  The entanglement generation of two two-level giant atoms coupled to a
photonic waveguide, which is formed by a Su-Schrieffer-Heeger (SSH) type
coupled-cavity array is studied. Here, each atom is coupled to the waveguide
through two coupling points. The two-atom separate-coupling case is studied,
and 16 coupling configurations are considered for the coupling-point
distributions between the two atoms and the waveguide. Quantum master equations
are derived to govern the evolution of the two atoms and characterize atomic
entanglement by calculating the concurrence of the two-atom states. It is found
that the two giant-atom entanglement depends on the coupling configurations and
the coupling-point distance of the giant atoms. In particular, the entanglement
dynamics of the two giant atoms in 14 coupling configurations depend on the
dimerization parameter of the SSH waveguide. According to the self-energies of
the two giant atoms, it is found that ten of these 16 coupling configurations
can be divided into five pairs. It is also showed that the delayed sudden birth
of entanglement between the two giant atoms is largely enhanced in these five
pairs of coupling configurations. This work will promote the study of quantum
effects and coherent manipulation in giant-atom topological-waveguide-QED
systems.
