A quantum simulator is a controllable device governed by the laws of quantum mechanics that replicates the conditions of a physical system or process. Recent works suggest that ultracold fermions in optical lattices can be used as quantum simulators to investigate the propagation of relativistic particles in curved gravitational backgrounds. Herein, we find a lattice model describing the physics of Dirac fermions in an homogeneous, isotropic and expanding (2+1) dimensional universe.
Remarkably, we observe traces of the explicit time-dependence of the metric in the form of ”Hubble friction”. We argue that the model encountered is experimentally realizable with the current state-of-the-art techniques in ultracold atoms. This could pave the way for a novel approach to problems typically restricted to high energy particle physics or cosmology.
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