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Optics Express

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

Jun Jian, 潘建松, 赵竹芳, Xin Wang, Yong Qin, Wenliang Liu, Yuqing li, Xiaofan Zhou, Jizhou Wu, V. B. Sovkov, Liantuan Xiao, Suotang Jia, Jie Ma

Published May 28, 2026• 0 citations

Abstract

We experimentally investigate the superfluid-Mott insulator transition in a 23 Na 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.

DOI: 10.1364/oe.603556

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We experimentally investigate the superfluid-Mott insulator transition in a 23 Na 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.

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Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.

We study the superfluid--Mott insulator (SF-MI) transition of spin-1 bosons interacting antiferromagnetically in an optical lattice. Starting from a Bose-Hubbard tight-binding model for spin-1 bosons, we obtain the zero-temperature phase diagram by a mean-field approximation. We find that the MI phase with an even number of atoms per site is a spin singlet state, while the MI phase with an odd number of atoms per site has spin 1 at each site in the limit of

t=0

, where

t

is the hopping matrix element. We also show that the superfluid phase is a polar state as in the case for a spin-1 Bose condensate in a harmonic trap. It is found that the MI phase is strongly stabilized against the SF-MI transition when the number of atoms per site is even, due to the formation of singlet pairs. We derive the effective spin Hamiltonian for the MI phase with one atom per site and briefly discuss the spin order in the MI phase.

Mott insulator to superfluid phase transitions and unconventional superfluid phases in spin-orbit coupled Bose-Einstein condensate in one dimensional, square and hexagonal optical lattices are investigated using decoupling approximation and variational Gutzwiller wave function. We considered a system with two components. In the first part, we used decoupling approximation along side perturbation to chart the phase diagrams of the system in the absence of spin-orbit coupling. Our results show that the occupation number of the species, interspecies interaction and the ratio of the hopping matrix of the species dictate the critical point and the separation of the insulating phases. Applying decoupling approximation to spin-orbit coupled Bose-Einstein condensate in one dimensional optical we find that spin-orbit coupling reduces the phase boundary of Mott insulator-superfluid transition and also modifies the critical point in a way that the critical point reduces as the coupling strength increases. In the second part, we applied the variational Gutzwiller wave function to spin-orbit coupled Bose-Einstein condensate in square and hexagonal lattice. Our results show that the geometry of the optical lattice plays a role in the transition. We find that the mean-field Mott insulator-superfluid phase transition boundary of hexagonal lattice is smaller than that of square lattice for the same system. Finally, we showed that the Gutzwiller variational approach gives us access to the twisted superfluid phase realized in the system. The nonuniformity of the superfluid phase is different for the two lattices.

The transition from a superfluid to a Mott-insulator (MI) phase has been observed in a Bose-Einstein condensate (BEC) of ytterbium (Yb) atoms in an optical lattice. An all-optically produced BEC of

^{174}\text{Y}\text{b}

atoms was loaded into three-dimensional optical lattices produced by a 532 nm laser beam. The interference pattern was measured after releasing the quantum gas from the trapping potential. As increasing the optical lattice depth, we observed the disappearance of the interference patterns, which is a signature of entering the MI regime. This result is an important step into studies by using a combination of the MI state and the ultranarrow optical transition of ultracold alkaline-earth-metal-like atoms.

The superfluid to one-dimensional Mott-insulator transition of a 87Rb Bose-Einstein condensate is demonstrated. In the experiment, we apply a one-dimensional optical lattice, formed by two laser beams with a wavelength of 852 nm, to a three dimensional BEC in a shallow trap. We use Kapitza-Dirac scattering to determine the depth of the optical lattice without knowledge of its exact geometry. We further study the dynamics of the transition as well as steady-state phase behavior specific to the one-dimensional case.