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

TL;DR

This paper derives an explicit quasienergy expression and analyzes the time evolution of a two-level quantum system under a periodic external field using Floquet theory and Heun equations.

Contribution

It provides a new analytical solution for the quasienergy and time evolution of a driven two-level system without solving the connection problem of the Heun equation.

Findings

Explicit quasienergy expression derived

Time evolution over a full period calculated

Series solutions of the confluent Heun equation used

Abstract

We investigate the analytical solution of a two-level system subject to a monochromatical, linearly polarized external field that was published a couple of years ago. 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.