Chaotic enhancement of microwave excitation for chaotic Rydberg atoms

In 1982 Shushkov and Flambaum discussed the effect of weak interaction enhancement due to a complex structure of ergodic eigenfunctions in nuclei. The basic idea of this effect is that in complex systems an eigenfunction, represented in some basis, has a large number $M$ of randomly fluctuating components so that their typical value is $1/\sqrt{M}$. Due to this, the matrix elements for interparticle interaction are $V_{int} \sim 1/\sqrt{M}$ while the distance between mixed levels is $\Delta E\sim 1/M$. As a result, according to the perturbation theory, the admixture factor $\eta$ is strongly enhanced: $\eta\sim V_{int}/\Delta E\sim \sqrt{M}$ as compared to the case in which eigenfunctions have only few components $(M \sim 1)$. This effect was investigated and well confirmed in experiments with weak interaction enhancement for scattering of polarized neutrons on nuclei. Recently a similar effect of interparticle interaction enhancement was discussed for two interacting particles in disordered solid state systems [69]. Here, a short range interaction produces a strong enhancement of the localization length leading to a qualitative change of physical properties (see section 3.7). This shows that the effect is quite general and can take place in different systems.

In [82,91,93,98] such an enhancement in atomic physics is studied for atoms interacting with electromagnetic fields. Such process becomes especially interesting for highly excited atoms (hydrogen or Rydberg atoms) in microwave fields where absorption of many photons is necessary in order to ionize electrons. Until now this problem was studied only in the case in which the electron dynamics, in absence of microwave field, is integrable (see section 3.4). A quite different situation, investigated in [82,91,93,98], appears when the electron's motion in the atom is already chaotic in the absence of microwave field. An interesting example of such situation is an hydrogen atom in a strong static magnetic field or alkali atoms in a static electric field. The properties of such atoms have been extensively studied in the last decade and it has been shown that the eigenfunctions are chaotic, and that several properties of the system can be described by Random Matrix Theory. Due to that the interaction of such an atom with a microwave field is strongly enhanced so that the localization length becomes much larger, approximately by factor $n_0$, than the corresponding one in the absence of magnetic fields (or static electric filed). As a result, the quantum delocalization border, which determines the ionization threshold, drops by factor $\sqrt{n_0}$. In addition, due to internal chaos the microwave ionization can be studied in a regime when the microwave frequency is much smaller than the Kepler frequency ( $\omega \ll 1/n_0^3$). In such a case up to 1000 photons are required to ionize an atom at $n_0=60, \omega n_0^3 = 0.03$ and only the theory of dynamical localization can describe ionization process in this situation. The drop in the quantum delocalization border for alkali atoms in a static field is in a qualitative agreement with the experimental results of Gallagher (Univ. of Virginia, USA) and Beterov (Inst. of Semiconductor Physics, Novosibirsk). Also the group of Kleppner (MIT, USA) works in a very similar regime. Therefore, the above theory can be tested experimentally. The results obtained in [91,93,98] form the basis of thesis of G.Benenti (hold at Milano Univ. in February 1998).