Resonant three-photon ionization of atomic hydrogen in a finite-bandwidth laser field and a static electric field

We derive a set of density matrix equations describing laser photo-excitation and ionization of atomic hydrogen in the presence of an external electric field. The equations are relevant as a description of multiphoton ionization of hydrogen (or deuterium) atoms in laser-produced transient plasmas. The laser wavelength is 243 nm, so that the photoionization is resonant with the 2 s 1/2 level. The electric field causes Stark mixing of the 2 s 1/2 level with the 2 p 1/2 and 2 p 3/2 levels. Because the electric field is taken in the same direction as the linear polarization of the laser, only states with equal m j are coupled, and the atom can be described with a four-level density matrix. The laser bandwidth is taken into account by using the stochastic model of a chaotic laser field introduced by Zoller [1]. We present a few calculations of the probabilities for ionization and excitation of a single hydrogen atom as a function of laser intensity and wavelength.