Stationary solution of a weak-driven open Jaynes-Cummings system of a degenerate two-level atom coupled to an arbitrary-polarized cavity field

TL;DR

This paper derives an analytical stationary solution for a weakly driven open Jaynes-Cummings system with a degenerate two-level atom, revealing how the effective coupling depends on the driving field's elliptic angle and enabling experimental control.

Contribution

It provides the first analytical stationary density matrix solution for a degenerate two-level atom coupled to an arbitrary-polarized cavity, using Morris-Shore transformation.

Findings

System behaves as a non-degenerate two-level system with a single effective coupling constant.

Analytic expressions for atomic emission and cavity transmission spectra are derived.

The effective coupling depends solely on the elliptic angle of the driving field.

Abstract

Analytical solution for the stationary density matrix is derived, by using the Morris-Shore transformation, for an open Jaynes-Cummings system of a two-level atom with Zeeman sublevel degeneracy coupled to an arbitrary-polarized cavity mode. In the limit of weak excitation with the number of quantum in the system not exceeding one, we have obtained the stationary solution of the master equation up to the first order of the driving field intensity. We have also derived the analytic expressions for the excitation spectra of atomic spontaneous emission and cavity transmission. Our results show that the system can be regarded as a non-degenerate two-level system with a single effective coupling constant which depends only on the elliptic angle of the driving field as long as the atom-cavity coupling is not too strong. A precise condition for this approximation is derived. This work provides a theoretical ground for experimentally realizing a Jaynes-Cummings system with a coupling constant continuously varied for various cavity quantum electrodynamics studies.