Ionization in a quantized electromagnetic field

An analytical expression for a matrix element of the transition from a bound state of an electron in an atom to continuum states is obtained by solving the problem of interaction of the electron with a quantized electromagnetic field. This expression is used to derive formulas for the photoelectron spectrum and the rate of ionization of the simplest model atomic system upon absorption of an arbitrary number of photons. The expressions derived are analyzed and compared with the corresponding relationships obtained via other approaches. It is demonstrated that there are differences as compared to the case of the classical field. In particular, the photoelectron spectrum exhibits dips due to the destructive interference of the transition amplitudes in the quantized electromagnetic field.