  Topological quantum interference emerges from the interplay between quantum
mechanics and topology. We present evidence for two types of such interference
phenomenon that can result from the quantum dynamics of initial topological
states. We realize both types of topological quantum interference in a pumped
non-Hermitian Su-Schrieffer-Heeger lattice that can be implemented by creation
and coherent control of excitonic states of trapped neutral atoms. On quenching
the system from the topological to the gapless phases and then back again, we
find that interference patterns develop in the gapless phase and also after
switching back to the topological phase. These patterns occur both as
many-excitation interferences generated in the presence of pumping the atoms at
the end sites, and as one- and two-excitation interferences seen in the absence
of pumping when starting with edge excitations. Investigation of the excitation
dynamics shows that these interference patterns originate from the topological
nature of the initial states and are very different from quantum interferences
originating from non-topological states of the lattice. Our results also reveal
that unlike well-known situations where topological states are protected
against local perturbations, in the non-Hermitian SSH systems resulting from
driving the excited state populations, a local dissipation at each lattice site
can suppress both the topological interference and the total population of the
lattice.
