Quantum interference of topological states in a pumped Su-Schrieffer-Heeger lattice

We propose a realization of topological quantum interference in a pumped non-Hermitian Su-Schrieffer-Heeger (SSH) lattice that can be implemented by creation and coherent control of excitonic states of trapped neutral atoms. Our approach is based on quenching the system from the topological to the gapless phase and then back again, by switching the value of the laser phase controlling the lattice potential. We find interference patterns following switching in the occupation probabilities of excitations on lattice sites. These occur both as many-excitation interferences in the presence of pumping, and interferences seen in the absence of pumping when starting with edge excitations. Investigation of the excitation dynamics shows that these interference patterns which originate from the topological nature of the initial states, are very different from 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 these non-Hermitian SSH systems a local dissipation at each lattice site can suppress both the topological interference and the total population of the lattice.