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- Wannier-Stark systems (7)
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We study the transitions between the ground and excited Wannier states induced by a weak ac field. Because the upper Wannier states are several order of magnitude less stable than the ground states, these transitions decrease the global stability of the system characterized by the rate of probability leakage or decay rate. Using nonhermitian resonant perturbation theory we obtain an analytical expression for this induced decay rate. The analytical results are compared with exact numerical calculations of the system decay rate.

The quasienergy spectrum of a Bloch electron affected by dc-ac fields is known to have a fractal structure as function of the so-called electric matching ratio, which is the ratio of the ac field frequency and the Bloch frequency. This paper studies a manifestation of the fractal nature of the spectrum in the system "atom in a standing laser wave", which is a quantum optical realization of a Bloch electron. It is shown that for an appropriate choice 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 classically chaotic scattering conditions show good agreement with theoretical predictions based on random matrix theory.

The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time dependent systems. For an anharmonic oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings.