Gravity induced entanglement of multiple massive particles with large spin

We investigate the generation rate of the quantum entanglement in a system composed of multiple massive particles with large spin, where the mass of a single particle can be split into multiple trajectories by a generalized Stern-Gerlach interferometer. Taking the coherent spin states (CSS) as the initial state and considering the gravitational interaction due to Newtonian potential, we compute the generation rate of the entanglement for different configurations of the setup. Explicitly, the optimal polar angles of the spin are found numerically for systems with three and four particles, respectively. We conclude that the amount of the entanglement increases with the number of particles as well as the spin, and the configuration of the prism with a particle at the center generates the best rate of the entanglement.