Atoms in ultra-intense laser fields

In this review, the authors examine theoretical models of atoms dressed by intense fields. They review the breakdown of lowest-order perturbation theory and those 'essential states' methods adopted to include Rabi frequencies, Stark shifts, induced widths and continuum dressing. Methods more suitable for super-strong fields are described, such as Floquet and Volkov methods and the direct numerical integration of the Schrodinger equation. Such methods are used to provide completely non-perturbative strong field descriptions of atomic dynamics. The authors conclude with a brief examination of the relativistic effects expected to be important when high intensity ultrashort pulse lasers are employed in strong field physics.