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

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.

10 pages, 5 figures, 1 appendix, accepted for publication in EPJP, Comments welcome

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• Observation of topological transitions in interacting quantum circuits
• Measuring a topological transition in an artificial spin 1/2 system
• Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit
• Quantum simulation of gravitational-like waves in minisuperspace with an artificial qubit
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