  Topological photonic systems offer light transport that is robust against
defects and disorder, promising a new generation of chip-scale photonic devices
and facilitating energy-efficient on-chip information routing and processing.
However, present quasi one-dimensional designs, such as the
Su-Schrieffer-Heeger (SSH) and Rice-Mele (RM) models, support only a limited
number of nontrivial phases due to restrictions on dispersion band engineering.
Here, we experimentally demonstrate a flexible topological photonic lattice on
a silicon photonic platform that realizes multiple topologically nontrivial
dispersion bands. By suitably setting the couplings between the one-dimensional
waveguides, different lattices can exhibit the transition between multiple
different topological phases and allow the independent realization of the
corresponding edge states. Heterodyne measurements clearly reveal the ultrafast
transport dynamics of the edge states in different phases at a femto-second
scale, validating the designed topological features. Our study equips
topological models with enriched edge dynamics and considerably expands the
scope to engineer unique topological features into photonic, acoustic and
atomic systems.
