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We calculate the frequency of collective modes of a one-dimensionalrepulsively interacting Fermi gas with high-spin symmetry confined in harmonictraps at zero temperature. This is a system realizable with fermionicalkaline-earth-metal atoms such as $^{173}$Yb, which displays an exactSU($\kappa$) spin symmetry with $\kappa\geqslant2$ and behaves like a spinlessinteracting Bose gas in the limit of infinite spin components$\kappa\rightarrow\infty$, namely high-spin bosonization. We solve thehomogeneous equation of state of the high-spin Fermi system by using Betheansatz technique and obtain the density distribution in harmonic traps based onlocal density approximation. The frequency of collective modes is calculated byexactly solving the zero-temperature hydrodynamic equation. In the limit oflarge number of spin-components, we show that the mode frequency of the systemapproaches to that of a one-dimensional spinless interacting Bose gas, as aresult of high-spin bosonization. Our prediction of collective modes is inexcellent agreement with a very recent measurement for a Fermi gas of$^{173}$Yb atoms with tunable spin confined in a two-dimensional tight opticallattice.

Collective mode evidence of high-spin bosonization in a trapped one-dimensional atomic Fermi gas with tunable spin