Phase space structures and ionization dynamics of hydrogen atom in elliptically polarized microwaves

The multiphoton ionization of hydrogen atoms in a strong elliptically polarized microwave field exhibits complex features that are not observed for ionization in circular and linear polarized fields. Experimental data reveal high sensitivity of ionization dynamics to the small changes of the field polarization. The multidimensional nature of the problem makes widely used diagnostics of dynamics, such as Poincar\'{e} surfaces of section, impractical. We analyze the phase space dynamics using finite time stability analysis rendered by the fast Lyapunov Indicators technique. The concept of zero--velocity surface is used to initialize the calculations and visualize the dynamics. Our analysis provides stability maps calculated for the initial energy at the maximum and below the saddle of the zero-velocity surface. We estimate qualitatively the dependence of ionization thresholds on the parameters of the applied field, such as polarization and scaled amplitude.