Nonlinear Landau-Zener Processes in a Periodic Driving Field

TL;DR

This paper investigates how a periodic driving field influences nonlinear Landau-Zener processes in a many-body system, revealing complex dynamical behaviors and potential applications in controlling mean-field dynamics.

Contribution

It provides a comprehensive analysis of the effects of periodic driving on nonlinear Landau-Zener processes, highlighting differences from linear cases and exploring chaos and population transfer.

Findings

Periodic driving alters phase dependence of Landau-Zener transitions.

Nonlinearity can enhance population transfer even in adiabatic regimes.

Chaos emerges in the mean-field dynamics under certain driving conditions.

Abstract

Effects of a periodic driving field on Landau-Zener processes are studied using a nonlinear two-mode model that describes the mean-field dynamics of a many-body system. A variety of different dynamical phenomena in different parameter regimes of the driving field are discussed and analyzed. These include shifted, weakened, or enhanced phase dependence of nonlinear Landau-Zener processes, nonlinearity-enhanced population transfer in the adiabatic limit, and Hamiltonian chaos on the mean field level. The emphasis of this work is placed on how the impact of a periodic driving field on Landau-Zener processes with self-interaction differs from those without self-interaction. Aside from gaining understandings of driven nonlinear Landau-Zener processes, our findings can be used to gauge the strength of nonlinearity and for efficient manipulation of the mean-field dynamics of many-body systems.