Virtual photons and causality in the dynamics of a pair of two-level atoms

Abstract

The dynamics of an initially bare pair of two-level atoms at distance R is investigated. The pair is coupled to the vacuum radiation field in the multipolar scheme and in the dipole approximation.The Heisenberg equations of motion for various atomic operators are obtained neglecting terms O(e') and for t smaller than the spontaneous relaxation time. A rigorous proof of causality in the atom-atom interaction is given. Interatomic correlations, however, are shown to develop for

Causality and localization operators

“…For atomic sources, it has been shown that, some quantities as correlations of excitation between two atoms or of the electromagnetic field are non zero at two spacetime points with spacelike separation [3,4,5]. Instead local quantities, as the excitation of a second atom [6,7], appear to depend causally on the source. Recently causal behavior of local e.m. field operator has been obtained while in the correlation functions is present a non local source independent part, that may be attributed to the zero point field fluctuations [8,9].…”

Nonlocal quantum-field correlations and detection processes in quantum-field theory

“…We have then shown that the UDD detection probability causally responds to the field generated by the source and is not characterized by nonlocal effects,apart from the source-independent vacuum contribution related to the UDD sensitiveness to zero point fluctuations. Anyway this term must not be considered to describe the appearance of non-locality due to the variations of the source and can in principle be taken into account to interpret the results [21,22,32]. On the other hand the response function of the GD model gives source dependent terms in the detection probability rate that correspond to an instantaneous spreading of source effects over the whole space.…”

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

“…In particular, Hegerfeldt reopened the question of nonlocality and causality in the QED context on a quite general basis [14][15][16][17][18][19][20]. Specific calculations have shown that the dynamics of local atomic or field operators is causal, but that the correlation of atomic excitations of two spatially separated atoms exhibits a nonlocal behaviour, being different from zero even if the two atomic sites have a spacelike separation [17,21]. Non-local terms appear also in the spatial correlations of the energy density during the dynamical dressing/undressing of a static source interacting with the relativistic scalar field [22].…”