A Quantum Coherence Microscope in the Hubbard Regime
Quantum coherence underlies collective quantum phenomena and emerging quantum technologies. Quantum gas microscopes have transformed quantum simulation by providing projective snapshots of many-body states with single-atom resolution, but spatially resolved measurements of off-diagonal correlations have remained elusive. Here, using the Talbot effect, we introduce a quantum coherence microscope that maps off-diagonal correlations onto site-resolved density signals with near-single-site resolution. We use this technique to locally probe the superfluid-Mott transition in a layer of a three-dimensional optical lattice and to measure coherence beyond nearest neighbors in an engineered potential landscape. By mapping off-diagonal correlations onto density signals through controlled Talbot evolution, this work opens new possibilities for accessing observables beyond the density basis through tailored matter-wave evolution and recapture.