This Master 2 internship proposal focuses on coherent processes in matter waves with engineered symmetries and interactions, exploring the quantum effects that challenge classical diffusive behaviors. Classical particles in chaotic systems experience diffusion and ergodicity, but in the quantum realm, interference can lead to phenomena like localization, breaking this diffusion. Coherent forward and backward scattering, influenced by system symmetries, is a key aspect of this. Additionally, understanding how localization and ergodicity evolve in many-body systems with interactions is an area of active research. The Cold Atoms team at LCAR in Toulouse studies quantum chaos experimentally, using rubidium atoms in optical lattice traps. They previously observed chaos-assisted dynamical tunneling and recently measured coherent scattering peaks with matter waves. This internship will develop new engineered dynamics using cold atoms to further investigate the role of symmetries and interactions in chaotic dynamics. The candidate will use numerical models and experimental setups, including engineered symmetries in synthetic lattices and the study of interactions in tunneling dynamics. Besides the actual experimental setup currently used, a new (quite advanced) experimental setup is being developed to explore many-body quantum chaos with enhanced stability, optical access, and control over optical potentials I the course of the PhD project following the internship.