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, where N can 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 large N of 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, reaching T / 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.