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Abstract

In this work we focus on Bose-Einstein condensates for two particular purposes. First, as a system for which the analysis of spatial entanglement is worthwhile, given its two regimes (relativistic/nonrelativistic) regarding the dispersion rela- tion of Bogoliubov quasiparticles. It is therefore a promising scenario to put to test the formalism around entanglement entropies computation from a quantum field theoretical approach, providing a setting to look further into questions re- lated to its divergences in a relativistic quantum field theory. We put forward results for condensates of one- and two-dimensional spatial geometries, to find a self-regularised theory in the ultraviolet, and an agreement with the literature in all the expected results. Furthermore, we give new results regarding the crossover behaviour from nonrelativistic to relativistic regimes. Our calculations are done considering a condensate of infinite extent. The second aim is to implement the condensate as a quantum simulator for relativistic fields in curved spacetimes, building background geometries which can be both, spatially curved and time- dependent, being able to simulate the class of FLRW universes. We provide the theoretical construct of such a simulator, and its successful experimental implementation, with results related to the detection of particle production in curved spacetimes. Both topics of inquiry are interesting in and of themselves, while taken together they present the opportunity to look into the question of entanglement in different spacetime geometries, including causally disconnected regions, in an experimental context.