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arXiv:1712.09874 · Journal of Physics B Atomic Molecular and Optical Physics

Two-dimensional simulation of quantum reflection

Emanuele Galiffi, Christoph Sünderhauf, Maarten DeKieviet, Sandro Wimberger

Published Apr 6, 2017• 10 citations
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Abstract

Abstract A propagation method for the scattering of a quantum wave packet from a potential surface is presented. It is used to model the quantum reflection of single atoms from a corrugated (metallic) surface. Our numerical procedure works well in two spatial dimensions requiring only reasonable amounts of memory and computing time. The effects of the surface corrugation on the reflectivity are investigated via simulations with a paradigm potential. These indicate that our approach should allow for future tests of realistic, effective potentials obtained from theory in a quantitative comparison to experimental data.

DOI
10.1088/1361-6455/aa66e2

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Abstract A propagation method for the scattering of a quantum wave packet from a potential surface is presented. It is used to model the quantum reflection of single atoms from a corrugated (metallic) surface. Our numerical procedure works well in two spatial dimensions requiring only reasonable amounts of memory and computing time. The effects of the surface corrugation on the reflectivity are investigated via simulations with a paradigm potential. These indicate that our approach should allow for future tests of realistic, effective potentials obtained from theory in a quantitative comparison to experimental data.
A method for the solution of the time-dependent Schrödinger equation in two dimensions is presented which is based on the hydrodynamic analogy to quantum mechanics. The continuum introduced in that analogy is approximated by a finite number of particles, whose trajectories are computed. The procedure is applied here to the dynamics of a Gaussian wave packet on a two-dimensional quadratic potential surface containing a saddle point. Comparison with the known analytical solution indicates that the method is capable of accurate results with substantially less computer time required than in methods previously employed.
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A method for the solution of the time-dependent Schrödinger equation in two dimensions is presented which is based on the hydrodynamic analogy to quantum mechanics. The continuum introduced in that analogy is approximated by a finite number of particles, whose trajectories are computed. The procedure is applied here to the dynamics of a Gaussian wave packet on a two-dimensional quadratic potential surface containing a saddle point. Comparison with the known analytical solution indicates that the method is capable of accurate results with substantially less computer time required than in methods previously employed. This particular check problem was chosen because of its close relationship to the wave-packet dynamics of chemical reaction rates.
We study the influence of atom-surface interactions close to the surface on the confinement properties in a recently proposed model [A. Jurisch and H. Friedrich, Phys. Lett. A 349, 230 (2006)] for quantum reflection traps and test the reliability of the sharp-step approximation used there. Accurate numerical calculations show a dependence of the surviving particle fraction on characteristic potential lengths determined by the behavior of the interaction in the limits $r\ensuremath{\rightarrow}0$ and $r\ensuremath{\rightarrow}\ensuremath{\infty}$ of the atom-surface distance rrr. For interactions dominated by the retarded potential proportional to 1∕r41∕{r}^{4}1∕r4 we find that the simplified sharp-step potential reproduces the behavior of the trapped atoms well, both qualitatively and quantitatively.
A short time propagation algorithm for the reduced density matrix is derived to model the interaction of a quantum particle with a moving corrugated surface. The algorithm includes dissipative terms, which can be derived directly from the full Hamiltonian. The scattering of He from a corrugated Cu surface is examined as a function of incident energy and angle and the temperature of the substrate, with a focus on the nature of trapping. It is found that corrugation can make a significant contribution to trapping, even on a metal surface. Energy exchange with the phonons is shown to significantly modify the nature of diffraction mediated selective adsorption.