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Physical Review A

van der Waals interactions between excited-state atoms and dispersive dielectric surfaces

M. Fichet, F. Schuller, Daniel Bloch, M. Ducloy

Published Feb 1, 1995• 100 citations

Abstract

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.

DOI: 10.1103/physreva.51.1553

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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 modulation of the reflection coefficient for a frequency-modulated (FM) light beam incident on the interface between a dielectric and an atomic vapor. The vapor is described as a gas of resonant, Doppler-broadened, two-level systems, with transition frequency and linewidth arbitrarily depending on the atom-dielectric distance. The atoms are supposed to get deexcited at collisions with the surface. The transient atomic response is calculated to first order in the incident field, for both incoming and desorbed atoms. The reflection coefficient, evaluated to first order in the vapor dipole polarization, leads to a formal expression of the reflectivity modulation, valid for arbitrary atom-surface interaction potentials. One first discusses the reflection signal in absence of wall interactions, for arbitrary modulation frequencies. At large frequencies, it allows one to monitor both vapor absorption and dispersion. Second, the formal theory is applied to the case of a Van der Waals-London surface attraction exerted on the atomic vapor. Both normal and oblique beam incidences are considered. One shows how the vapor dispersion signal is red-shifted and strongly distorted by the appearance of vapor-surface long-range interactions, and how it can be used to monitor these interactions. At non-normal incidences, the lineshapes get Doppler-broadened.

Selective reflection spectroscopy at an interface with a low-density resonant vapor, especially when combined with a frequency modulation technique, is a high-resolution Doppler-free tool for probing atoms interacting with a surface. We analyze different types of relevant surface interaction, emphasizing the spectral consequences of a van der Waals surface attraction associated to a

z^{-3}

potential dependence (

z

: distance to the wall). We present detailed results of two series of experiments at a Cs vapor/dielectric window interface on the 6S

_{1/2}

-6P

_{3/2}

(

\lambda = 852

nm) resonance line and on the 6S

_{1/2}

-7P second resonance line (

\lambda = 455

nm and 459 nm). Lineshape analysis at various pressures consistently shows that a van der Waals-type surface attraction has to be considered to interpret strong lineshape distortions and resonance shift. The attractive strengths are found to be equal respectively to

\approx 2

kHz

\mu

m

^3

and

\approx 20

kHz

\mu

m

^3

, independently of the considered hyperfine component, within the experimental accuracy. It yields also typical parameters of pressure broadening and shift, which are shown to originate in collisional processes, at densities where the medium is opaque. Theoretical expectations for the VW strength are discussed on the basis of the results of atomic theory. The predicted values are smaller, by a typical factor of 2, than those deduced from the experiments. The validity of the theory, when applied to a dielectric interface, is discussed and seems questionable when the frequency of virtual atomic transitions involved in the van der Waals attraction potential lies in the dielectric window absorption range.

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.

The Casimir-Polder potential for interaction between an excited atom and a ground-state one in the retarded case is obtained with the help of perturbation technique. The potential drops as ${R}^{\ensuremath{-}2}$ with the distance between the atoms [E. A. Power and T. Thirunamachandran, Phys. Rev. A 47, 2539 (1993)]. It results in divergent integrals for interaction between an excited atom and a dilute gas medium. We investigate interaction between two atoms embedded in a dielectric medium with the help of a method that enables us to make calculations beyond the perturbation technique. We take into account absorption of photons in the medium. This approach solves the problem of divergence. We consider interaction between an excited atom and a planar dielectric gas medium of ground-state atoms. We show that the retarded interaction between an excited atom and a gas of ground-state atoms is not oscillating but follows a simple power law. We show that to obtain a conventional nonretarded expression for the van der Waals force between an excited atom and a dilute gas, the distance between the atom and the interface should be much smaller than the free mean path of a photon in the medium. Interaction between an excited atom and a hemisphere of ground-state atoms is considered.

van der Waals interactions, as a result of the exchange of photons between particles, can be altered by modifying the environment through which these photons propagate. As a consequence, phenomena such as the Rydberg blockade mechanism between highly excited atoms or excitons can be controlled by adding reflecting surfaces. We provide the quantum electrodynamic framework for the van der Waals interaction in the nonretarded limit that is relevant for long-wavelength transitions, such as those between Rydberg systems, and show its intimate connection with common static dipole-dipole interactions, thereby providing a generalization to include macroscopic bodies.