We show that the ultracold H̄ atoms below 10−6 K are reflected from the surface with the probability , which is determined entirely by the van der Waals‐Casimir tail of the atom‐wall interaction and contains information on the retardation effects. We found, that the lifetime of cold H̄ bouncing on the conducting surface in the gravitational field of Earth is τ = ℏ/(2Mg|Ima|) ≃ 0.11 s. The measurement of that lifetime in conjunction with the here presented calculation of the scattering length a allows determination of the gravitational force Mg acting on the antihydrogen atom.
We investigate the interaction of ultracold antihydrogen with a conducting surface, focusing on the phenomenon of quantum reflection. We calculate the reflection probability as a function of incident atom energy. We find that, for ground-state
H atoms (with $T<{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, the probability of reflection is $R\ensuremath{\simeq}1\ensuremath{-}kb$, where
k is the momentum of the atom and
b=2174.0a.u. is a constant determined solely by the van der Waals--Casimir tail of the atom-wall interaction. We show that quantum reflection, which suppresses the direct contact of ultracold atoms with the surface, allows for the possibility of confinement and storage of sufficiently cold antihydrogen atoms. We calculate the lifetime of
H atoms enclosed in between solid walls. We develop a theory of
H in a waveguide and propose some applications, notably the measurement of retardation corrections in the long-range component of the antiatom-wall potential. We demonstrate the existence of quantized states for antihydrogen atoms falling onto conducting surface in the gravitational field of Earth. We calculate the lifetime of ultracold
H in its lowest gravitational state and obtain $\ensuremath{\tau}=(Mgb∕2\ensuremath{\Elzxh}{)}^{\ensuremath{-}1}\ensuremath{\simeq}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, where
Mg is a gravitational force acting on the antiatom. We propose that measurement of this lifetime may provide a new test for the gravitational properties of antimatter.
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.
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.
An overview of the antiatom interactions with matter is given in the context of the ongoing efforts to trap and cool antihydrogen at CERN. We show how the atom‐antiatom scattering can, in addition to annihilation, result in a number of collisional reactions such as elastic scattering, rearrangement to protonium and positronium, and even radiative association leading to formation of unusual short‐lived atom‐antiatom molecules. We also show that sufficiently cold antiatoms can be reflected from material walls. The rates for these reactions are of interest for the experiments with antihydrogen atoms at CERN, they probe the feasibility of collisional cooling of antihydrogen and they contribute to the understanding of stability of matter in contact with antimatter in general.
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.