  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.
