State University of New York (SUNY) at Buffalo Amherst United States
Topology, which originates from mathematics and deals with quantities that preserve their values during any continuous deformation, has firmly emerged as a new paradigm for describing new phases of matter since its first applications to condensed matter systems over three decades ago. To date, the SSH Hamiltonian serves as an archetypical model for describing topological physics and designing practical structures. However, the topological features of this conventional model are limited to only two dispersion bands, thereby permitting only a limited range of quantum numbers and consequently restricting the accessible nontrivial phases. Much can be gained from richer models with a large range of nontrivial phases that can be manipulated systematically to control the formation of independent topological states. Here, we demonstrate the formation and control of topological edge states associated with multiple topological quantum numbers in a discrete photonic lattice.