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The Journal of Chemical Physics

Application of the complex rotation method to the study of resonance states of atoms at a corrugated surface

T. Maniv, Erik Engdahl, Nimrod Moiseyev

Published Jan 15, 1987• 24 citations
Publisher

Abstract

The complex rotation method is applied to the calculation of complex poles of the scattering matrix for atoms selectively trapped at a corrugated, static surface. The method is found to be extremely efficient and accurate even for highly corrugated surfaces, for which the use of more conventional methods is known to be in trouble. The method also provides insight into the trapping processes, revealing that for a simple harmonic corrugation there is a critical value of the corrugation amplitude, below which the trapping process is dominated by the coupling between adjacent diffraction channels, while above this critical value the coupling between more distant channels dominates.

DOI
10.1063/1.452339

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The complex rotation method is applied to the calculation of complex poles of the scattering matrix for atoms selectively trapped at a corrugated, static surface. The method is found to be extremely efficient and accurate even for highly corrugated surfaces, for which the use of more conventional methods is known to be in trouble. The method also provides insight into the trapping processes, revealing that for a simple harmonic corrugation there is a critical value of the corrugation amplitude, below which the trapping process is dominated by the coupling between adjacent diffraction channels, while above this critical value the coupling between more distant channels dominates.
A novel concept of complex quasiprobability Q(x) is proposed for atoms selectively trapped on a static, corrugated surface. The real part of Q(x) is the probability that the position vector of a trapped atom will have a projection x on the nominal surface plane, while Im[Q(x)]/‖Q(x)−1‖ is a local measure of the strength of the coupling between different diffraction channels, which leads to desorption of the trapped atoms from the surface. A method of calculating Q(x), based on the complex coordinate method, is presented and discussed. Applying this method to a model atom–surface potential which includes one-dimensional steps, it is shown that while the probability to find a trapped atom is enhanced around the top of a step, desorption is most likely to occur from the middle of the terraces.
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.
We develop the scattering approach for the dispersive force on a ground state atom on top of a corrugated surface. We present explicit results to first order in the corrugation amplitude. A variety of analytical results are derived in different limiting cases, including the van der Waals and Casimir-Polder regimes. We compute numerically the exact first-order dispersive potential for arbitrary separation distances and corrugation wavelengths, for a Rubidium atom on top of a silicon or gold corrugated surface. We consider in detail the correction to the proximity force approximation, and present a very simple approximation algorithm for computing the potential.
We calculate the dispersive force between a ground-state atom and a nonplanar surface. We present explicit results for a corrugated surface, derived from the scattering approach at first order in the corrugation amplitude. A variety of analytical results in different limiting cases, including the van der Waals and Casimir-Polder regimes, is derived. We compute numerically the exact first-order dispersive potential for arbitrary separation distances and corrugation wavelengths for a rubidium atom on top of a silicon or gold corrugated surface. We discuss in detail the inadequacy of the proximity force approximation, and present a simple but adequate approximation for computing the potential.
In this work, a full quantum study of the scattering of He atoms off single CO molecules, adsorbed onto the Pt(111) surface, is presented within the formalism of quantum trajectories provided by Bohmian mechanics. By means of this theory, it is shown that the underlying dynamics is strongly dominated by the existence of a transient vortitial trapping with measurable effects on the whole diffraction pattern. This kind of trapping emphasizes the key role played by quantum vortices in this scattering. Moreover, an analysis of the surface rainbow effect caused by the local corrugation that the CO molecule induces on the surface, and its manifestation in the corresponding intensity pattern, is also presented and discussed.
A corrugated magnetic reflector is realized by adding a bias field to a static magnetic mirror. This permits real-time manipulation of a cold-atom cloud on time scales down to 100 \ensuremath{\mu}s. We show that rotation of the bias field generates a traveling corrugation of adjustable depth and velocity. Momentum is transferred from the traveling wave to the atoms, resulting in a displacement of the cloud that depends on the wave velocity. This is a step towards a new method of manipulation in which neutral atoms could be transported across the surface by surfing along the moving wave.