  We study the behavior of the Rabi oscillations of a driven central spin
(qubit) coupled to an antiferromagnetic spin bath (environment). It is found
that the decoherence behavior of the central spin depends on the detuning,
driving strength, the qubit-bath coupling and an important factor, associated
with the number of the coupled atoms, the detailed lattice structure, and the
temperature of the environment. If the detuning exists, the Rabi oscillations
may show the behavior of collapses and revivals; however, if the detuning is
zero, such a behavior will not appear. We investigate the weighted frequency
distribution of the time evolution of the central spin inversion and give this
phenomenon of collapses and revivals a reasonable explanation. We also discuss
the decoherence and the pointer states of the qubit from the perspectives of
the von Neumann entropy. It is found that the eigenstates of the qubit
self-Hamiltonian emerge as the pointer states in the weak system-environment
coupling limit.
