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arXiv:quant-ph/0411033 · Journal of Modern Optics

Vacuum field correlations and three-body Casimir–Polder potential with one excited atom

Roberto Passante, Franco Persico, Lucia Rizzuto

Published Sep 20, 2005• 16 citations
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Abstract

The three-body Casimir–Polder potential between one excited and two ground-state atoms is evaluated. A physical model based on the dressed field correlations of vacuum fluctuations is used, generalizing a model previously introduced for three ground-state atoms. Although the three-body potential with one excited atom is already known in the literature, our model gives new insights on the nature of non-additive Casimir–Polder forces with one or more excited atoms.

DOI
10.1080/09500340500106733

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Optics and Spectroscopy•Sep 1, 2007•1 citation
The three-body Casimir–Polder potential between one excited and two ground-state atoms is evaluated. A physical model based on the dressed field correlations of vacuum fluctuations is used, generalizing a model previously introduced for three ground-state atoms. Although the three-body potential with one excited atom is already known in the literature, our model gives new insights on the nature of non-additive Casimir–Polder forces with one or more excited atoms.
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.
The Casimir-Polder force on a single atom in the presence of microscopic magneto-electric bodies is studied within the framework of macroscopic quantum electrodynamics. In the first part, time-independent perturbation theory is used show that the static Casimir-Polder force on a ground-state atom in the presence of an arbitrary arrangement of bodies can be expressed in terms of the atom's polarisability and the scattering part of the Green tensor characterising the bodies. This result is used to verify the origin of the force and to study various bodies of simple shapes. In the second part, a genuinely dynamical approach is developed by starting from the operator Lorentz force. It is found that the dynamics of the force on initially excited atoms is governed by irreversible spontaneous decay in the case of weak atom-field coupling, while Rabi oscillations may arise for strong atom-field coupling.
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.