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arXiv · quant-ph/0111132

Wannier-Stark resonances in optical and semiconductor superlattices

M. Glueck·A. R. Kolovsky·H. J. Korsch
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Abstract

In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.

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M. Glueck, A. R. Kolovsky, H. J. Korsch. 2002-03-18. Wannier-Stark resonances in optical and semiconductor superlattices. https://doi.org/10.1016/s0370-1573(02)00142-4

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