The phase of a degenerate Fermi gas

In quantum mechanics, each particle is described by a complex valued wave function characterized by amplitude and phase. When many particles interact each other, cooperative phenomena give rise to a quantum many-body state with a specific quantum coherence. What is the interplay between particle's phase coherence and many-body quantum coherence? Over the years, such question has been object of profound analysis in quantum physics. Here, we demonstrate how state of the art quantum technology allows to explore the question operatively. To this end, we study the time-dependent interference formed by releasing an interacting degenerate Fermi-gas from a specific matter-wave circuit in an effective magnetic field. Particle phase coherence, indicated by the first-order correlator, and many-body quantum coherence, indicated by the noise correlator, are displayed as distinct features of the interferogram. Particle phase coherence produces spiral interference of the Fermi orbitals at intermediate times. Many-body quantum coherence emerges at long times. The coupling between particles coherence and many-body coherence is reflected in a specific dependence of the interference pattern on the effective magnetic field.