Photonic quadrupole topological insulator using orbital-induced synthetic flux

The rich physical properties of multiatomic molecules and crystalline structures are determined, to a significant extent, by the underlying geometry and connectivity of atomic orbitals. This orbital degree of freedom has also been used effectively to introduce structural diversity in a few synthetic materials including polariton lattices nonlinear photonic lattices and ultracold atoms in optical lattices. In particular, the mixing of orbitals with distinct parity representations, such as \(s\) and \(p\) orbitals, has been shown to be especially useful for generating systems that require alternating phase patterns, as with the sign of couplings within a lattice. Here we show that by further breaking the symmetries of such mixed-orbital lattices, it is possible to generate synthetic magnetic flux threading the lattice. This capability allows the generation of multipole higher-order topological phases in synthetic bosonic platforms, in which \(\pi\) flux threading each plaquette of the lattice is required, and which to date have only been implemented using tailored connectivity patterns. We use this insight to experimentally demonstrate a quadrupole photonic topological insulator in a two-dimensional lattice of waveguides that leverage modes with both \(s\) and \(p\) orbital-type representations. We confirm the nontrivial quadrupole topology of the system by observing the presence of protected zero-dimensional states, which are spatially confined to the corners, and by confirming that these states sit at the band gap. Our approach is also applicable to a broader range of time-reversal-invariant synthetic materials that do not allow for tailored connectivity, e.g. with nanoscale geometries, and in which synthetic fluxes are essential.