VIRTUAL PHOTONS, CAUSALITY AND ATOMIC DYNAMICS IN SPONTANEOUS EMISSION

The time-dependent electric energy density surrounding a two-level atom fixed at r = 0 is studied, the atom being taken in its excited state at t = 0 and the field being initially in the vacuum state. The atom-field coupling includes both rotating and counter-rotating terms. The energy density of the spontaneously emitted field in the rotating wave approximation is shown to behave noncausally, while in the presence of the complete coupling it is shown to vanish outside a sphere of radius r = ct centred on the atom. The deviations of atomic dynamics from the exponential Wigner–Weisskopf behaviour during spontaneous decay are shown to be deeply influenced by the counter-rotating terms. It is concluded that the virtual photons induced by the counter-rotating terms in the atom-field coupling are essential in order to ensure causality and cannot be neglected in any accurate treatment of spontaneous emission. © 1990 Taylor & Francis Ltd.