Multiband Topological Heterojunctions on the Surface Nanoscale Axial Photonics Platform

Abstract: Analogue Hamiltonian simulation (AHS) in photonic systems can be an enticing alternative to direct experimental study of complex Hamiltonian systems as a result of the low cost and high degree of control one can have over the system's properties. Notably, the field of topological photonics has emerged in the last decade primarily by simulating tight-binding models of electrons within topologically nontrivial condensed-matter systems. Optical simulation of topologically nontrivial Hamiltonians requires optical resonators with minimal loss and well-matched frequencies whose intersite coupling can also be precisely controlled. The Surface Nanoscale Axial Photonics (SNAP) platform satisfies all these requirements, exhibiting ultra-low loss operation and sub-angstrom fabrication precision, making it an excellent platform for AHS. In this work, we experimentally demonstrate the first topologically nontrivial photonic SNAP devices by coupling together axial modes of adjacent SNAP microresonators to form a variety of Su-Schrieffer-Heeger (SSH) lattices. The devices manifest numerous distinct topological band structures corresponding to each axial mode of the microresonators, enabling us to observe behavior both close to and far from the topological-trivial phase transition. We further expand the scope of topological SNAP systems to contain not just higher-order generalizations of SSH lattices, but junctions between multiband lattices with dissimilar topological phases created by coupling up to 21 uniform and well-matched SNAP microresonators. Analyzing such "heterojunctions" necessitated our development of generalized topological polarization methods. We thus demonstrate the exceptional promise of the SNAP platform for AHS of 1D topological insulators, and also open the door to the potential for simulating >2 dimensional systems by utilizing nonlinear interactions.