Cold atom experiments worldwide play a prominent role in the spectacular advances taking place in our exploration of the quantum world. In particular they gave rise to the field of Quantum Simulation, where specific model Hamiltonians and/or quantum many-body states are engineered in the lab. To kick-start this research line in Flanders, we are setting up a Bose-Einstein Condensate (BEC) experiment. Such a condensate consists of at least a few ten thousand atoms that are cooled to a temperature of a micro-Kelvin or less. In this regime the physics is essentially that of an interacting quantum field theory. Our set-up has a state-of-the-art system for generating flexible trapping potentials which will allow us to develop several original experiments on non-equilibrium phenomena for quantum fields. We aim to design protocols for generating time-averaged traps and study their relation with Floquet dynamics. More broader aspects of the dynamical behaviour of BECs will be probed by applying finely tuned quenches or driving sequences. In this way we will target specific excitations - phonons and solitons - thereby shedding new light on relaxation, (pre-)thermalizaton and quantum turbulence. Finally, we plan to devise specific experiments for maximizing the signatures of dynamical pair creation, with the ultimate goal of detecting the analogue gravity version of the Hawking effect. In summary, this project aims to realize a quantum simulator for quantum fields.