Universal criticality across spin states: superfluid to Mott insulator transition of an SU(3) spin-1 BEC in a 1D optical lattice.

We experimentally investigate the superfluid-Mott insulator transition in a 23Na spin-1 Bose-Einstein condensate (BEC) with approximate SU(3) spin-rotation symmetry, focusing on the role of spin configurations in shaping the critical behavior. Rabi oscillation images of sodium atoms (F = 1) among three magnetic sublevels in an optical lattice are obtained, with experimental results aligning well with theoretical predictions, indicating robust quantum coherence in the lattice. The phase transition from the superfluid to the Mott insulator is observed by varying the lattice depth. We find the critical behavior is universal for different spin states, which is attributed to the SU(3) rotation symmetry among the spin components. The experimentally proposed critical regimes are consistent with the theoretical estimation given by the Thomas-Fermi approximation and strong-coupling expansion. These findings demonstrate that the SF-MI transition exhibits relatively unchanged critical behavior across different spin states due to SU(3) symmetry, revealing the universal phase transition for different spin configurations.