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Physical Review B

Two-phonon assisted selective adsorption

Wilhelm Brenig, Christian Mosch

Published Nov 17, 2010• 2 citations
Publisher

Abstract

The bound-state-plus-two-phonon resonances in scattering of atoms by surface phonons are considered in detail. We compute the dependence of single phonon transition probabilities on the initial energy performing large-scale coupled channel calculations. It turns out that the resonances in this case are relatively strong and sharp. Furthermore, due to a new implementation we are able to consider two- and three-phonon resonances in the scattering in full detail. It turns out the two phonon resonances should be observable but three phonon resonances not.

DOI
10.1103/physrevb.82.193407

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The bound-state-plus-two-phonon resonances in scattering of atoms by surface phonons are considered in detail. We compute the dependence of single phonon transition probabilities on the initial energy performing large-scale coupled channel calculations. It turns out that the resonances in this case are relatively strong and sharp. Furthermore, due to a new implementation we are able to consider two- and three-phonon resonances in the scattering in full detail. It turns out the two phonon resonances should be observable but three phonon resonances not.
We develop a multidimensional coupled-channel method suitable for studying the interplay of bound-state resonance and phonon-assisted scattering of inert gas atoms from solid surfaces in one, two, and three dimensions. This enables us to get insight into the features that depend on the dimensionality of inelastic resonant processes typically encountered in low-energy He atom scattering from surfaces, in general, and to elaborate on the observability of recently conjectured near threshold resonances in scattering from Einstein phonons, in particular.
We present a detailed study of the bound-state phonon-mediated resonances in atom-surface scattering that extends our earlier work [\ifmmode \check{S}\else \v{S}\fi{}iber and Gumhalter, Phys. Rev. B 71, 081401 (2005)]. Previous results obtained within the restricted Fock space coupled-channel algorithm are reconsidered in view of the enlargement and refinement of the basis of quantum states used in the calculation. The convergence demonstrated in this procedure reinforces the usefulness of the developed algorithm.
The quantum mechanical treatment of the elastic scattering of atoms from a crystal surface provides valuable information, such as surface properties and gas-surface interaction potentials. However, since it is based on the stationary state solution, it does not provide the details of the scattering process in the neighborhood of the surface, especially when atoms are physically adsorbed. In this thesis, the time evolution of the scattering process is treated in 2D with a model potential, V(x, z) = -|g|δ(z) + λδ(z)cos(2πx/a), using the Gaussian wave packet approach. The focus is on the case where the Gaussian wave packet makes a transition into a selective adsorption state because it can provide information on the probability density of selectively adsorbed particles as well as the details of the scattering process in the neighborhood of the surface. The obtained Gaussian wave packet solution shows a transition into a selective adsorption state. However, the probability density of selectively adsorbed particles cannot be accurately determined because the Gaussian wave packet constructed from the Born approximate time-independent wave function does not conserve the total probability density.
Results from four different approximations to the phonon-assisted quantum adsorption rate for cold atoms on a 2D material are compared and contrasted: (1) a loop expansion (LE) based on the atom-phonon coupling, (2) non-crossing approximation (NCA), (3) independent boson model approximation (IBMA), and (4) a leading-order soft-phonon resummation method (SPR). The SPR method treats the adsorbed atom as a surface polaron where the phonon cloud accompanying the bound atom is a phonon coherent state. We conclude that, of the four approximations considered, only the SPR method gives a divergence-free result in the large membrane regime at finite temperature. The other three methods give an adsorption rate that diverges in the limit of an infinite surface.
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.
We study phonon-mediated transitions between translational levels of an atom in a surface-induced potential. We present a general master equation governing the dynamics of the translational states of the atom. In the framework of the Debye model, we derive compact expressions for the rates for both upward and downward transitions. Numerical calculations for the transition rates are performed for a deep silica-induced potential allowing for a large number of bound levels as well as free states of a cesium atom. The total absorption rate is shown to be determined mainly by the bound-to-bound transitions for deep bound levels and by bound-to-free transitions for shallow bound levels. Moreover, the phonon emission and absorption processes can be orders of magnitude larger for deep bound levels as compared to the shallow bound ones. We also study various types of transitions from free states. We show that, for thermal atomic cesium with a temperature in the range from $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}400\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in the vicinity of a silica surface with a temperature of 300K300\phantom{\rule{0.3em}{0ex}}\mathrm{K}300K, the adsorption (free-to-bound decay) rate is about two times larger than the heating (free-to-free upward decay) rate, while the cooling (free-to-free downward decay) rate is negligible.