Localization condition for two-level systems

TL;DR

This paper investigates the conditions under which two-level quantum systems become localized when subjected to periodic external fields, emphasizing the importance of matching the system's dynamics with the external potential's period.

Contribution

It derives necessary conditions for localization in two-level systems and thoroughly analyzes a model with a periodic delta-function potential.

Findings

Localization occurs when the system's dynamics are periodic with the same period as the external potential.

The study provides a general criterion for localization based on the time-evolving matrix analysis.

A specific model with a periodic delta-function potential confirms the theoretical conditions.

Abstract

The dynamics of two-level systems in an external periodic field are investigated in general. The necessary conditions of localization are obtained through analysing the time-evolving matrix. It is found that localization is possible if not only is the dynamics of the system periodic, but also its period is the same as that of the external potential. A model system in a periodic $\delta$-function potential is studied thoroughly.