Anisotropic atom-surface interactions in the Casimir-Polder regime

Abstract

The distance-dependence of the anisotropic atom-wall interaction is studied. The central result is the 1/z 6 quadrupolar anisotropy decay in the retarded Casimir-Polder regime. Analysis of the transition region between non-retarded van der Waals regime (in 1/z 3 ) and Casimir-Polder regime shows that the anisotropy cross-over occurs at very short distances from the surface, on the order of 0.03λ, where λ is the atom characteristic wavelength. Possible experimental verifications of this distance dependence are discussed. PACS numbers: 34.35.+a, 03.75.Be, 12.20.Fv The force between neutral polarisable systems is a ubiquitous phenomenon in nature, with many applications in physics, chemistry, biology. . . A paramount example is the long-range interaction potential between neutral microscopic quantum systems, like atomic systems, and a solid surface. For plane surfaces this interaction is usually governed by a power-law attractive potential [1,2]. For atom-surfaces distances z smaller than the wavelengths of the optical transitions involved in the atomic polarisability, the interaction is of the dipoleinduced dipole type, and governed by the well-known non-retarded van der Waals potential in −C 3 /z 3 , which reflects the correlations of dipole fluctuations [1]. At larger distances, retardation effects get important, and asymptotically lead to a −C 4 /z 4 potential, as demonstrated in the pioneering work of Casimir and Polder [2].Atom (molecule) -surface forces are central in numerous scientific and technological domains: surface adsorption of atoms, gas-surface equilibrium, cavity QED [3], quantum reflection of atoms on surfaces [4], microelectromechanical systems [5], research for a fifth fundamental force [6], etc. In most of the above studies, the interaction potential has to be treated in its full distance range (retarded and non-retarded), but is generally considered scalar. However the atom-surface potential has a cylindrical symmetry around the surface normal, and exhibits a quadrupolar component which may get important for non-scalar energy levels. Anisotropic surface potential strongly alters the internal dynamics and symmetry of nearby atomic systems. For example, surfaceinduced symmetry break and internal level coupling have been observed on rare-gas metastable states scattered at material surfaces [7]. From previous experimental studies of the anisotropic potential, on can underline two points: (i) on one hand, in selective reflection (SR) studies -generally sensitive to a λ/2π distance (∼ 100 nm) * Corresponding author: martial.ducloy@univ-paris13.fr from the surface (see e.g.[8]) -, the influence of the anisotropic potential has not been observed, although SR spectroscopy gives access to the excited atomic response [9]; (ii) on the other hand, in beam scattering studies, the range of the anisotropic interaction appears to be always smaller than 10 nm -in general 5 nm or less - [10]. Thus one can state that up to now those anisotropic characteristics have been observed in the non-retarded regime. Ind...

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