The Hubbard model, containing only the minimum ingredients of nearest
neighbor hopping and on-site interaction for correlated electrons, has
succeeded in accounting for diverse phenomena observed in solid-state
materials. One of the interesting extensions is to enlarge its spin symmetry to
SU(N>2), which is closely related to systems with orbital degeneracy. Here we
report a successful formation of the SU(6) symmetric Mott insulator state with
an atomic Fermi gas of ytterbium (173Yb) in a three-dimensional optical
lattice. Besides the suppression of compressibility and the existence of charge
excitation gap which characterize a Mott insulating phase, we reveal an
important difference between the cases of SU(6) and SU(2) in the achievable
temperature as the consequence of different entropy carried by an isolated
spin. This is analogous to Pomeranchuk cooling in solid 3He and will be helpful
for investigating exotic quantum phases of SU(N) Hubbard system at extremely
low temperatures.Comment: 20 pages, 6 figures, to appear in Nature Physic
