Generalized Adiabatic Impulse Approximation

TL;DR

This paper extends the adiabatic impulse approximation to multilevel quantum systems, providing a practical method to analyze non-adiabatic transitions and interference effects with good numerical agreement.

Contribution

The paper introduces a generalized adiabatic impulse approximation for multilevel systems, enabling easier numerical evaluation of complex non-adiabatic dynamics.

Findings

The approximation matches exact numerical results for Landau-Zener models.

Derived conditions for destructive interference in multilevel systems.

Validated the method's effectiveness in analyzing multilevel quantum dynamics.

Abstract

Non-adiabatic transitions in multilevel systems appear in various fields of physics, but it is not easy to analyze their dynamics in general. In this paper, we propose to extend the adiabatic impulse approximation to multilevel systems. This approximation method is shown to be equivalent to a series of unitary evolutions and facilitates to evaluate the dynamics numerically. In particular, we analyze the dynamics of the Landau-Zener grid model and the multilevel Landau-Zener-St\"uckelberg-Majorana interference model, and confirm that the results are in good agreement with the exact dynamics evaluated numerically. We also derive the conditions for destructive interference to occur in the multilevel system.