"The control of the interaction between light and matter has made impressive progress in the latest two decades, paving the way for applications in quantum technologies. Such progress also lies on the advances in cooling and trapping techniques, which allow the preparation of atomic ensembles at very low temperatures. The coupling of light to different degrees of freedom in atomic ensembles is a very promising playground to investigate new quantum phenomena. An interesting case with a large potential to unveil new physics is that of the coupling of the multimode quantized motion of an atomic ensemble to optical modes confined in a cavity. The dynamics of the atomic motion is expected to be strongly modified by the cavity photons mediating the interactions between collective vibrational modes (phonons).In the present project I intend to construct the theoretical framework to characterize the dynamics of an atomic array inside a cavity resonator in terms of a new quantum interface between light and the collective atomic motion. I will propose the protocols to obtain squeezed phonon modes and multipartite phonon entanglement, with the use of an optical quantum reservoir. I will study the relationship between the quantum state of the intracavity phonon-photon coupled system and the light leaking out of the cavity. I will thus theoretically explore the requirements and find the optimal conditions to use this system for quantum information and metrology. In the last part of the project, I will extend the model to include the coupling of light to internal degrees of freedom of the atoms, like their spin. Such a hybrid system where the interplay between light, motion and spin can be controlled opens new avenues in the field of quantum optics, in particular with perspectives for quantum simulations of complex system.The project will be realised at the University of Saarland (Germany) in the group of G. Morigi, and will include intense exchange with experimental groups."