Probing metric fluctuations with the spin of a particle in a quantum simulation

Exploring potential empirical manifestations of quantum gravity is a challenging pursuit. In this study, we utilise a lattice representation of a (2+1)D massive gravity toy model interacting with Dirac fermions that can support specific spacetime fluctuations. We focus on the evolution of the fermion's spin due to its coupling to spacetime fluctuations. To monitor these dynamics, a minimal model is required that comprises two bosonic modes describing spacetime geometry fluctuations coupled to the spin of the fermion. A possible emulation of this system involves encoding spin degrees of freedom in the electronic states of an atom coupled to a bimodal optical cavity that provides the two bosonic modes. Our proposal introduces a novel approach for modelling the effect of interactions between quantum gravity and matter that can be probed with current technology.