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Journal of Physics B Atomic Molecular and Optical Physics

Causality, non-locality and three-body Casimir–Polder energy between three ground-state atoms

Roberto Passante, Franco Persico, Lucia Rizzuto

Published Jul 24, 2006• 15 citations
Publisher

Abstract

The problem of relativistic causality in the time-dependent three-body Casimir–Polder interaction energy between three atoms, initially in their bare ground-state, is discussed. It is shown that the non-locality of the spatial correlations of the electromagnetic field emitted by the atoms during their dynamical self-dressing may become manifest in the dynamical three-body Casimir–Polder interaction energy between the three atoms.

DOI
10.1088/0953-4075/39/15/s15

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The problem of relativistic causality in the time-dependent three-body Casimir–Polder interaction energy between three atoms, initially in their bare ground-state, is discussed. It is shown that the non-locality of the spatial correlations of the electromagnetic field emitted by the atoms during their dynamical self-dressing may become manifest in the dynamical three-body Casimir–Polder interaction energy between the three 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 time-dependent Casimir-Polder force arising during the time evolution of an initially bare two-level atom, interacting with the radiation field and placed near a perfectly conducting wall, is considered. Initially the electromagnetic field is supposed to be in the vacuum state and the atom in its ground state. The analytical expression of the force as a function of time and atom-wall distance is evaluated from the time-dependent atom-field interaction energy. Physical features and limits of validity of the results are discussed in detail.
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.