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 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.
We propose experiments with atomic hydrogen gas at ultra-low temperatures T < 100 μ K when the thermal energy of atoms is comparable with the changes of their potential energy in the Earth gravity field. At these conditions we suggest implementing a gravitational spectroscopy for studies of quantum properties of ultra-cold atomic hydrogen and its interactions with matter and gravity, similar to experiments with ultra-cold neutrons (Nesvizhevsky et al. Nature 415 , 297 2002 ). A magnetic trap used for reaching the Bose-Einstein Condensation (Fried et al. Phys. Rev. Lett. 81 , 3811 1998 ) can be used for cooling a large number of H atoms below 1 mK. Evaporative cooling over the trap barrier allows effective cooling of the vertical degree of freedom of the trapped atoms. Releasing these ultra-slow atoms from the trap onto the cold surface of superfluid helium will allow studies of quantum bounces and stationary gravitational states of H atoms in the potential well created by this surface and the field of Earth gravity. Experimental study of properties of gravitational quantum states of hydrogen and quantum reflection of ultracold hydrogen from surface would be of major importance for designing similar experiments with antihydrogen, which are currently prepared in CERN.