Loss of adiabaticity with increasing tunneling gap in non-integrable multistate Landau-Zener models

Abstract

We consider the simplest non-integrable model of multistate Landau-Zener transition. In this model two pairs of levels in two tunnel coupled quantum dots are swept passed each other by the gate voltage. Although this 2 * 2 model is non-integrable, it can be solved analytically in the limit when the inter-level energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar 2 * 1 model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In 2 * 1 model, the probability for a particle, residing at time t -> -\infty in one dot, to remain in the same dot at t -> \infty falls off exponentially with tunnel coupling. By contrast, in 2 * 2 model, this probability grows exponentially with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as manifestation of the Dicke effect.

8 pages, 3 figures

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• Nonadiabatic Phase Transition with Broken Chiral Symmetry
• Nonadiabatic dissociation of molecular Bose-Einstein condensates: competition between chemical reactions
• Landau-Zener transition between two quantum dots coupled by resonant tunneling
• Effect of decay of the final states on the probabilities of the Landau-Zener transitions in multistate non-integrable models
• Electric circuit analog of Landau-Zener tunneling using time-varying elements