Realizing a spatially correlated lattice interferometer

Atom interferometers provide a powerful tool for measuring physical constants and affirming fundamental physics with unprecedented precision. The sensitivity of atom interferometers is significantly enhanced by optical lattices and coherent atomic sources. However, their interplay gives rise to additional complexities and intriguing phenomena. Here, we report on realizing a Ramsey-Bord\'e interferometer of coherent matter waves modified by a moving optical lattice in a gravitational field, and explore a resulting multipath interference with tunable coherence. We investigate spatial correlations of atoms both within the lattice and between two arms by interferometry, and observed the emerging multiple interference peaks of the Bose-Einstein condensate with sublattice site resolution. Our findings agree well with simulations, paving the way for high-precision interferometry and exploring rich interferometer phenomena using ultracold atoms.