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arXiv:1312.6018 · International Journal of Modern Physics Conference Series

Quantum reflection of antihydrogen in the GBAR experiment

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

Published Jan 1, 2014• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s2010194514602658

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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.
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.
We study quantum reflection of antihydrogen atoms from matter slabs due to the van der Waals--Casimir-Polder potential. By taking into account the specificities of antihydrogen and the optical properties and width of the slabs, we calculate realistic estimates for the potential and quantum reflection amplitudes. Next we discuss the paradoxical result of larger reflection coefficients estimated for weaker potentials in terms of the Schwarzian derivative. We analyze the limiting case of reflections at small energies, which are characterized by a scattering length and have interesting applications for trapping and guiding antihydrogen using material walls.
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.
Collisions between ultracold atoms and material surfaces are characterized by the reflection of the atomic matter wave from the attractive Casimir-Polder potential. This quantum reflection is particularly relevant to experiments such as GBAR, which will determine the gravitational acceleration of a cold antihydrogen atom by timing its fall onto a detection plate. In this thesis, the Casimir-Polder potential is computed from the electromagnetic scattering properties of the atom and surface and it is found to depend notably on the dielectric response, thickness and density of the medium. We show that reflection on this potential is associated with a breakdown of the semiclassical approximation and that it is enhanced for slow atoms and weak potentials. Liouville transformations relate Schrödinger equations with different potential landscapes but identical scattering properties. We gain new insights on the problem of quantum reflection on a potential well by mapping it onto an equivalent problem of tunneling through a wall. We also discuss the effect of gravity on the atomic wavepacket and its implications for free fall experiments with atoms. When combined with quantum reflection from a horizontal mirror, gravity can be used to trap particles in long lived states with promising applications for metrology. In particular, we suggest a scheme to improve the precision of the GBAR experiment by reducing the velocity dispersion of the falling atoms.
We study the quantum reflection of ultracold antihydrogen atoms bouncing on the surface of a liquid helium film. The Casimir-Polder potential and quantum reflection are calculated for different thicknesses of the film supported by different substrates. Antihydrogen can be protected from annihilation for as long as 1.3 s on a bulk of liquid 4 He, and 1.7 s for liquid 3 He. These large lifetimes open interesting perspectives for spectroscopic measurements of the free fall acceleration of antihydrogen. Variation of the scattering length with the thickness of a film of helium shows interferences which we interpret through a Liouville transformation of the quantum reflection problem.