  We study the generation of quantum entanglement between two giant atoms
coupled to a one-dimensional waveguide. Since each giant atom interacts with
the waveguide at two separate coupling points, there exist three different
coupling configurations in the two-atom waveguide system: separated, braided,
and nested couplings. Within the Wigner-Weisskopf framework for single coupling
points, the quantum master equations governing the evolution of the two giant
atoms are obtained. For each coupling configuration, the entanglement dynamics
of the two giant atoms is studied, including the cases of two different atomic
initial states: single- and double-excitation states. It is shown that the
generated entanglement depends on the coupling configuration, phase shift, and
atomic initial state. For the single-excitation initial state, there exists
steady-state entanglement for these three couplings due to the appearance of
the dark state. For the double-excitation initial state, an entanglement sudden
birth is observed via adjusting the phase shift. In particular, the maximal
entanglement for the nested coupling is about one order of magnitude larger
than those of separate and braided couplings. In addition, the influence of the
atomic frequency detuning on the entanglement generation is studied. This work
can be utilized for the generation and control of atomic entanglement in
quantum networks based on giant-atom waveguide-QED systems, which have wide
potential applications in quantum information processing.
