Figure 1

Classical phase space of driven hydrogen, generated by the Hamiltonian (1), for ${\omega }_0=1$ and $F_0=0.041$, and spanned by the action-angle variables of the unperturbed atom, at $\omega t=0$. Nondispersive quantum wave packets are localized at the center of the principal elliptic island (concentric structure in the middle of the plot) and move along the resonantly driven Kepler orbit sketched in the inset (the arrow shows the direction of the driving force at the outer turning point), in phase with the driving field. For the chosen parameters, a prominent, higher order nonlinear $5:1$ resonance strongly affects the tunneling coupling of the principal island’s eigenstates to the surrounding chaotic sea. This resonance is expressed by the fivefold structure right within the outermost torus which confines the principal island.Reuse & Permissions

Figure 2

Comparison of the exact quantum decay rates of the wave packet states (symbols) with the semiclassical prediction for their mean value ${\overline{\Gamma }}_{\mathrm{wp}}$ [solid line, given by Eqs. (8, 9)] and the standard deviation [dashed lines, see Eq. (10)]. The rates are plotted as a function of the principal quantum number $n_0$ of the Rydberg orbit along which the wave packet is launched. The quantum results were obtained for the same field parameters as Fig. 1. Open circles and diamonds distinguish different basis sizes form the numerical diagonalization. For $n_0\le 150$, the basis was chosen such as to resolve all bound states with an ionization potential larger and equal to the one-photon energy $\omega$. For $n_0>150$, only bound states below $2n_0$ were numerically resolved.Reuse & Permissions