  We theoretically investigate how the initial state influence the entanglement
dynamics between two and three two-level atoms with dipole-dipole interaction
(DDI) coupled to a whispering-gallery-mode (WGM) microtoroidal cavity. Two
different cases, where the two atoms are coupled symmetrically or
asymmetrically to the two WGMs through evanescent fields, are discussed in
detail. Considering two types of initial states between the atoms and the
symmetric regime, we show that for the initial entangled state, the sudden
death and birth, as well as the freezing of the entanglement, can be obtained
by adjusting both the scattering strength between the modes and the DDI,
differently from the initial product state. Moreover, we note that the atomic
entanglement generation is more susceptible to the scattering strength
variation between the modes than to the DDI. In addition, for the asymmetric
regime, the entanglement generation is strongly dependent on the atomic
location and the scattering strength. Similar results are obtained for the case
of three atoms coupled to a microtoroidal cavity, even in the presence of
losses.
