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arXiv:1510.00866 · Journal of Physics B Atomic Molecular and Optical Physics

Quantum ballistic experiment on antihydrogen fall

A Yu Voronin, Валерий Викторович Несвижевский, Gabriel Dufour, Serge Reynaud

Published Feb 15, 2016• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/49/5/054001

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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.
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.
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.
The framework of this thesis is the GBAR collaboration at CERN, which aims to measure the free fall acceleration of antimatter . In this thesis, we study the quantum reflection of the antihydrogen on the detector, caused by the Casimir-Polder interaction that we calculate for different materials. We find a particularly high quantum reflection for an antihydrogen atom on a surface of liquid helium. We then present a complete description of the gravitational quantum states, mixing gravity and Casimir-Polder interaction. For this purpose, we revisit the theory of collisions in the case of the Casimir-Polder potential through a new "effective range theory", obtained after a Liouville transform. The knowledge of gravitational quantum states leads us to propose a new method of measuring free fall acceleration, by creating quantum interferences between these states. A statistical analysis of the interference pattern thus obtained is carried out, leading to an improvement in the accuracy until three orders of magnitude compared to the initial free-fall experiment. Finally, we study in detail the influence of the disorder at the level of the plate of detection, the latter being in fact not a perfect surface. We calculate the effect of this disorder on the fluctuations of the Casimir-Polder potential itself, and observe a different behavior in law for the conductivity models such as the plasma model and the Drude model.
In the GBAR experiment, cold antihydrogen atoms will be left to fall on an annihilation plate with the aim of measuring the gravitational acceleration of antimatter. Here, we study the quantum reflection of these antiatoms due to the Casimir-Polder potential above the plate. We give realistic estimates of the potential and quantum reflection amplitudes, taking into account the specificities of antihydrogen and the optical properties of the plate. We find that quantum reflection is enhanced for weaker potentials, for example above thin slabs, graphene and nanoporous media.