  We study the non-Markovian dynamics of a qubit made up of a two-level atom
interacting with an electromagnetic field (EMF) initially at finite
temperature. Unlike most earlier studies where the bath is assumed to be fixed,
we study the coherent evolution of the combined qubit-EMF system, thus allowing
for the back-action from the bath on the qubit and the qubit on the bath in a
self-consistent manner. In this way we can see the development of quantum
correlations and entanglement between the system and its environment, and how
that affects the decoherence and relaxation of the system. We find
non-exponential decay for both the diagonal and non-diagonal matrix elements of
the qubit's reduced density matrix in the pointer basis. From the diagonal
elements we see the qubit relaxes to thermal equilibrium with the bath. From
the non-diagonal elements, we see the decoherence rate beginning at the usually
predicted thermal rate, but changing to the zero temperature decoherence rate
as the qubit and bath become entangled. These two rates are comparable, as was
shown before in the zero temperature case [C. Anastopoulos and B. L. Hu, Phys.
Rev. A {\bf 62} (2000) 033821]. On the entanglement of a qubit with the EMF
under this type of resonant coupling we calculated, for the qubit reduced
density matrix, the fidelity and the von Neumann entropy, which is a measure of
the purity of the density matrix. The present more accurate non-Markovian
calculations predict lower loss of fidelity and purity as compared with the
Markovian results. Generally speaking, with the inclusion of quantum
correlations between the qubit and its environment, the non-Markovian processes
tend to slow down the drive of the system to equilibrium, prolonging the
decoherence and better preserving the fidelity and purity of the system.
