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We analyze the two main physical observables related to the momenta ofstrongly correlated SU($N$) fermions in ring-shaped lattices pierced by aneffective magnetic flux: homodyne (momentum distribution) and self-heterodyneinterference patterns. We demonstrate how their analysis allows us to monitorthe persistent current pattern. We find that both homodyne and self-heterodyneinterference display a specific dependence on the structure of the Fermidistribution and particles' correlations. For homodyne protocols, the momentumdistribution is affected by the particle statistics in two distinctive ways.The first effect is a purely statistical one: at zero interactions, thecharacteristic hole in the momentum distribution around the momentum$\mathbf{k}=0$ opens up once half of the SU($N$) Fermi sphere is displaced. Thesecond effect originates from interaction: the fractionalization in theinteracting system manifests itself by an additional `delay' in the flux forthe occurrence of the hole, that now becomes a depression at $\mathbf{k}=0$. Inthe case of self-heterodyne interference patterns, we are not only able tomonitor, but also observe the fractionalization. Indeed, the fractionalizedangular momenta, due to level crossings in the system, are reflected indislocations present in interferograms. Our analysis demonstrate how the studyof the interference fringes grants us access to both number of particles andnumber of components of SU($N$) fermions.

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