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arXiv:2509.14652 · Physical review. B./Physical review. B

Zero-energy resonances in ultracold hydrogen sticking to liquid helium films of finite thickness

R. Karakhanyan, Валерий Викторович Несвижевский, Aleksei Semakin, Sergey Vasiliev, A. Yu. Voronin

Published Jan 2, 2026• 0 citations
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Abstract

We investigated quantum states of ultracold hydrogen atoms in a combined potential comprising the H-He film interaction in the presence of a substrate and the Earth gravitational field. We show that the shift and width of the gravitational quantum states are determined by the complex scattering length for the H-He film-substrate potential. We demonstrate that for specific helium film thicknesses above a substrate, zero-energy resonances occur if the combined potential supports a bound state exactly at the threshold. This effect leads to a complete restructuring of the bound states spectrum. The dynamics of gravitational levels as a function of the van der Waals interaction depth controlled by the helium film thickness is analyzed. It reveals the critical thicknesses at about 6.1 and 1.8 nm, at which resonances appear in the case of the conductive substrate. With imaginary integral operators, we incorporate non-perturbatively the inelastic effects originating from the ripplon coupling. The inelastic effects show dramatic changes in the sticking-coefficient behavior near the critical points. The enhanced sticking coefficients provide a probe for studying critical phenomena and measuring atom-surface interaction parameters with unprecedented sensitivity.

