The studies of nonlinear mechanics have shown that the so called regime of dynamic chaos should be considered as typical rather than exceptional situation [1]. An important example of a physical system with distinct properties of trajectory instability is a highly excited hydrogen-like atom in a monochromatic electric microwave field of frequency and intensity F [2]. The studies [2] of time evolution of Rydberg electron (RE) moving in a Coulomb potential in presence of a microwave field have demonstrated that onset of the global dynamic chaos in semi-classical trajectories exhibits a threshold, which depends on the intensityF. For the given value of n_{0}, this threshold field F_{c} can be found from the relation
; (1)
If F > F_{c}, the evolution of the RE acquires the character of the so-called K -systems, i.e., strongly locally unstable Hamiltonian system with intense trajectory mixing in phase space and with rapid uncoupling of correlations between angular dynamic variables [1]. This means that for intensities F above the critical value F_{c} the motion of the RE in the energy space is unstable (i.e., the separate stochastic layers combine to form the stochastic “sea”) [2]. Or else, for a fixed field intensity F = F_{c} there exists a well-defined boundary n_{0} that separates the region n > n_{0} of chaotic motion from the region n < n_{0} of regular motion.
In hydrogen-like alkali atoms the field intensity F relates to the boundary value via dipole matrix elements
between the Rydberg states [3]:
(2)
(3)
The parameter plays the role of a diffusion coefficient describing stochastic migration of the RE through energy levels in the region [3]. Due to such migration, the so called RE diffusion ionization in the microwave field can take place [2].
A semi-classical approach to the treatment of radiative processes was developed in [4, 5]. A simple reason for suppression of radiative processes (the Cooper minimum in atomic photoionization cross sections) was formulated in terms of classical orbits of RE. It was quantitatively shown that the values of become close to zero provided the difference between quantum defects has a half-integer value. The latter corresponds to the situation when a Rydberg l-state is situated exactly in the middle between two l’-states. This can be realized in an experiment with Na np-states, employing the Stark shift of levels by an external electrical field. This enables blocking the dynamic chaos regime when the l-state is exactly between two l'-states, since formally . In that case the region of global instabilities vanishes and the motion of RE is regular for all bound levels up to the very ionization continuum. Tuning the Stark shift away from the two-photon resonance allows one to vary the diffusion coefficient D_{ε} and, hence, to tune the threshold between the zones of chaotic and regular dynamics.