Two Frequency Microwave Ionization of Hydrogen Rydberg Atoms: Experiment and Theory

Hydrogen Rydberg atoms with principal quantum number n_0 = 57 and n_0 = 64 are subjected to bichromatic microwave fields and their excitation above a fixed cutoff quantum number n_sp{c}{q} = 87 (= "ionization") is recorded. The fast atomic beam apparatus, the double resonance method used to create the Rydberg atoms and the detection method is described. The frequency Omega_2 and field F_2 provided by the second microwave source were kept fixed, while the "ionization" probability as a function of either the frequency Omega _1 or the field F_1 provided by the first source was determined. I present 10%, 20% and 30% "ionization" thresholds for Omega _1 = 28GHz, Omega_2 = 34.998GHz, for n_0 = 57 and 64, and Omega_1 = 29GHz, Omega_2 = 34.998GHz and n _0 = 57, and the "ionization" probability for n_0 = 57, Omega _2 = 34.998GHz and fixed fields as a function of Omega_1 between 24 and 31 GHz. I present a general theory to analytically derive iterative Poincare mapping equations using Melnikov theory, and apply it to the one dimensional hydrogen atom subjected to monochromatic and bichromatic fields. The bifurcation sequences of the principal fixed points of the resulting mappings are studied. 10% "ionization" thresholds are modelled for monochromatic and bichromatic fields and compared to experimentally and numerically determined ones. The agreement is good. I conclude that the mappings derived provide a good description for the global classical dynamics. The "ionization" probability as a function of Omega_1, for fixed fields and frequency can be understood by studying the overlapping resonances of the electron motion with the two driving fields.