Elementary particle physics is entering a spectacular new era in which experiments at the Large Hadron Collider (LHC) at CERN will soon start probing some of the deepest questions in physics, such as: Why is gravity so weak? Do elementary particles have substructure? What is the origin of mass? Are there new dimensions? Can we produce black holes in the lab? Could there be other universes with different physical laws? While the LHC pushes the energy frontier, the unprecedented precision of Atom Interferometry, has pointed me to a new tool for fundamental physics. These experiments based on the quantum interference of atoms can test General Relativity on the surface of the Earth, detect gravity waves, and test short-distance gravity, charge quantization, and quantum mechanics with unprecedented precision in the next decade. This ERC Advanced grant proposal is aimed at setting up a world-leading European center for development of a deeper theory of fundamental physics. The next 10 years is the optimal time for such studies to benefit from the wealth of new data that will emerge from the LHC, astrophysical observations and atom interferometry. This is a once-in-a-generation opportunity for making ground-breaking progress, and will open up many new research horizons.