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    Orbital optical Raman lattice

    Zhi-Hao Huang1,2,*, Kou-Han Ma1,2,*, Bao-Zong Wang1,2, W. Vincent Liu3,4, and Xiong-Jun Liu1,2,4,†

    • 1International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China
    • 2Hefei National Laboratory, Hefei 230088, China
    • 3Department of Physics and Astronomy and IQ Initiative, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
    • 4International Quantum Academy, Shenzhen 518048, China

    • *These authors contributed equally to this work.
    • †Contact author: xiongjunliu@pku.edu.cn

    Phys. Rev. A 113, 023301 – Published 2 February, 2026

    DOI: https://doi.org/10.1103/zdrw-kcpf

    Abstract

    The 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 by proposing an alternative 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: a uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and a two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density-wave patterns and by the chiral and antichiral topological edge excitations with a staggered Chern-number distribution as predicted here for supersolid phases. 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.

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