Tracking quantum state evolution by the Berry curvature with a two-level system

TL;DR

This paper explores how the Berry curvature in a driven two-level quantum system can be used to track and control the system's state evolution, revealing topological structures and their physical implications.

Contribution

It introduces a method to connect Berry curvature with the dynamics of a two-level system, enabling state tracking and manipulation through topological analysis.

Findings

Identification of sphere and torus topologies in parameter space

Demonstration of state evolution tracking via Berry curvature

Physical manifolds including gapped regions probed by Berry curvature

Abstract

We investigate two kinds of topological structures (sphere and torus) spanned by the controlled parameters of a driven two-level system's Hamiltonian, and consider the connection between the structures and the system's dynamics. We discuss the Berry curvature obtained through the dynamical response method, show the certain physical and observable manifolds including the gapped region probed by integrating the Berry curvature, and demonstrate the system's state evolution can be tracked and manipulated by extracting the Berry curvature.