Abstract
We describe an original approach for the accurate description of alkali-metal Rydberg states exposed to intense electromagnetic fields. Our method combines Floquet and R-matrix theory, complex dilation of the Hamiltonian, a Sturmian basis set to describe the atomic degrees of freedom (including the continuum), and, last but not least, an efficient parallel implementation of the Lanczos algorithm on some of the most powerful supercomputers currently available. Without adjustable parameters, this ab initio approach opens a route to the comprehensive understanding of an abundance of laboratory data on the microwave ionization of one-electron Rydberg states. The versatility of our theoretical/numerical machinery is illustrated in the specific case of microwave driven lithium, faithfully mimicking every single step of the laboratory experiment.