We predict the existence of antihydrogen atom long-living quasistationary states, localized near a curved material surface due to quantum reflection from the van der Waals--Casimir potential. Such states are an atom-wave analog of the whispering-gallery (WG) modes, known in acoustics, optics, and neutron physics. We argue that the WG states of antihydrogen atoms could be regarded as a close analog of recently predicted gravitational states of antihydrogen where the centrifugal potential plays the role of the linear gravitational potential. We point out a method for the precision measurement of anti-atom-matter interactions, based on the study of interference of WG antihydrogen states.
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.
The ‘whispering gallery’ effect has been known since ancient times for sound waves in air, later in water and more recently for a broad range of electromagnetic waves: radio, optics, Roentgen and so on. It is intensively used and explored due to its numerous crucial applications. It consists of wave localization near a curved reflecting surface and is expected for waves of various natures, for instance, for neutrons and (anti)atoms. For (anti)matter waves, it includes a new feature: a massive particle is settled in quantum states, with parameters depending on its mass. In this talk, we present the first observation of the quantum whispering-gallery effect for matter particles (cold neutrons) 1-2. This phenomenon provides an example of an exactly solvable problem analogous to the ‘quantum bouncer’; it is complementary to recently discovered gravitational quantum states of neutrons3. These two phenomena provide a direct demonstration of the weak equivalence principle for a massive particle in a quantum state. Deeply bound long-living states are weakly sensitive to surface potential; highly excited short-living states are very sensitive to the wall nuclear potential shape. Therefore, they are a promising tool for studying fundamental neutron–matter interactions, quantum neutron optics and surface physics effects. Analogous phenomena could be measured with atoms and anti-atoms 4-5.
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 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 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 present a theoretical study of the motion of the antihydrogen atom (
Hˉ) in the Earth's gravitational field above a material surface. We predict that
Hˉ atom, falling in the Earth's gravitational field above a material surface, would settle in long-living quantum states. We point out a method of measuring the difference in energy of
Hˉ in such states that allow us to apply spectroscopy of gravitational levels based on atom-interferometric principles. We analyze a general feasibility to perform experiments of this kind. We point out that such experiments provide a method of measuring the gravitational force (
Mg) acting on
Hˉ and they might be of interest in a context of testing the Weak Equivalence Principle for antimatter.