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arXiv:1212.5678 · Physical Review A

Quantum reflection of antihydrogen from nanoporous media

Gabriel Dufour, R. Guérout, Astrid Lambrecht, Валерий Викторович Несвижевский, Serge Reynaud, A. Yu. Voronin

Published Feb 19, 2013• 30 citations
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Abstract

We study quantum reflection of antihydrogen atoms from nanoporous media due to the Casimir-Polder potential. Using a simple effective medium model, we show a dramatic increase of the probability of quantum reflection of antihydrogen atoms if the porosity of the medium increases. We discuss the limiting case of reflections at small energies, which have interesting applications for trapping and guiding antihydrogen using material walls.

DOI
10.1103/physreva.87.022506

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We study quantum reflection of antihydrogen atoms from nanoporous media due to the Casimir-Polder potential. Using a simple effective medium model, we show a dramatic increase of the probability of quantum reflection of antihydrogen atoms if the porosity of the medium increases. We discuss the limiting case of reflections at small energies, which have interesting applications for trapping and guiding antihydrogen using material walls.
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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.
An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville transformation of the Schr\"odinger equation and a Langer coordinate adapted to problems with a classical turning point. Reflection on the Casimir-Polder attractive well is replaced by reflection on a repulsive wall, and the problem is then viewed as an ultracold atom trapped inside a cavity with gravity and Casimir-Polder potentials acting, respectively, as top and bottom mirrors. We calculate numerically Casimir-Polder shifts of the energies of the cavity resonances and propose an approximate treatment which is precise enough to discuss spectroscopy experiments aimed at tests of the weak-equivalence principle on antihydrogen. We also discuss the lifetimes by calculating complex energies associated with cavity resonances.
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We consider the interaction of antiatoms with a solid surface and present calculations of the reflection probability using the exact retarded potential for the antihydrogen impinging on the ideally conducting surface. We present the reflection probability as a function of collision energy and show that the sufficiently cold ¯ H atoms are reflected (rather than annihilated) from the surface, which opens prospects for storing and guiding antiatoms between material walls. The reflection probability in the ultracold regime is determined entirely by the van der Waals–Casimir tail of the atom–wall interaction and contains information on the retardation effects. We argue on the possibility of exploiting the ultracold antihydrogen–surface interactions as a probe of the electrodynamical and gravitational properties of an antiatom. We found that the lifetime of cold ¯ H bouncing on the surface in the gravitational field of Earth is τ = ¯2Mg|Im a|) � 0.11 s. The measurement of that lifetime in conjunction with our calculation of the scattering lengtha allows determination of the gravitational force Mg on the antihydrogen atom.
The GBAR experiment will time the free fall of cold antihydrogen atoms dropped onto an annihilation plate to test the universality of free fall on antimatter. In this contribution, we study the quantum reflection of the anti-atom resulting from the Casimir-Polder attraction to the plate. We evaluate the Casimir-Polder potential and the associated quantum reflection amplitudes and find that reflection is enhanced for weaker potentials. A Liouville transformation of the Schrödinger equation is used to map the quantum reflection problem onto an equivalent problem of scattering on a barrier, leading to an intuitive understanding of the phenomenon.