Landau-Zener transition between two levels coupled to continuum

TL;DR

This paper investigates how coupling to a continuum affects Landau-Zener transitions in a two-level quantum system, revealing an enhanced survival probability due to a second-order virtual tunneling process.

Contribution

It introduces a model accounting for weak continuum coupling on both levels, showing an additional effective coupling mechanism during Landau-Zener transitions.

Findings

Survival probability in level i is enhanced due to continuum coupling.

Second-order virtual tunneling creates an effective coupling between levels.

The effect is significant for short times after crossing the continuum.

Abstract

For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, {\em i}, to survive the transition and to remain in the first level, depends exponentially on the square of the tunnel matrix element between the two levels. This result remains valid when the second level, {\em f}, is broadened due to e.g. coupling to continuum [V. M. Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. If the level, {\em i}, is also coupled to continuum, albeit much weaker than the level {\em f}, a particle, upon surviving the transition, will eventually escape. However, for shorter times, the probability to find the particle in the level {\em i} after crossing {\em f} is {\em enhanced} due to the coupling to continuum. This, as shown in the present paper, is the result of a second-order process, which is an {\em additional coupling between the levels}. The underlying mechanism of this additional coupling is virtual tunneling from {\em i} into continuum followed by tunneling back into {\em f}.