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Physical Review A

Dispersion interaction between two atoms out of thermal equilibrium with external electromagnetic fields

Yu. B. Sherkunov

Published Mar 5, 2009• 37 citations
Publisher

Abstract

The van der Waals--Casimir-Polder potential is calculated for two atoms out of equilibrium with external thermal electromagnetic field. The effects of absorption and spontaneous or stimulated emission are shown to strongly modify the potential. We demonstrate that the potential decays like ${R}^{\ensuremath{-}2}$ at large distances (much slower than at the equilibrium) can be attractive, repulsive, and resonant depending on the initial states of the atoms and electromagnetic field.

DOI
10.1103/physreva.79.032101

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The van der Waals--Casimir-Polder potential is calculated for two atoms out of equilibrium with external thermal electromagnetic field. The effects of absorption and spontaneous or stimulated emission are shown to strongly modify the potential. We demonstrate that the potential decays like R\ensuremath−2{R}^{\ensuremath{-}2}R\ensuremath−2 at large distances (much slower than at the equilibrium) can be attractive, repulsive, and resonant depending on the initial states of the atoms and electromagnetic field.
Abstract We generalize the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji (the DDC formalism) in the fourth order for two atoms in interaction with scalar fields in vacuum to a thermal bath at finite temperature T, and then calculate the interatomic interaction energy of two ground-state atoms separately in terms of the contributions of thermal fluctuations and the radiation reaction of the atoms and analyze in detail the thermal corrections to the van der Waals and Casimir–Polder interactions. We discover a particular region, i.e. λ 3 β 4 ≪ L ≪ λ with L, β and λ denoting the interatomic separation, the wavelength of thermal photons and the transition wavelength of the atoms respectively, where the thermal corrections remarkably render the van der Waals force, which is usually attractive, repulsive, leading to an interesting crossover phenomenon of the interatomic interaction from attractive to repulsive as the temperature increases. We also find that the thermal corrections cause significant changes to the Casimir–Polder force when the temperature is sufficiently high, resulting in an attractive force proportional to TL −3 in the λ ≪ β ≪ L region, and a force that can be either attractive or repulsive and even vanishing in the β ≪ λ ≪ L region depending on the interatomic separation.
The Casimir-Polder (C-P) interaction between an atom and a surface, described as early as 1948, but observed much later on, is now a topic of broad interest, as connected to fundamental problems of quantum fluctuations, with the atomic energy levels renormalized by the wall-dependent vacuum fluctuations. Dependence of the C-P interaction with the equilibrium temperature is predicted, but had not been observed until now. However, more pronounced effects were predicted in an out-of-equilibrium situation, and were remarkably observed on a Rb BEC, at 6-10 μm from the wall, with the vacuum temperature (~ 300K) strongly differing from the surface temperature (~ 1000 K).
We consider the van der Waals force involving excited atoms in general environments, constituted by magnetodielectric bodies. We develop a dynamical approach studying the dynamics of the atoms and the field, mutually coupled. When only one atom is excited, our dynamical theory suggests that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating. We show how this latter force can be related to the known oscillating Casimir-Polder force on an excited atom near a (ground-state) body. Our force also reveals a population-induced dynamics: for times much larger that the atomic lifetime the atoms will decay to their ground states leading to the van der Waals interaction between ground-state atoms.
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.
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.