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arXiv:0902.3235 · Physical Review A

Dispersive interactions between atoms and nonplanar surfaces

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

Published Aug 27, 2009• 70 citations
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Abstract

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.

DOI
10.1103/physreva.80.022119

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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.
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.
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.
Van der Waals forces between atoms and molecules are universally assumed to act along the line separating them. Inspired by recent works on effects which can propel atoms parallel to a macroscopic surface via the Casimir-Polder force, we predict a lateral van der Waals force between two atoms, one of which is in an excited state with nonzero angular momentum and the other is isotropic and in its ground state. The resulting force acts in the same way as a planetary gear, in contrast to the rack-and-pinion motion predicted in works on the lateral Casimir-Polder force in the analogous case, for which the force predicted here is the microscopic origin. We illustrate the effect by predicting the trajectories of an excited caesium in the vicinity of ground-state rubidium, finding behavior qualitatively different to that if lateral forces are ignored.
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.
van der Waals interactions between atoms and dielectric surfaces are reinvestigated. To describe the nonretarded interaction potential between a dispersive dielectric surface and an atom in an arbitrary internal energy state, we derive a general expression in terms of an integral, over real frequency, of the combined atom and surface polarizabilities. It is shown that, for excited atoms, the expression is equivalent to the one obtained by Wylie and Sipe [Phys. Rev. A 32, 2030 (1985)]. We thus demonstrate how to extend this approach to excited atoms interacting with birefringent dielectrics. For isotropic dielectrics, a method of integration in closed form allows us to derive an approximate formula for the van der Waals interaction constant in terms of resonance frequencies and oscillator strengths of both the atom and the dielectric. Frequency-dependent ``dielectric reflection'' coefficients are introduced for virtual atomic dipole couplings either in absorption or in emission. In absorption, the reflection coefficient is always positive and smaller than unity. In emission, it may take arbitrary values, positive or negative (corresponding to van der Waals repulsion). Such a behavior is shown to be related to resonant excitation exchange between the atomic system and the dielectric medium, when an atomic transition frequency gets in resonance with a dielectric absorption band. Numerical calculations performed for the cesium-sapphire system are shown to be in good agreement with data obtained by selective-reflection spectroscopy. Finally, experimental tests of the birefringent character of the sapphire response are discussed.