Resonant analogue configurations in atomic condensates

As a contribution to a memorial volume, we provide a comprehensive discussion of resonant configurations in analogue gravity, focusing on its implementation in atomic condensates and combining review features with original insights and calculations. In particular, we analyze the analogues of the Andreev and Hawking effects using a microscopic description based on the Bogoliubov approximation. We contemplate several resonant scenarios whose efficiency to enhance anomalous scattering processes is compared to that of non-resonant setups. The presence of quantum signatures in analogue configurations, such as the violation of Cauchy-Schwarz inequalities or entanglement, is analyzed, observing that resonant configurations highly increase the entanglement signal, especially for the Andreev effect. We also discuss how these results have served as inspiration for the rapidly expanding field of quantum information in high-energy colliders. Finally, we study the physics of black-hole lasers as further examples of resonant analogue structures, distinguishing three stages in its time evolution. For short times, we compute the linear and non-linear spectrum for different models. For intermediate times, we generalize the current analysis of the BHL-BCL crossover. For long times, we discuss the emerging concept of spontaneous Floquet state and its potential implications.