Orbital Optical Raman Lattice

The spin and orbital are two basic degrees and freedom, which play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we propose an orbital optical Raman lattice to investigate 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. The interplay between them results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which features a global topological chiral orbital current, and the two-dimensional spin-orbital supersolid phase, characterized by the spin and orbital angular momentum density wave patterns. The former has topological Bogoliubov excitations characterized by a uniform Chern number, while the spin-orbit supersolid phase hosts topological excitations with staggered Chern numbers which protect the chiral and antichiral edge modes in the neighboring supersolid clusters. Our finding may open up a new direction in exploring SOC and high-orbital physics in optical lattices, and shall also advance the experimental progress of supersolids in higher dimensions.