Gravity induced entanglement of multiple massive particles with large spin

TL;DR

This work studies gravity-induced entanglement among multiple massive particles with large spin using a generalized Stern-Gerlach interferometer that splits each particle into $2j+1$ trajectories. Entanglement arises solely from Newtonian gravitational interactions among particles, and is quantified via negativity to distinguish quantum correlations in mixed states. By numerically optimizing the spin angles for configurations with $N=3$ and $N=4$, the authors show that entanglement grows with both the number of particles and the single-particle spin, with the Prism-center configuration delivering the fastest entanglement generation and requiring shorter evolution times (e.g., $t\approx1.2\,\mathrm{s}$ for $N=4$, $J=2$). They also analyze decoherence in short- and long-wavelength limits, finding increased resilience to short-wavelength noise for larger $N$ and $j$, while long-wavelength decoherence can be mitigated by cooling. Overall, the results indicate practical pathways to enhance gravity-induced entanglement in multi-particle, large-spin systems and inform experimental designs for testing quantum aspects of gravity.

Abstract

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.

Figures (13)

• Figure 1: The allowable configurations for the system consisting of three particles with large spins.
• Figure 2: The contour plot for the entanglement entropy over $(\theta_A, \theta_C)$ plane for different configurations with three particles at $t=2$s. The specific configuration is labeled on the top of each subfigure.
• Figure 3: The contour plot for the entanglement entropy over $(\theta_A, \theta_C)$ plane for different values of $\theta_B$ in the $Prism/Parallel$ configuration with three particles at $t=2$s.
• Figure 4: The evolution of the entanglement entropy for various configurations and spins.
• Figure 5: Three typical configurations for the system consisting of four particles with large spins.