  The Su-Schrieffer-Heeger (SSH) model perhaps is the easiest and the most
basic model for topological excitations. Many variations and extensions of the
SSH model have been proposed and explored to better understand both fundamental
and novel aspects of topological physics. The SSH4 model has been proposed
theoretically as an extended SSH model with higher dimension (the internal
dimension changes from two to four). It has been proposed that the winding
number in this system can be determined through a higher-dimensional extension
of the mean chiral displacement measurement, however this has not yet been
verified in experiment. Here we report the realization of this model with
ultracold atoms in a momentum lattice. We verify the winding number through
measurement of the mean chiral displacement in a system with higher internal
dimension, we map out the topological phase transition in this system, and we
confirm the topological edge state by observation of the quench dynamics when
atoms are initially prepared at the system boundary.
