Power-Law Decay in the Ionization of H Rydberg Atoms

We consider a classical study of the ionization of hydrogen Rydberg atoms by circularly polarized microwaves (CPM) in the frequency regime, where typically diffusive manner of the ionization is observed 1,2]. The CPM field pulse shape and the atomic initial state influence on the survival probability, S, are investigated in the two-dimensional (2D) Hamiltonian model 3]. This is motivated by the fact that it is possible experimentally to prepare circular states, e.g. by the crossed fields method 4]. For such states and for states with not too large eccentricity the simplified 2D model should be a good approximation of the three-dimensional life for high enough states. Ionization of highly excited hydrogen atoms by linearly polarized microwaves (LPM) has been studied in the last twenty years (e.g. see 5,6]). The very first experimental results 7] were explained theoretically 8] using Monte-Carlo classical simulations. Classically, the ionization occurs due to the break up of the Kolmogorov-Arnold-Moser (KAM) tori when the microwave amplitude is large enough, hence the ionization threshold can be associated with the onset of classical chaos. Therefore, in the presence of an external periodic force we can observe the escape process of an electron to the continuum from a certain phase-space region defined by the initial conditions. For Hamiltonian systems, the escape may be slowed down significantly due to the presence of the remnants of KAM tori (Cantori) and one can observe the power-law (algebraic) decay S ~ t-z from the region containing KAM stability islands rather than exponential decay S ~ exp(-t), in the limit of large time t.