Phase coherence in a homogeneous fermionic Hubbard system

Phase coherence, characterized by well-defined relative phases between quantum states, plays an essential role in a wide range of quantum phenomena, such as quantum entanglement, superconductivity and superfluidity. Interference patterns of ultracold fermionic atoms, observed after ballistic expansion from optical lattices, provide direct access to fundamental properties of strongly correlated system, including phase coherence and non-local correlations. However, phase coherence in fermionic lattices is inherently fragile and remains challenging to access, as it is strongly suppressed by finite temperature and spatial inhomogeneity. Here, we report the observation and quantitative characterization of interference patterns in a low-temperature, homogeneous fermionic Hubbard system. First-order correlation is extracted from the interference patterns, directly reflecting the short-range phase coherence. By mapping the first-order correlation as a function of lattice filling and interaction strength, we observe a crossover from metal to a Mott insulator. In addition, the emergence of long-range phase coherence associated with the superfluid phase is also manifested in our system.