  The discovery of the quantization of particle transport in adiabatic pumping
cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked
the Chern number, a topological invariant characterizing the quantum Hall
effect in two-dimensional electron gases, with the topology of dynamical
periodic systems in one dimension. Here, we demonstrate its counterpart for
higher-order topology. Specifically, we show that adiabatic cycles in
two-dimensional crystals with vanishing dipole moments (and therefore zero
overall particle transport) can nevertheless be topologically nontrivial. These
cycles are associated with higher-order topology and can be diagnosed by their
ability to produce corner-to-corner transport in certain metamaterial
platforms. We experimentally verify the corner to corner transport associated
with this topological pump by using an array of photonic waveguides
adiabatically modulated in their separations and refractive indices. By mapping
the dynamical phenomenon demonstrated here from two spatial and one temporal
dimensions to three spatial dimensions, our observations are equivalent to the
observation of chiral hinge states in a three-dimensional second-order
topological insulator.
