Carlos Fulgado (IFT)

One of the most striking phenomena within the realm of Quantum Field Theory in Curved Spacetimes is the creation of particles as a consequence of the expansion of the universe. We study this effect for the case of Dirac fermions and propose a cold-atom gravitational analogue to implement this effect in controlled tabletop experiments. We begin by reviewing the formalism to describe Dirac fermions in a (1+1)-dimensional FRW spacetime and derive the equations that describe particle production, showing some relevant results. After this, and as a first step towards its implementation in a quantum simulator, 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, we show that for a Wilson-type discretization of the Dirac field, the asymptotic Minkowski vacua connected by an intermediate expansion correspond to symmetry-protected topological groundstates, and have a boundary manifestation in the form of zero-modes exponentially localised to the spatial boundaries. This allows one to explore the interaction between them and the expanding background. We then present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices, which would allow for the exploration of new domains in QFT in curved spacetimes, such as interacting theories, in the future. Additionally, we describe this model using the framework of fermionic Gaussian States, establishing a link between our research and the domain of quantum information. This approach not only affords us insights into various facets of the system, including its entanglement structure and propagation, but also underscores the close connection between our study and previous research on quantum quenches. Finally, some work on how to implement interactions withing this scheme is presented, paving the way for the study of the interplay between interacting QFTs, entanglement and particle production.