Maxwell Quasiparticles Emerged in Optical Lattices

We construct a two-dimensional tight-binding model of an optical lattice, where the low energy excitations should be described by the spin-1 Maxwell equations in the Hamiltonian form, and such linear dispersion excitations with pesudospin-1 are so called as the Maxwell quasiparticles. The system has rich topological features, for examples, the threefold degeneracy points called Maxwell points may have nontrivial $\pm 2\pi$ Berry phases and the anomalous quantum Hall effect with spin-momentum locking may appear in topological Maxwell insulators. We propose realistic schemes for realizing the Maxwell metals/insulators and detecting the intrinsic properties of the topological Maxwell quasiparticles with ultracold atoms in optical lattices.