Floquet theory of the analytical solution of a periodically driven two-level system

ABSTRACT

We investigate the analytical solution of a two-level system subject to a monochromatical, linearly polarized external field that was first published in 2007. In particular, we derive an explicit expression for the quasienergy. Moreover, we calculate the time evolution of a typical two-level system over a full period by evaluating series solutions of the confluent Heun equation. This is possible without invoking the connection problem of this equation since the complete time evolution of the system under consideration can be reduced to that of the first quarter-period. As a physical application we consider the work performed on a two-level system.

COMMUNICATED BY:

• Salvatore Leonardi

Keywords:

• Floquet theory
• two-level system
• quasienergy
• confluent Heun differential equation

2010 Mathematics Subject Classification:

• 33E30

Acknowledgments

We sincerely thank the members of the DFG Research Unit FOR2692 for fruitful discussions, especially we are indebted to Jochen Gemmer for hints to the literature on the subject of Section 3.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was funded by the Deutsche Forschungsgemeinschaft (DFG) grant nos. SCHN 615/25-1 and HO 1771/8-1.