Extension of Floquet theory to include continuum as well as bound atomic states yields a practical technique for computation of multiphoton ionization rates in the region where rms field strengths approach the strength of the internal atomic fields.
The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.
High-frequency Floquet theory (HFFT) is again applied to photoionization in a linearly polarized field of the hydrogen atom in its ground state. The new feature is the systematic use of a two-pole approximation to represent both the dressed potential (with two positive charges) and the coupling responsible for one-photon ionization (with two charges of opposite sign). Within such a scheme, both the initial bound and the final continuum states can be very accurately determined. The final continuum state is obtained by deriving, from Floquet theory, an equation involving a source term. The model accounts reasonably well, even at rather low frequencies, for the stabilization of the atom in an intense field and supports the claim that HFFT represents the photoionization rate with a golden rule expression involving dressed states.