Spontaneous emission competes with stimulated emission in many interactions of light with matter. In the usual analyses which describe the interaction of an atom with a coherent optical field, the spontaneous emission characteristics, e.g., probability and spectral distribution, are not determined. The spontaneous emission from an atom which interacts with a coherent light wave is considered. The competition between coherent photons and spontaneous photons is treated in detail for a system consisting of a stationary atom, an open cavity and spatial fields. In the model chosen, a multilevel atom which spontaneously decays by interacting with spatial fields has two nondegenerate states coupled by an interaction with a single mode of the cavity. The Laplace-transformed Schrodinger equation is solved for specified initial conditions of the system. It is found that the interaction with the coherent field modifies the spectral distribution of spontaneous radiation from the atom. For spontaneous transitions involving an atomic state which interacts with the coherent field, the spectral distributions can no longer be described by Lorentzian functions. The new distributions exhibit a broadening and splitting for strong interactions between the atom and the coherent field. It is shown that the qualitative features of these distributions can be predicted from the energy-level diagram of the atom-cavity system. The net probability of the system gaining a coherent or cavity photon is calculated by integrating over the emitted spontaneous frequencies. The equivalence of this approach to the method of computing probabilities by integrating over time is demonstrated by using Parseval's theorem.
By analogy with the Wigner-Weisskopf model, spontaneous emission of an atom is considered in a spatially periodic field of the resonance counter-propagating waves. The Bloch state obtained by the interaction of the initially excited (unexcited) atom with a field of the counter-propagating waves plays the role of the excited (ground) state of the free atom. The spontaneous emission probability averaged over polarizations is shown to become anisotropic, with the symmetry axis directed along the wave propagation path. The anisotropy is caused by the spatially periodic distribution of the wave function of the translational motion of an atom in the external field. The degree of anisotropy depends on the position of Bloch energy levels in the allowed bands of the energy spectrum.