A time-dependent theory of resonant multiphoton ionization of atoms by short pulses: I. weak-field results for the two-photon ionization of caesium

In this and the subsequent paper, we develop a time-dependent theory of resonant multiphoton ionization of an atom by a laser pulse, whose envelope is taken to be a hyperbolic secant in time. The choice of this shape enables us to solve the time-dependent Schrodinger equation analytically for an n-state system, of which up to (n - 1) levels can be in resonance with the ground state for part of the time. Using the expressions deduced for excited-state amplitudes, a closed-form representation for continuum amplitudes is derived, from which the photoelectron energy spectrum is calculated. Stark shifts of the bound states explicitly retained in the eigenfunction expansion due to coupling to omitted levels are included perturbatively. The theory is applied in this paper to the two-photon ionization of caesium by weak fields. A new kind of structure is predicted. The results are compared to the spectrum generated by a weak rectangular pulse. Strong fields are analysed in the following paper. © 1995 IOP Publishing Ltd.