Low-Energy Test of Quantum Gravity via Angular Momentum Entanglement

Currently envisaged tests for probing the quantum nature of the gravitational interaction in the low-energy regime typically focus either on the quantized center-of-mass degrees of freedom of two spherically-symmetric test masses or on the rotational degrees of freedom of non-symmetric masses under a gravitational interaction governed by the Newtonian potential. In contrast, here we investigate the interaction between the angular momenta of spherically-symmetric test masses considering a tree-level relativistic correction related to frame-dragging that leads to an effective dipolar interaction between the angular momenta. In this approach, the mass of the probes is not directly relevant; instead, their angular momentum plays the central role. We demonstrate that, while the optimal entangling rate is achieved with a maximally delocalized initial state, significant quantum correlations can still arise between two rotating systems even when each is initialized in an eigenstate of rotation. Additionally, we examine the robustness of the generated entanglement against typical sources of noise and observe that our combination of angular momentum and spherically-symmetric test-masses mitigates the impact of many common noise sources.