We propose a novel scheme to generate and manipulate bipartite and tripartite entanglement and Bell nonlocality in a closed-loop three-mode optomechanical system, where two optical modes are simultaneously coupled to a mechanical mode via typical optomechanical interactions and also coupled to each other through field transmission. This configuration gives rise to a phase-sensitive coupling, in which the relative phase directly controls the population distribution between two optical modes, enabling coherent redistribution of quantum correlations. By tuning this relative phase, we achieve deterministic switching of bipartite entanglement between two optical-mechanical pairs, as well as tunable genuine tripartite entanglement among three modes. Employing the displaced-parity measurement, we construct both the bipartite and tripartite Bell inequalities in phase space and observe maximal violations of approximately
2.32 and
3, respectively, which coincide exactly with the values achievable for ideal bipartite and tripartite Einstein-Podolsky-Rosen states. Counterintuitively, we find that the tripartite Bell nonlocality can persist even when the genuine tripartite entanglement is absent, providing deeper insight into the relationship between these two types of quantum correlations. Furthermore, we systematically analyze the effects of mechanical dissipation and thermal noise, identifying the parameter regions where Bell violation survives under realistic experimental conditions. Our results establish a comprehensive framework for generating, controlling, and verifying multipartite quantum correlations, paving the way towards phase-tunable quantum networks and noise-resilient tests of quantum foundations.
The bipartite entanglement in ideal noninteracting Fermi gas system with spin-1/2 and pseudospin-1/2 degrees of freedom was investigated.Because of the enlarging of state space by two degrees of freedom,the distribution of bipartite entanglement of fermions whose number is no more than four is similar to the entanglement distribution of two fermions and completely different with the distribution of multiparticle entanglement in spin-1/2 noninteraction Fermi gas.The relative entangled distance of two fermions in two degrees of freedom system is about 2.7 times larger than that of single spin-1/2 system.Entanglement between two fermions of one degree of freedom always equals zero,which means that this entanglement or quantum correlation comes from interactions of system.