Analogue Hawking radiation in Bose-Einstein condensates

This Thesis develops in the field of analogue gravity, a branch of physics which relies on a specific correspondence that exists between fluid dynamics and curved spacetimes; thanks to that, effects which are hard to study in the gravitational context are investigated in the realm of hydrodynamics with the hope that the consequent results could be transferred back to the cosmological domain and give us better insights in the gravitational context. In this Thesis, I try to introduce the reader to the realm of analogue gravity and to the concepts of Bose-Einstein condensation, Hawking radiation and its analogue counterpart (Chapter 1 and 2); then in Chapter 3 and 4 I describe the details of our work. In the past years, we have developed two directions of research, both aimed at the characterization of the analogue Hawking radiation in Bose-Einstein condensates. One side of our work had the purpose of investigating the results obtained in recent experiments apt to the detection of the analogue Hawking radiation in a quantum gas. Our results are very important in the description of the phenomena and give insights on how to develop future experiments (Chapter 3). The other side of our work aimed at the characterization of this effect from a theoretical point of view by means of an innovative approach, which allows for a much deeper and more detailed description of the radiation and helps shine new light on this effect (Chapter 4). In Chapter 5 we briefly discuss the possible developments of our studying, highlighting the missing pieces of this field and suggesting possible ways to approach the existing problems.