Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue

We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime, focusing on a (1+1)-dimensional case in which the evolution of the scale factor is set by the equations of Jackiw-Teitelboim gravity. As a first step towards a quantum simulation of this phenomenon, we consider two possible lattice regularizations, which allow us to explore the interplay of particle production and topological phenomena in spacetimes with a boundary. In particular, for a Wilson-type discretization of the Dirac field, the asymptotic Minkowski vacua connected by the intermediate expansion corresponds to symmetry-protected topological groundstates, and have a boundary manifestation in the form of zero-modes exponentially localized to the spatial boundaries. We show that particle production can also populate these zero modes, which contrasts with the situation with a na\"ive-fermion discretization, in which conformal zero-mass fields exhibit no particle production. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices, which requires real-time control of the Raman-beam detuning according to the scale factor of the simulated spacetime, as well as band-mapping measurements.