Magnus expansion method for two-level atom interacting with few-cycle pulse

TL;DR

This paper develops an analytic approach using the Magnus expansion to describe the dynamics of a two-level atom interacting with a few-cycle laser pulse, providing insights into its applicability and limitations.

Contribution

The authors derive fourth-order Magnus expansion formulas for two-level systems with arbitrary pulse shapes and analyze their convergence, offering a complementary method to existing approaches.

Findings

Derived explicit formulas for atomic states under small pulse areas.

Identified the convergence limitations of the Magnus expansion.

Compared the method's accuracy with previous approaches.

Abstract

Using the Magnus expansion to the fourth order, we obtain analytic expressions for the atomic state of a two-level system driven by a laser pulse of arbitrary shape with small pulse area. We also determine the limitation of our obtained formulas due to limited range of convergence of the Magnus series. We compare our method to the recently developed method of Rostovtsev et al. (PRA 2009, 79, 063833) for several detunings. Our analysis shows that our technique based on the Magnus expansion can be used as a complementary method to the one in PRA 2009.