A simplified method for calculating the ac Stark shift of hyperfine levels

TL;DR

This paper introduces a simplified Green's function-based method, $E^{[2+]}$, for calculating the ac Stark shift of hyperfine levels, offering accuracy comparable to third order perturbation theory with easier implementation.

Contribution

The paper develops the $E^{[2+]}$ method, a new simplified approach for calculating hyperfine level shifts that is easier to use and incorporate data into, compared to traditional third order perturbation theory.

Findings

$E^{[2+]}$ closely matches TOPT results for differential light shifts.

The method is simple to implement and incorporate atomic data.

Validity conditions for the $E^{[2+]}$ method are analyzed.

Abstract

The ac Stark shift of hyperfine levels of neutral atoms can be calculated using the third order perturbation theory(TOPT), where the third order corrections are quadratic in the atom-photon interaction and linear in the hyperfine interaction. In this paper, we use Green's function to derive the $E^{[2+\epsilon]}$ method which can give close values to those of TOPT for the differential light shift between two hyperfine levels. It comes with a simple form and easy incorporation of theoretical and experimental atomic structure data. Furthermore, we analyze the order of approximation and give the condition under which $E^{[2+\epsilon]}$ method is valid.