Influence of virtual transitions on spontaneous emission of an excited atom in vacuum

Time evolution of an excited two-level atom in free space is theoretically discussed in the Schrödinger picture by explicitly taking into account the virtual transitions that are made possible by the counter-rotating terms in the Hamiltonian of the atom-field system. It is found that, because of these virtual transitions, the atom's relaxation from its excited state is expedited as compared with the case of rotating-wave approximation. It is also found that due to the introduction of a cut-off frequency to the vacuum modes to make the nonrelativistic Hamiltonian valid, the probability to find the atom in its ground state with one photon emitted is no longer an exponential function of time even when the counter-rotating terms are absent.