DOI
10.1103/7dnl-4zpp

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We investigated quantum states of ultracold hydrogen atoms in a combined potential comprising the H-He film interaction in the presence of a substrate and the Earth gravitational field. We show that the shift and width of the gravitational quantum states are determined by the complex scattering length for the H-He film-substrate potential. We demonstrate that for specific helium film thicknesses above a substrate, zero-energy resonances occur if the combined potential supports a bound state exactly at the threshold. This effect leads to a complete restructuring of the bound states spectrum. The dynamics of gravitational levels as a function of the van der Waals interaction depth controlled by the helium film thickness is analyzed. It reveals the critical thicknesses at about 6.1 and 1.8 nm, at which resonances appear in the case of the conductive substrate. With imaginary integral operators, we incorporate non-perturbatively the inelastic effects originating from the ripplon coupling. The inelastic effects show dramatic changes in the sticking-coefficient behavior near the critical points. The enhanced sticking coefficients provide a probe for studying critical phenomena and measuring atom-surface interaction parameters with unprecedented sensitivity.
The role of shape resonances and many-body effects on universal quantum sticking of ultracold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable representation of the Dyson equation. We derive the self-energy renormalization of the transition amplitude between an ultracold scattering atom and the bound states on the surface in order to elucidate the role of virtual phonon exchanges in the limiting behavior of the sticking probability. We demonstrate that, to first order in the interactions for finite ranged atom–surface potentials, virtual phonons can only rescale the strength of the atom–surface coupling and do not rescale the range of the coupling. Thus, universal sticking behavior at ultralow energies is to be expected for all finite ranged potentials. We demonstrate that the onset of the universal sticking behavior depends greatly on the position of the shape resonance of the renormalized potential and for sufficiently low energy shape resonances, deviations from the universal s(E)∝√E can occur near these energies. We believe that this accounts for many of the low energy sticking trends observed in the scattering of submillikelvin H atoms from superfluid 4He films.
A study is made of the interaction between hydrogen atoms and the surface elementary excitations of superfluid "He. Calculations for the sticking probability and for the energy and effective mass of a hydrogen atom bound to the surface are presented. As a first step in the calculations, we formulate the Hamiltonian describing a hydrogen atom interacting with the surface of "He in its ground state together with the interaction coupling to the surface elementary excitations (the ripplons). The derivation is based on the association of the surface ground state with a flat surface and the excited states with a sinusoidally varying height of the surface. The interaction potential is derived by summing a *He-H atom-atom pair potential over helium atoms below the surface. The atom-atom pair potential is chosen so that the derived surface potential is a Morse potential with parameters which are fitted to the effective surface potential derived by Mantz and Edwards for a hydrogen atom interacting with N-1 helium atoms. The energy and angle dependent sticking probability, S(E,θ), and the thermally averaged sticking probability, S(T), are calculated. Results are compared with the experimental value of S(T), S(T)=0.035±0.005, measured for the temperature range 0.18<T<0.27K. The possibility that a hydrogen atom bound above the surface may exhibit polaronic behaviour is investigated. The energy of the hydrogen surface "polaron" and its effective mass are calculated using perturbation theory. The hydrogen atom is found to be weakly coupled to the surface elementary excitations, and therefore the polaronic effects are weak. The contribution to these results from virtual transition to free states is emphasized.
We present the results of experiments measuring the film thickness dependence of the sticking probability for H on superfluid {sup 4}He for H atom temperatures of 0.3-5.0 mK. Data is presented for 3 nm to 1 mm thick films on a silver sinter substrate. For the 0.3 mK H atoms, the sticking probability varies from 0.4 for a film 3 nm thick to 6 x 10{sup -3} for films thicker than 100 nm. In the case of the thick films the temperature dependence of the sticking probability is consistent with the observation of pure quantum reflection. Our data are in reasonable agreement with recent theoretical calculations.
The zero energy scattering limit of inelastic molecule–surface scattering is studied within the context of a multiphonon expansion of the molecule–bath wave function. By assuming that at low scattering energies the expansion may be truncated at first order in the phonon operators, we derived a closed form solution to the Lippmann Schwinger equation for the scattering wave function which includes a nonlocal and energy dependent self-energy term which correctly incorporates virtual phonon transitions in the elastic channel. The closure relation results from the use of a discrete spectral (ℒ2) form of the inelastic channel Greens functions. We compute the zero energy limit of these wave functions and discuss the trapping and reflection of cold atoms from ultracold surfaces. Our results indicate that for realistic atom surface interactions the low energy limit of the sticking coefficient, s, can deviate markedly from the expected s∝E1/2 behavior and is shown to approach a constant nonzero limiting value. This trend is consistent with recent experimental work involving the sticking of spin polarized hydrogen atoms on liquid He films.
We investigate the possibility of ultracold neutron (UCN) storage in quantum states defined by the combined potentials of the Earth's gravity and the neutron optical repulsion by a horizontal surface of liquid helium. We analyze the stability of the lowest quantum state, which is most susceptible to perturbations due to surface excitations, against scattering by helium atoms in the vapor and by excitations of the liquid, comprised of ripplons, phonons, and surfons. This is an unusual scattering problem since the kinetic energy of the neutron parallel to the surface may be much greater than the binding energies perpendicular. The total scattering time of these UCNs at 0.70.70.7 K is found to exceed 1 h, and rapidly increases with decreasing temperature. Such low scattering rates should enable high-precision measurements of the sequence of discrete energy levels, thus providing improved tests of short-range gravity. The system might also be useful for neutron $\ensuremath{\beta}$-decay experiments. We also sketch new experimental propositions for level population and trapping of ultracold neutrons above a flat horizontal mirror.
We have generalized the BOUND and MOLSCAT packages to allow calculations in basis sets where the monomer Hamiltonians are off diagonal and used this capability to carry out bound-state and scattering calculations on $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ and $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ as a function of magnetic field. Following the bound-state energies to the point where they cross thresholds gives very precise predictions of the magnetic fields at which zero-energy Feshbach resonances occur. We have used this to locate and characterize two very narrow Feshbach resonances in $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$. Such resonances can be used to tune elastic and inelastic collision cross sections, and sweeping the magnetic field across them will allow a form of quantum control in which separated atoms and molecules are associated to form complexes. For the first resonance, where only elastic scattering is possible, the scattering length shows a pole as a function of magnetic field and there is a very large peak in the elastic cross section. For the second resonance, however, inelastic scattering is also possible. In this case the pole in the scattering length is dramatically suppressed and the cross sections show relatively small peaks. The peak suppression is expected to be even larger in systems with stronger inelasticity. The results suggest that calculations on ultracold molecular inelastic collisions may be much less sensitive to details of the potential energy surface than has been believed.