Thermodynamics of a deeply degenerate SU(N)-symmetric Fermi gas

Many-body quantum systems can exhibit a striking degree of symmetry unparallelled in their classical counterparts. In real materials SU(N) symmetry is an idealization, but this symmetry is pristinely realized in fully controllable ultracold alkaline-earth atomic gases. Here, we study an SU(N)-symmetric Fermi liquid of(87)Sr atoms, whereNcan be tuned to be as large as 10. In the deeply degenerate regime, we show through precise measurements of density fluctuations and expansion dynamics that the largeNof spin states under SU(N) symmetry leads to pronounced interaction effects in a system with a nominally negligible interaction parameter. Accounting for these effects, we demonstrate thermometry accurate to 1% of the Fermi energy. We also demonstrate record speed for preparing degenerate Fermi seas enabled by the SU(N)-symmetric interactions, reachingT/T-F = 0.22 with 10 nuclear spin states in 0.6 s working with a laser-cooled sample. This, along with the introduction of a new spin polarizing method, enables the operation of a three-dimensional optical lattice clock in the band insulating regime. Ultracold alkaline-earth fermionic atoms with large number of nuclear spin states possess SU(N) symmetry. That deeply affects their interaction properties, and allows a Fermi gas of these atoms to be cooled quickly to the quantum degenerate regime.