Interference and Short-Range Correlation in Fermionic Hubbard Gases.

The interference patterns of ultracold atoms, observed after ballistic expansion from optical lattices, encode essential information about strongly correlated lattice systems, including phase coherence and nonlocal correlations. While the interference of lattice bosons has been extensively investigated, quantitative studies of the lattice fermion interference remain challenging. Here, we report the observation and quantitative characterization of interference patterns in low-temperature, homogeneous fermionic Hubbard gases. We develop a general method to extract the quasimomentum distribution and the first-order correlation function from these patterns. In the noninteracting limit, the coherence length remains very close to the average spacing between identical fermions over a wide range of fillings, revealing the fundamental upper bound imposed by Pauli exclusion on first-order coherence. By tuning the interaction strength and filling, we identify their interplay in the suppression of first-order coherence across the metal-to-Mott-insulator crossover. Moreover, at half filling, the measured correlations agree well with quantum Monte Carlo calculations and remain finite in the strong repulsion regime, revealing virtual tunneling and the underlying superexchange physics.