  The exact quantum dynamics of the reduced density matrix of two coupled spin
qubits in a quantum Heisenberg XY spin star environment in the thermodynamic
limit at arbitrarily finite temperatures is obtained using a novel operator
technique. In this approach, the transformed Hamiltonian becomes effectively
Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum
electrodynamics. This special operator technique is mathematically simple and
physically clear, and allows us to treat systems and environments that could
all be strongly coupled mutually and internally. To study their entanglement
evolution, the concurrence of the reduced density matrix of the two coupled
central spins is also obtained exactly. It is shown that the dynamics of the
entanglement depends on the initial state of the system and the coupling
strength between the two coupled central spins, the thermal temperature of the
spin environment and the interaction between the constituents of the spin
environment. We also investigate the effect of detuning which in our model can
be controlled by the strength of a locally applied external magnetic field. It
is found that the detuning has a significant effect on the entanglement
generation between the two spin qubits.
