This project focusses on realizing and studying a new hybrid ultra-cold atom-ion system for studying quantum many-body physics. It combines state-of-the-art technologies in quantum optics and quantum gases. The proposed system of cold (fermionic) atoms interacting with ion crystals has surprising analogies with natural solid state systems and molecules, with now by fermionic 6Li atoms in place of electrons and heavy 174Yb+ ions in place of ionic cores. In particular, an atomic band structure may arise with tunable atom-phonon interactions. The proposed experimental approach is inspired by advances in pioneering experiments with hybrid atom-ion systems. By using a new atom-ion combination that has the highest experimentally feasible mass ratio of 29 (Li and Yb+), heating due to the dynamical trapping potential of the ions is suppressed. This eliminates an important road block in existing hybrid atom-ion experiments towards reaching deep into the quantum regime. I will use optical micro-traps in conjunction with segmented ion traps to study the system in a regime with a small number of atoms (1-100) and ions. This offers unprecedented control over the quantum states of atoms and ions. Engineering non-classical states in the ions will allow for quantum enhanced measurements of the combined atom-ion system, with single atom and single collision resolution. State-dependence in the atom-ion interactions can be employed to engineer quantum potentials for the atoms, leading to large scale ion-atomic Schrödinger cat-type entanglement.