Final Activity Report Summary - GWATOMIFO (Matter-wave gravitational wave interferometers) The aim of our Project is to address future techniques and experiments, to study gravitational waves. The observation of such a form of radiation would provide a direct evidence of the mechanisms and laws governing the cosmos and its fabrics, that is it would be a manifestation of the predictions of the general theory of relativity. Some of most exciting phenomena that gravitational waves could bring a wealth of informations on, are supernova explosions and interactions in binary systems that would lead to collisions and fusions. These processes are so strong that the space-time of the Universe would be modified. The produced change would not occur simultaneously and ubiquitously across the cosmos, but would propagate at the speed of light. This is the reason for scientists to refer to such metric perturbations as "gravitational waves".Our ambitious Project has explored an innovative technique, to make this form of radiation interact with a quantum microscopic object, so as to extract important informations on the Universe. Recently, the degree of experimental ability and precision achieved in the field of atom interferometry has become so promising, that a series of analyses on the potential benefits of its applications in gravitational wave astronomy has been an interesting argument for discussion among scientists. Actually there is a new scientific community that is forming, across the field of general relativity and quantum mechanics; its very first meeting has been the Workshop on Gravitational Waves and Atom Interferometry. This international event has been organised by the Supervisor of the Project, in collaboration with Guglielmo Tino.To help the reader to understand the relevance of such a multidisciplinary area, we review the two problems, at whose intersection our Project and investigations are dedicated. One informs the usefulness of the practical devices and how they can be improved. The second is the theoretical description of the interaction of macroscopic and microscopic entities.As for the first point, the state-of-the-art in atom interferometry is advancing at an unprecedented pace. This is going to enable unimaginable investigations, but we must also optimise a detector assembly, its configuration and design parameters to achieve the degree of sensitivity that is necessary. This requires a complete understanding of both the signal that is begin sought and the detector we devise to observe that. Thus a full characterisation of the interactions of the system, with all other forces that might mask the signal of interest is needed, so as to estimate how loud the signal must be to be revealed. We have completed such a characterisation and are ready to compare the predictions of our models with tests and measurements on a small-scale prototype, as it has been done for currently operating long baseline interferometers, in the past.The second problem is the understanding of the interaction of an elusive entity, such as the gravitational waves generated by rotating pulsars or black holes (or even as a stochastic background following the big-bang) with the internal states of a microscopic object. Some in-depth issues in this process are still controversial and, because of the fundamental laws of physics that are involved, our investigations are still work in progress, with some implications being particularly relevant for the response of atom interferometers to gravitational waves at low frequency. This band would be of great interest from a scientific point of view and for this reason we are focusing on this problem.