Multifrequency resonance transitions in the ionization of hydrogen by a single-frequency microwave field

The ionization of hydrogen in strong microwave fields is a fundamental prob lem in atomic physics and nonlinear dynamics. Transitions between dressed s tates take place simultaneously at several resonance frequencies when a str ong static held is added parallel to a linearly polarized microwave field o f comparable strength. We present a quantum-mechanical treatment of this in tricate problem which reproduces its distinctive features very well. A clea r picture of the roles of the fields emerges through an innovative mapping of the perturbation Hamiltonian. This mapping also has the computational ad vantage of collapsing the infinite sums over off-shell matrix elements into simpler on-shell expressions.