Suppressing excitations in the nonlinear Landau-Zener model

TL;DR

This paper demonstrates that nonlinear dynamics in a generalized Landau-Zener model can suppress excitations and coherences, effectively acting as a shortcut to adiabaticity, which simplifies analysis of complex quantum systems.

Contribution

It introduces a generalized energy spectrum and shows that nonlinearity can be used to suppress excitations, providing a novel approach to control quantum dynamics.

Findings

Nonlinear dynamics suppress excitations in the Landau-Zener model.

The nonlinear term acts as an effective shortcut to adiabaticity.

A generalized energy spectrum is introduced for analysis.

Abstract

Many complex quantum systems can be described by effectively nonlinear dynamics. While such dynamics have many appealing characteristics, they also make the analysis significantly more involved. This is due to the fact that only a few analytical treatments exist, and that the language of quantum mechanics is built for linear operators. For instance, the very formulation of the quantum adiabatic theorem requires the underlying dynamics to be linear. In this work we show that in a generalized Landau-Zener model, nonlinear dynamics can be leveraged to suppress excitations and coherences of the corresponding linear scenario. To this end, we introduce a generalized "energy spectrum", which is defined by the expectation values of the energy under the stationary states. As a main result, we show that the nonlinear term in the evolution equation acts like an effective shortcut to adiabaticity for the linear Landau-Zener problem.