Fractal stabilization of Wannier-Stark resonances

The quasienergy spectrum of a Bloch electron affected by dc-ac fields is kn own to have a fractal structure as a function of the so-called electric mat ching ratio, which is the ratio of the ac field frequency and the Bloch fre quency. This paper studies a manifestation of the fractal nature of the spe ctrum in the system "atom in a standing laser wave", which is a quantum-opt ical realization of a Bloch electron. It is shown that for an appropriate c hoice of the system parameters the atomic survival probability (a quantity measured in laboratory experiments) also develops a fractal structure as a function of the electric matching ratio. Numerical simulations under classi cally chaotic scattering conditions show good agreement with theoretical pr edictions based on random matrix theory.