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#### Year of publication

- 2001 (2) (remove)

#### Keywords

- Amplitude-Phase Method (1)
- Control (1)
- Milne Equation (1)
- Parametric Excitation (1)
- Wannier-Stark states (1)
- absorption spectrum (1)
- interband tunneling (1)
- metastable states (1)
- semiconductor superlattice (1)

A harmonic oscillator subject to a parametric pulse is examined. The aim of the paper is to present a new theory for analysing transitions due to parametric pulses. The new theoretical notions which are introduced relate the pulse parameters in a direct way with the transition matrix elements. The harmonic oscillator transitions are expressed in terms of asymptotic properties of a companion oscillator, the Milne (amplitude) oscillator. A traditional phase-amplitude decomposition of the harmonic-oscillator solutions results in the so-called Milne's equation for the amplitude, and the phase is determined by an exact relation to the amplitude. This approach is extended in the present analysis with new relevant concepts and parameters for pulse dynamics of classical and quantal systems. The amplitude oscillator has a particularly nice numerical behavior. In the case of strong pulses it does not possess any of the fast oscillations induced by the pulse on the original harmonic oscillator. Furthermore, the new dynamical parameters introduced in this approach relate closely to relevant characteristics of the pulse. The relevance to quantum mechanical problems such as reflection and transmission from a localized well and mechanical problems of controlling vibrations is illustrated.

Wannier-Stark states for semiconductor superlattices in strong static fields, where the interband Landau-Zener tunneling cannot be neglected, are rigorously calculated. The lifetime of these metastable states was found to show multiscale oscillations as a function of the static field, which is explained by an interaction with above-barrier resonances. An equation, expressing the absorption spectrum of semiconductor superlattices in terms of the resonance Wannier-Stark states is obtained and used to calculate the absorption spectrum in the region of high static fields.