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Optics and Spectroscopy

Casimir-Polder interaction of excited media

Yu. B. Sherkunov

Published Sep 1, 2007• 1 citation
Publisher

Abstract

The potential of long-range interaction between two dissimilar atoms, one of which is excited, drops as 1/R 2 with the distance for the Casimir-Polder limit of large distances in comparison with the wave-length of atom transitions (E.A. Power and T. Thirunamachandran, Phys. Rev. A 51, 3660 (1995)). It is shown that such a dependence, obtained with the help of perturbation technique, results in a divergence for the interaction potential between an excited atom and a medium of dilute gas. We develop a nonperturbative method based upon quantum Green’s functions (Yu. Sherkunov, Phys. Rev. A 72, 052703 (2005)) to calculate the interaction potential for an excited atom and a ground-state atom embedded in a dielectric medium, taking into account the absorption of photons in the dielectric medium. The exponential suppression of the interaction between the atoms is demonstrated. The force acting on an excited atom near the interface of dilute gas medium is calculated. The result is no more divergent. The force between gas media in Casimir-Polder regime is calculated as well.

DOI
10.1134/s0030400x0709007x

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The potential of long-range interaction between two dissimilar atoms, one of which is excited, drops as 1/R 2 with the distance for the Casimir-Polder limit of large distances in comparison with the wave-length of atom transitions (E.A. Power and T. Thirunamachandran, Phys. Rev. A 51, 3660 (1995)). It is shown that such a dependence, obtained with the help of perturbation technique, results in a divergence for the interaction potential between an excited atom and a medium of dilute gas. We develop a nonperturbative method based upon quantum Green’s functions (Yu. Sherkunov, Phys. Rev. A 72, 052703 (2005)) to calculate the interaction potential for an excited atom and a ground-state atom embedded in a dielectric medium, taking into account the absorption of photons in the dielectric medium. The exponential suppression of the interaction between the atoms is demonstrated. The force acting on an excited atom near the interface of dilute gas medium is calculated. The result is no more divergent. The force between gas media in Casimir-Polder regime is calculated as well.
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.
Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.
We present the first direct measurements of Casimir-Polder forces between solid surfaces and atomic gases in the transition regime between the electrostatic short-distance and the retarded long-distance limit. The experimental method is based on ultracold ground-state Rb atoms that are reflected from evanescent wave barriers at the surface of a dielectric glass prism. Our novel approach does not require assumptions about the potential shape. The experimental data are compared to the theoretical predictions valid in the different regimes. They agree best with a full QED calculation.
We consider the Casimir-Polder interaction between two atoms, one in the ground state and the other in its excited state. The interaction is time dependent for this system, because of the dynamical self-dressing and the spontaneous decay of the excited atom. We calculate the dynamical Casimir-Polder potential between the two atoms using an effective Hamiltonian approach. The results obtained and their physical meaning are discussed and compared with previous results based on a time-independent approach, which uses a nonnormalizable dressed state for the excited atom.
A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the K7,K9,{K}_{7}, {K}_{9},K7​,K9​, and K11{K}_{11}K11​ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.
We present a formula for the body-assisted van der Waals interaction potential between two atoms, one or both being prepared in an excited energy eigenstate. The presence of an arbitrary arrangement for a material environment is taken into account via the Green function. The resulting formula supports one of two conflicting findings recorded. The consistency of our formula is investigated by applying it for the case of two atoms in free space and comparing the resulting expression with the one found from the limiting Casimir-Polder potential between an excited atom and a small dielectric sphere.