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Scattering approach to dispersive atom-surface interactions

Diego A. R. Dalvit, Riccardo Messina, Paulo A. Maia Neto, Astrid Lambrecht, Serge Reynaud

Published Jan 1, 2009• 1 citation
OpenAlex

Abstract

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.

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Gustavo A Moreno, Diego A R Dalvit, Esteban Calzetta

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arXiv:0904.0238•New Journal of Physics•Mar 9, 2010•14 citations
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.
The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. Here, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework connecting both limiting cases, and is intended as a bridge between advanced quantum mechanics and field-theoretic treatments of dispersion forces, suitable for graduate-level courses or specialized readers.
Understanding the Casimir-Polder (CP) attraction between ultracold atoms and dielectric surfaces is of fundamental importance to the design and miniaturization of atom chips [1] and for understanding quantum reflection from, and sticking to, the surface [2 - 6]. So far, calculations have focussed on planar dielectrics, either semi-infinite or of finite width [7-9], and non-planar geometries including corrugated surfaces [10], spheres and carbon nanotubes [11-12]. Here, we present a simple scheme, based on the Pairwise-Summation (PWS) approximation, for estimating the CP interaction between a ground-state alkali atom and a dielectric volume of arbitrary shape. The PWS approximation integrates the van der Waals interaction between two ground-state atoms over the many atoms in the surface volume. We relate the microscopic polarizability of atoms in the surface to the bulk dielectric constant via the Clausius-Mossotti relation within the Lorentz local-field theory. We find that the CP potential depends strongly on both the geometry and density of the surface, which modify the fluctuation spectrum of the electromagnetic field that couples the alkali atoms to the dielectric. We compare our results with known analytical expressions for the CP potential near planar surfaces and use them to investigate how BECs interact with, and may quantum reflect from, curvilinear surface structures.
We theoretically investigate Rydberg atom pair potentials of Rb atoms in front of a perfectly conducting plate. The pair potentials are perturbed by both the Casimir-Polder potential acting on a single atom and the scattering contribution to the interatomic interaction. In contrast to the pair potentials in free space, at atom-surface distances ${d}_{s}\ensuremath{\lesssim}4\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$, avoided crossings appear. In the associated potential wells that are entirely due to dispersion interactions with the surface, there exist vibrational bound states, i.e., Rydberg macrodimers, with ground-state energies of up to $E=\ensuremath{-}68\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ and radial expectation values of the order of several $\ensuremath{\mu}\mathrm{m}$.