  Unlike the fundamental forces of the Standard Model the quantum effects of
gravity are still experimentally inaccessible. Rather surprisingly quantum
aspects of gravity, such as massive gravitons, can emerge in experiments with
fractional quantum Hall liquids. These liquids are analytically intractable and
thus offer limited insight into the mechanism that gives rise to quantum
gravity effects. To thoroughly understand this mechanism we employ a
graphene-like system and we modify it appropriately in order to realise a
simple (2+1)-dimensional massive gravity model. More concretely, we employ
(2+1)-dimensional Dirac fermions, emerging in the continuous limit of a
fermionic honeycomb lattice, coupled to massive gravitons, simulated by bosonic
modes positioned at the links of the lattice. The quantum character of gravity
can be determined directly by measuring the correlations on the bosonic atoms
or by the interactions they effectively induce on the fermions. The similarity
of our approach to current optical lattice configurations suggests that quantum
signatures of gravity can be simulated in the laboratory in the near future,
thus providing a platform to address question on the unification theories,
cosmology or the physics of black holes.
