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arXiv:quant-ph/0611136 · Journal of Physics B Atomic Molecular and Optical Physics

Nonlocal field correlations and dynamical Casimir–Polder forces between one excited- and two ground-state atoms

Roberto Passante, Franco Persico, Lucia Rizzuto

Published May 1, 2007• 5 citations
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Abstract

The problem of nonlocality in the dynamical three-body Casimir–Polder interaction between an initially excited and two ground-state atoms is considered. It is shown that the nonlocal spatial correlations of the field emitted by the excited atom during the initial part of its spontaneous decay may become manifest in the three-body interaction. The observability of this new phenomenon is discussed.

DOI
10.1088/0953-4075/40/10/020

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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.
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.
We consider the dynamical atom-surface Casimir-Polder force in the nonequilibrium configuration of an atom near a perfectly conducting wall, initially prepared in an excited state with the field in its vacuum state. We evaluate the time-dependent Casimir-Polder force on the atom and find that it shows an oscillatory behavior from attractive to repulsive both in time and in space. We also investigate the asymptotic behavior in time of the dynamical force and of related local field quantities, showing that the static value of the force, as obtained by a time-independent approach, is recovered for times much longer than the time scale of the atomic self-dressing but shorter than the atomic decay time. We then discuss the evolution of global quantities such as atomic and field energies and their asymptotic behavior. We also compare our results for the dynamical force on the excited atom with analogous results recently obtained for an initially bare ground-state atom. We show that new relevant features are obtained in the case of an initially excited atom, for example, much larger values of the dynamical force with respect to the static one, allowing for an easier way to single out and observe the dynamical Casimir-Polder effect.
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.