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Physical Review A

van der Waals interaction of an atom with the internal surface of a hollow submicrometer-size cylinder

Anton E. Afanasiev, Vladimir G. Minogin

Published Nov 10, 2010• 21 citations
Publisher

Abstract

We analyze the van der Waals interaction of an atom with the internal surface of a metal or dielectric submicrometer-sized cylinder and derive closed analytical equations for the van der Waals surface potential and force in the electrostatic approximation. We show that for a concave cylindrical surface the van der Waals potential energy can be up to four times larger than for a flat surface. This result is qualitatively explained by a reduction in the effective distance between the atom and the concave surface compared to that for a flat surface. We also evaluate the shape of an atomic beam propagating inside a hollow dielectric submicrometer-sized cylinder and we propose a scheme that will enable a precise measurement of the van der Waals constant ${C}_{3}$.

DOI
10.1103/physreva.82.052903

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We analyze the van der Waals interaction of an atom with the internal surface of a metal or dielectric submicrometer-sized cylinder and derive closed analytical equations for the van der Waals surface potential and force in the electrostatic approximation. We show that for a concave cylindrical surface the van der Waals potential energy can be up to four times larger than for a flat surface. This result is qualitatively explained by a reduction in the effective distance between the atom and the concave surface compared to that for a flat surface. We also evaluate the shape of an atomic beam propagating inside a hollow dielectric submicrometer-sized cylinder and we propose a scheme that will enable a precise measurement of the van der Waals constant C3{C}_{3}C3​.
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.
We calculate the atomic energy-level shift and the modified dipolar radiation rate inside a hollow dielectric cylinder and outside a solid cylinder using a quantum-mechanical linear-response formalism in the dipole approximation. We first derive the electromagnetic fields scattered by the cylindrical surface for an oscillating dipole inside and outside the cylinder. When an atom is located on the axis of the cylindrical hollow, we obtain analytic expressions of the atomic level shifts in two limiting cases: when bbb (radius of hollow) is very small, the level shift is proportional to ${b}^{\ensuremath{-}2}$ which is associated with the kinetic-energy change of the atomic electron, whereas when bbb is very large, the shift is proportional to ${b}^{\ensuremath{-}4}$ which is identified as the retarded (Casimir-Polder) interaction energy. Moreover, we calculate the atomic potentials as a function of the position of atoms in the hollow region, which is important for the atom-guiding experiment. We also calculate the decay rates and find enhanced rates inside and outside the cylinder. In particular, we compare the radiative properties of an atom inside the hollow cylinder with those between two plates, and those near a cylinder with near a single surface.
Within the frame of macroscopic quantum electrodynamics in causal media, a rigorous derivation of the van der Waals energy of an atomic system in the presence of an arbitrary arrangement of dispersing and absorbing dielectric bodies is given. As an application, the van der Waals potential of an atom in the presence of a dispersing and absorbing sphere is derived. Closed expressions for the long-distance (retardation) and short-distance (non-retardation) limits are given, and the effect of material absorption is discussed.
Molecular beams of rare gas atoms and D2{\mathrm{D}}_{2}D2​ have been diffracted from 100-nm-period SiNx{\mathrm{SiN}}_{x}SiNx​ transmission gratings. The relative intensities of the diffraction peaks out to the eighth order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals ${\ensuremath{-}C}_{3}/{l}^{3}$ interaction of the particles with the walls of the grating bars. The values of the C3{C}_{3}C3​ constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole polarizability.
We have observed the deflection of Rydberg atoms towards a metallic surface by the van der Waals force. Cs and Na atoms in states of principal quantum number n were sent between two parallel gold-coated mirrors, spaced by a gap w (2.1 \ensuremath{\mu}m\ensuremath{\le}w\ensuremath{\le}8.5 \ensuremath{\mu}m). We measured the value nm{n}_{m}nm​ at which the transmission cuts off and from the variation of nm{n}_{m}nm​ versus w, we obtained a measure of the atom-surface interaction. For 12<n<3012<n<3012<n<30 this interaction is 3--4 orders of magnitude larger than for ground-state atoms, and it obeys the scaling laws of the Lennard-Jones model.
The van der Waals atom-surface attraction, scaling as C 3 z −3 for z the atom-surface distance, is expected to be valid in the distance range 1–1000 nm, covering 8–10 orders of magnitudes in the interaction energy. A Cs vapour nanocell allows us to analyze the spectroscopic modifications induced by the atom-surface attraction on the 6 P 3/2 → 6 D 5/2 transition. The measured C 3 value is found to be independent of the thickness in the explored range 40–130 nm, and is in agreement with an elementary theoretical prediction. We also discuss the specific interest of exploring short distances and large interaction energy.