Fermion Production At The Boundary Of An Expanding Universe: A Cold-atom Gravitational Analogue

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Carlos Fulgado-Claudio, Jose M. Sánchez Velázquez, and Alejandro Bermudez

Instituto de Física Teórica, UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain.

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Abstract

We study the phenomenon of cosmological particle production of Dirac fermions in a Friedmann-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 correspond 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 naïve-fermion discretization, in which conformal zero-mass fields do not allow for 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 require real-time control of the Raman-beam detuning according to the scale factor of the simulated spacetime, as well as band-mapping measurements.

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Featured image: Pictorial representation of the phenomenon of particle production in an expanding universe. The dynamics of the background metric produces excitations of the field in pairs, which are interpreted as particles (represented in red) and antiparticles (represented in orange). For certain lattice discretizations of the field, the spatial boundaries of the spacetime can actually host zero-energy modes that are exponentially localized to the boundaries, and thus propagate in a lower effective dimension. We explore the phenomenon of particle production for such zero modes, which is a landmark of the interplay of topological vacua and the curved spacetime.

Popular summary

There is a striking phenomenon occurring for quantum fields in curved spacetimes, such as rapidly expanding geometries, which is gravitational particle production. Recently, there have been several experimental proposals within the realm of quantum simulations that can implement the dynamics of cosmological scenarios, paving thus the way for getting insights on several aspects of this phenomenon. We propose a new experimental setup to study fermion production in a cold-atom gravitational analogue.

Among the possibilities that this viewpoint enables, we focus on the interactions between cosmological particle production and topological phases, which are phases of matter governed by topological invariants. We consider a universe with reduced dimensionality, where the presence of these phases is manifested in the appearance of zero-modes exponentially localized to the spatial boundaries of the universe. This allows us to study how these modes interact with the expanding background and to tackle the differences with respect to the creation of propagating particles.

This framework allows for the study of exotic phases of matter within cosmological contexts, and it opens the way for the exploration of more complex models. For instance, interactions can be easily implemented, allowing thus for the study of non-perturbative phenomena. Also, it would be of great interest to generalise the experimental setup to higher-dimensional universes, where different topological phases would appear. These features can be easily implemented in our experimental scheme.

► BibTeX data

@article{FulgadoClaudio2023fermionproduction, doi = {10.22331/q-2023-06-21-1042}, url = {https://doi.org/10.22331/q-2023-06-21-1042}, title = {Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue}, author = {Fulgado-Claudio, Carlos and Vel{‘{a}}zquez, Jose M. S{‘{a}}nchez and Bermudez, Alejandro}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1042}, month = jun, year = {2023}<br /> }

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Time Stamp: Jul 20, 2022

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

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