Interactions and collective excitations in a SU($N$) Fermi gas

Ultracold fermions with SU($N>$2) symmetry offer a unique opportunity to study quantum dynamics and interaction effects in the large spin systems that have no analogue in condensed matter physics. In this poster, we present a set of experiments on the measurement of contact parameters and collective excitations with a SU($N$) Fermi gas of $^{173}$Yb atoms. First, we explore the short-range interaction effect via Tan's contact parameters in a multi-component Fermi gas with SU($N>$2) symmetry. The $s$-wave contact parameter is experimentally measured by recording the high-momentum tail of weakly interacting fermions. For a tunable number of spin component $N$ with a fixed number of atoms per component, we verify the linear increase in the contact with $N$ providing experimental confirmation of SU($N$) interactions. Furthermore, we explore the momentum distribution of SU($N$) fermions at the low momentum regime. Next, we measure collective excitations of a harmonically trapped two-dimensional SU($N$) Fermi gas. Various collective modes are investigated with a tunable number of spin component $N$ showing a decrease in the ratio of quadruple and dipole mode with $N$. Our work will pave the way for the experimental study of interacting SU($N$) Fermi gases with large spin.