Interference dynamics of matter-waves of SU($N$) fermions

Abstract

Interacting N-component fermions spatially confined in ring-shaped potentials display specific coherence properties. The orbital angular momentum per particle of such systems can be quantized to fractional values specifically depending on the particle-particle interaction. Here we demonstrate how to monitor the state of the system through homodyne (momentum distribution) and self-heterodyne system's expansion. For homodyne protocols, the momentum distribution is affected by the particle statistics in two distinctive ways. The first effect is a purely statistical one: at zero interactions, the characteristic hole in the momentum distribution around the momentum k=0 opens up once half of the SU(N) Fermi sphere is displaced. The second effect originates from the interaction: The fractionalization in the interacting system manifests itself by an additional "delay" in the flux for the occurrence of the hole, that now becomes a characteristic minimum at k=0. We demonstrate that the angular momentum fractional quantization is reflected in the self-heterodyne interference as specific dislocations in interferograms. Our analysis demonstrates how the study of the interference fringes grants us access to both number of particles and number of components of SU(N) fermions.