Spontaneous emission from Bloch states of a two-level atom in a periodic field of the biparabolic shape

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.