR in CERN aims to measure precisely the gravitational fall of ultracold antihydrogen atoms. In the ultracold regime, the interaction of antihydrogen atoms with a surface is governed by the phenomenon of quantum reflection which results in bouncing of antihydrogen atoms on matter surfaces. This allows the application of a filtering scheme to increase the precision of the free fall measurement. In the ultimate limit of smallest vertical velocities, antihydrogen atoms are settled in gravitational quantum states in close analogy to ultracold neutrons (UCNs). Positronium is another neutral system involving antimatter for which free fall under gravity is currently being investigated at UCL. Building on the experimental techniques under development for the free fall measurement, gravitational quantum states could also be observed in positronium. In this contribution, we review the status of the ongoing experiments and discuss the prospects of observing gravitational quantum states of antimatter and their implications.
We predict the existence of antihydrogen atom long-living quasistationary states, localized near a curved material surface due to quantum reflection from the van der Waals--Casimir potential. Such states are an atom-wave analog of the whispering-gallery (WG) modes, known in acoustics, optics, and neutron physics. We argue that the WG states of antihydrogen atoms could be regarded as a close analog of recently predicted gravitational states of antihydrogen where the centrifugal potential plays the role of the linear gravitational potential. We point out a method for the precision measurement of anti-atom-matter interactions, based on the study of interference of WG antihydrogen states.
The subjects presented here are very different. Their common feature is that they all involve quantum phenomena in a gravitational field: gravitational quantum states of ultracold antihydrogen above a material surface and measuring a gravitational interaction of antihydrogen in AEGIS, a quantum trampoline for ultracold atoms, and a hypothesis on naturally occurring gravitational quantum states, an Eötvös-type experiment with cold neutrons and others. Considering them together, however, we could learn that they have many common points both in physics and in methodology.