Quantum reflection of antihydrogen from nanoporous media

Abstract

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 1.3s on a bulk of liquid 4 He, and 1.7s 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.

Statistical approach to Casimir-Polder potentials in heterogeneous media

“…In strong contrast, at smaller distances fluctuations of the potential become larger than its mean, which is consequently no longer representative. In practice, this conclusion is crucial for measurements of quantum reflection [21,[31][32][33][34], and more generally for any measurement of the Casimir force involving heterogeneous materials.…”

Improved effective range expansion for Casimir–Polder potential

“…The re ection amplitude r(k) which describes the quantum re ection of the atom on the Casimir-Polder potential has been computed for antihydrogen falling down on di erent surfaces [35][36][37]. It goes to −1 at the limit of low energies, with an asymptotic approach to this limit described by a scattering length : For the ideal homogeneous potential V 4 , the length coincides with the length scale 4 [38,39], that is real.…”

Quantum ballistic experiment on antihydrogen fall

“…The bottom plate, being well-polished metallic surface, plays a role of mirror forH atoms with vertical velocities of a few cm/s. It was shown in [7,19,20,22] that the interaction of slow antiatoms with a material surface results in the reflection with a probability close to unity. This is explained by the effect of quantum (overbarrier) reflection ofH from the van-der Waals-Casimir-Polder potential between an (anti)atom and a material surface.…”

“…This lifetime could be significantly larger for silica surface or thin slabs [20]. H states between two horizontal plates, separated by a height h, differ from pure gravitational states due to the presence of the upper plate.…”