Suppressing excitations in the nonlinear Landau-Zener model

¹ Department of Physics, University of Maryland - Baltimore County, Baltimore, MD 21250, USA
² Quantum Science Institute, University of Maryland - Baltimore County, Baltimore, MD 21250, USA
³ National Quantum Laboratory - College Park, MD 20740, USA
⁴ School of Physics, University College Dublin - Belfield, Dublin 4, Ireland
⁵ Centre for Quantum Engineering, Science, and Technology, University College Dublin - Dublin 4, Ireland

Received: 17 June 2025
Accepted: 20 August 2025

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.