# Exceptional Points in a Non-Hermitian Topological Pump

## TL;DR

This paper explores how non-Hermiticity influences topological pumping, revealing a link between edge invariants and exceptional points, with experimental validation in a microwave network.

## Contribution

It uncovers the role of exceptional points in non-Hermitian topological pumps and demonstrates finite-system topological effects experimentally.

## Key findings

- Topological edge invariants relate to exceptional point winding numbers.
- Finite non-Hermitian systems can exhibit topologically nontrivial pumping.
- Experimental observation confirms theoretical predictions.

## Abstract

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. We show that this can be understood in terms of the effects 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.