Dynamics of multiphoton excitation and quantum diffusion in Rydberg atoms

We present a detailed two-dimensional (2D) quantal study of the dynamical evolution of microwave-driven Rydberg H atoms. We examine the range of validity of the conventional one-dimensional (1D) models and explore the frequency- and intensity-dependent excitation and ionization mechanisms. The main findings of this paper can be summarized as follows: (i) The excitation spectra of Rydberg H atoms are strongly frequency dependent and can be roughly grouped into three characteristically different regions, each with a different excitation mechanism. In this paper, we emphasize the study of the two major excitation mechanisms: quantum diffusion and multiphoton resonant excitation. The region dominated by quantum diffusion lies in the frequency range ${\ensuremath{\omega}}_{c}$${\ensuremath{\omega}}_{0}$${\ensuremath{\omega}}_{d}$, where ${\ensuremath{\omega}}_{0}$ is the rescaled field frequency (${\ensuremath{\omega}}_{0}$=\ensuremath{\omega}${n}_{0}^{3}$; ${n}_{0}$ is the principal quantum number of the initial state); ${\ensuremath{\omega}}_{c}$, the classical chaotic threshold; and ${\ensuremath{\omega}}_{d}$, the quantum delocalization border.In this region, quasienergy levels are strongly perturbed and mixed and excitation is efficient, leading to the so-called underthreshold photoelectric ionization phenomenon. On the other hand, we found a series of frequency regions (in ${\ensuremath{\omega}}_{0}$g${\ensuremath{\omega}}_{d}$) where the ionization is mainly due to multiphoton resonant excitation through the more isolated quasienergy avoided crossing points. (ii) The excitation pathways (1D versus 2D) are strongly intensity dependent. For microwave (rescaled) field strength ${\ensuremath{\varepsilon}}_{0}$ (\ensuremath{\equiv}\ensuremath{\varepsilon}${n}_{0}^{4}$) in the range ${\ensuremath{\varepsilon}}_{c}$${\ensuremath{\varepsilon}}_{0}$${\ensuremath{\varepsilon}}_{q}$ (where ${\ensuremath{\varepsilon}}_{c}$ is the onset of classical chaos and ${\ensuremath{\varepsilon}}_{q}$ the quantum delocalization threshold), large discrepancies exist between 1D and 2D results. It is found that the 1D model seriously underestimates the ionization probabilities and, more importantly, the dominant channels for Rydberg atom excitation and ionization proceed through ${n}_{2}$g0 ladders rather than the ${n}_{2}$=0 ladder, as often assumed in the 1D model. As field strength increases above ${\ensuremath{\varepsilon}}_{q}$, however, the 1D model improves significantly. (iii) The quantum localization phenomenon is observed in the classically chaotic region (${\ensuremath{\omega}}_{c}$${\ensuremath{\omega}}_{0}$${\ensuremath{\omega}}_{d}$) when the field strength ${\ensuremath{\varepsilon}}_{0}$ is less than ${\ensuremath{\varepsilon}}_{q}$. However, quantum delocalization can appear when ${\ensuremath{\varepsilon}}_{0}$g${\ensuremath{\varepsilon}}_{q}$. (iv) The stability of quantum diffusive motion is analyzed in terms of the quantal phase-space diagram and the autocorrelation function. The results lend support to the view that quantum mechanics can impose limitations on classical chaotic motion. (v) The way of turning on the field (sin\ensuremath{\omega}t or cos\ensuremath{\omega}t) does not affect significantly the dynamical evolution of the system. (vi)Finally, a computationally powerful new technique, invoking the use of artificial intelligence algorithms as well as the generalized Van Vleck perturbation theory for effectively reducing the dimensionality of the Floquet matrix, is introduced to facilitate the study of multiphoton resonant excitation of Rydberg atoms.