Exceptional points in a non-Hermitian topological pump

We investigate the effects of non-Hermiticity on topological pumping and uncover a connection between a topological edge invariant based on topological pumping and the winding numbers of exceptional points. In Hermitian lattices, it is known that the topologically nontrivial regime of the topological pump only arises in the infinite-system limit. In finite non-Hermitian lattices, however, topologically nontrivial behavior can also appear, and we show that this can be understood as the effect of encircling a pair of exceptional points during a pumping cycle. This phenomenon is observed experimentally in a non-Hermitian microwave network containing variable-gain amplifiers.