Atom interferometers have enabled us to measure forces with exceptionally high precision. Inevitably they average those forces over the free-fall paths of the atoms and thus over up to 10 meters, to take advantage of the quadratic scaling of sensitivity with time of flight. This precludes them from measuring localized forces, such as Casimir-Polder forces, or proposed short range interactions of physics beyond the standard model. To shrink these distances, interferometers have been holding the atoms against gravity in optical lattices which, unfortunately, causes dephasing due to speckles and imperfections of the laser beams. At UC Berkeley, I have built atom interferometers with laser beams that are resonantly amplified and mode-filtered in an optical cavity. Here, I propose to use a far off-resonant optical lattice in a high finesse cavity, which will enable ultra-long interferometry times (up to 10 seconds) to sense with unprecedented sensitivity. While building on my previous work, I will add distinct features like a dichromatic cavity for versatile atom manipulation, an advanced source for ultra-cold and dense atomic samples, and detection with single lattice site (about 500 nm) resolution. This will enable longer lattice holds and sensitive mapping of accelerations with ~1 μm resolution by running simultaneous atom interferometers in up to 100 adjacent lattice sites. These advances will empower us to study in particular: (1) Optically induced inter-particle interactions, in which the interaction strength can be tuned by means of applied optical laser power. This interaction will induce light shifts to close-by atoms, which can be used to quantum mechanically correlate atoms even over several μm. At high laser intensities, this interaction creates optically bound matter, as shown already in nano-sphere experiments, with binding strengths exceeding Van der Waals bounds8, opening the doors for a new class of light-induced collective phenomena and interferometry experiments with optical matter. (2) Atom-surface interactions: Within one mm of surfaces, rich opportunities to discover unconstrained hypothetical forces, large extra dimensions, or new scalar fields await. This is also the realm of forces induced by quantum vacuum fluctuations, like the Casimir-Polder interaction at zero and finite temperatures, including a longer-ranged force induced by blackbody radiation. We will characterize these forces in strength and spatial dependence (1 μm – 1 mm) with unprecedented precision. This will provide us with a better understanding of vacuum fluctuations and blackbody radiation, which may be relevant in astrophysical phenomena such as the Cosmic Microwave Background, or star formation. These projects will also develop technologies which pave the way to highly localized precision measurements of Newton´s constant through the gravitational Aharonov-Bohm effect, which may provide new insights on the way to understanding quantum gravity.