Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions

TL;DR

This paper provides exact analytical solutions for coherently exciting a two-level atom with a far-off resonant classical field, using Heun functions, enabling precise control of atomic excitation and applications like XUV generation.

Contribution

It introduces a class of exactly solvable pulse shapes for two-level atom excitation driven by far-off resonant fields, utilizing Heun functions for analytical solutions.

Findings

Exact solutions in terms of Heun functions for specific pulse shapes

Derivation of generalized pulse envelopes for coherent excitation

Potential applications in XUV generation

Abstract

We present an analytical treatment of coherent excitation of a Two-Level Atom driven by a far-off resonant classical field. A class of pulse envelope is obtained for which this problem is exactly solvable. The solutions are given in terms of Heun function which is a generalization of the Hypergeometric function. The degeneracy of Heun to Hypergeometric equation can give all the exactly solvable pulse shapes of Gauss Hypergeometric form, from the generalized pulse shape obtained here. We discuss the application of the results obtained to the generation of XUV.