Gravitationally Mediated Entanglement with Superpositions of Rotational Energies

Experimental proposals for testing quantum gravity-induced entanglement of masses (QGEM) typically involve two interacting masses which are each in a spatial superposition state. Here, we propose a QGEM experiment with two particles which are each in a superposition of rotational states, this amounts to a superposition of mass through mass-energy equivalence. Our proposal relies on the fact that rotational energy gravitates. This approach would test a feature unique to gravity since it amounts to sourcing a spacetime in superposition due to a superposition of 'charge'. We propose and analyse a concrete experimental protocol and discuss challenges.