We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two-dimensional optical lattice, focusing on the spin-1 spin-orbit-coupled system recently realized at the Joint Quantum Institute [Campbell et al., arXiv:1501.05984]. We find a rich quantum phase diagram where, in addition to the conventional phases---superfluid and insulator---contained in the spin-1 Bose-Hubbard model, there are new lattice symmetry breaking phases. For weak interactions, the interplay between two length scales, the lattice momentum and the spin-orbit wave vector, induce a phase transition from a uniform superfluid to a phase where bosons simultaneously condense at the center and edge of the Brillouin zone at a nonzero spin-orbit strength. This state is characterized by spin-density-wave order, which arises from the spin-1 nature of the system. Interactions suppress spin-density-wave order, and favor a superfluid only at the Brillouin zone edge. This state has spatially oscillating mean-field order parameters, but a homogeneous density. We show that the spin-density-wave superfluid phase survives in a two-dimensional harmonic trap, and thus establish that our results are directly applicable to experiments on $^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}$ , and $^{41}\mathrm{K}$ .We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two-dimensional optical lattice, focusing on the spin-1 spin-orbit-coupled system recently realized at the Joint Quantum Institute [Campbell et al., arXiv:1501.05984]. We find a rich quantum phase diagram where, in addition to the conventional phases---superfluid and insulator---contained in the spin-1 Bose-Hubbard model, there are new lattice symmetry breaking phases. For weak interactions, the interplay between two length scales, the lattice momentum and the spin-orbit wave vector, induce a phase transition from a uniform superfluid to a phase where bosons simultaneously condense at the center and edge of the Brillouin zone at a nonzero spin-orbit strength. This state is characterized by spin-density-wave order, which arises from the spin-1 nature of the system. Interactions suppress spin-density-wave order, and favor a superfluid only at the Brillouin zone edge. This state has spatially oscillating mean-field order parameters, but a homogeneous density. We show that the spin-density-wave superfluid phase survives in a two-dimensional harmonic trap, and thus establish that our results are directly applicable to experiments on $^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}$, and $^{41}\mathrm{K}$.

arXiv:1509.00005Physical review. B./Physical review. BFeb 1, 201614 citations

Orbital optical Raman lattice

Zhihao Huang, Kou-Han Ma, Bao‐Zong Wang +2 more

Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.

arXiv:2412.04009Physical Review ADec 23, 20250 citations

^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}

, and

^{41}\mathrm{K}