Unlike the fundamental forces of the Standard Model, such as electromagnetic, weak and strong forces, the quantum effects of gravity are still experimentally inaccessible. The weak coupling of gravity with matter makes it significant only for large masses where quantum effects are too subtle to be measured with current technology. Nevertheless, insight into quantum aspects of gravity is key to understanding unification theories, cosmology or the physics of black holes. Here we propose the simulation of quantum gravity with optical lattices which allows us to arbitrarily control coupling strengths. More concretely, we consider $(2+1)$-dimensional Dirac fermions, simulated by ultra-cold fermionic atoms arranged in a honeycomb lattice, coupled to massive quantum gravity, simulated by bosonic atoms positioned at the links of the lattice. The quantum effects of gravity induce interactions between the Dirac fermions that can be witnessed, for example, through the violation of Wicks theorem. The similarity of our approach to current experimental simulations of gauge theories suggests that quantum gravity models can be simulated in the laboratory in the near future.
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