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arXiv:1212.5676 · Physical Review A

Quantum reflection of antihydrogen from the Casimir potential above matter slabs

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

Published Jan 2, 2013• 51 citations
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Abstract

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.

DOI
10.1103/physreva.87.012901

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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.
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.
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.
We theoretically study the interference of the long-living quasi-stationary quantum states of antihydrogen atoms, localized near a concave material surface. Such states are an antimatter analogue of the whispering gallery states of neutrons and matter atoms, and similar to the whispering gallery modes of sound and electro-magnetic waves. Quantum states of antihydrogen are formed by the combined effect of quantum reflection from the van der Waals/Casimir–Polder (vdW/CP) potential of the surface and the centrifugal potential. We point out a method for precision studies of quantum reflection of anti-atoms from vdW/CP potential; this method uses the interference of the whispering gallery states of antihydrogen.
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.
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.