Entanglement enhancement of two giant atoms with multiple connection points in bidirectional-chiral quantum waveguide-QED system

We study the entanglement generation of two giant atoms within a one-dimensional bidirectional-chiral waveguide quantum electrodynamics (QED) system, where the initial state of the two giant atoms are $|e_a,g_b\rangle $. Here, each giant atom is coupled to the waveguide through three connection points, with the configurations divided into five types based on the arrangement of coupling points between the giant atoms and the waveguide: separate, fully braided, partially braided, fully nested, and partially nested. We explore the entanglement generation process within each configuration in both nonchiral and chiral coupling cases. It is demonstrated that entanglement can be controlled as needed by either adjusting the phase shift or selecting different configurations. For nonchiral coupling, the entanglement of each configuration exhibits steady state properties attributable to the presence of dark state. In addition, we find that steady-state entanglement can be obtained at more phase shifts in certain configurations by increasing the number of coupling points between the giant atoms and the bidirectional waveguide. In the case of chiral coupling, the entanglement is maximally enhanced compared to the one of nonchiral case. Especially in fully braided configuration, the concurrence reaches its peak value 1, which is robust to chirality. We further show the influence of atomic initial states on the evolution of interatomic entanglement. Our scheme can be used for entanglement generation in chiral quantum networks of giant-atom waveguide-QED systems, with potential applications in quantum networks and quantum communications.