Multipartite entanglement generation and dynamics of three giant atoms coupling to a one-dimensional waveguide

We study the multipartite entanglement generation and dynamics of three giant atoms coupling to a one-dimensional waveguide. By solving the time-delayed differential equations, we obtain the time evolution of the three-atom resulted state and concentrate on the non-Markovian effect, which is induced by the fact that the photon transmission time is taken into account, on the entanglement generation and dynamics. Our results imply that the multipartite entanglement generation and dynamics depend strongly on the accumulated phase characterizing the distance between the coupling points and the time delay for photon propagation in the waveguide. For the zero time delay, the entanglement generation takes a monotonic behavior. For the nonzero time delay, the entanglement generation and dynamics take an oscillation behavior to a stable value or to zero. The effect of different initial states on the multipartite entanglement generation is discussed. Under certain condition, the long-lived entangled state can be generated and the initial entangled state can preserve its entanglement in the time evolution. Our results can contribute to the understanding of multipartite entanglement generation of giant atoms coupling to a one-dimensional waveguide.