# Topological Amplification in Photonic Lattices

## TL;DR

This paper introduces a topological framework for analyzing quantum amplification in photonic lattices, demonstrating stable, disorder-robust non-reciprocal amplification using topological insulator models.

## Contribution

It establishes a formal link between singular value decomposition of non-Hermitian matrices and topological band theory in photonic systems, enabling new insights into quantum amplification.

## Key findings

- Topological phases enable stable quantum amplification.
- Amplification process is robust against disorder.
- Photonic cavities can be mapped to topological insulator models.

## Abstract

We present a characterization of topological phases in photonic lattices. Our theory relies on a formal equivalence between the singular value decomposition of the non-Hermitian coupling matrix and the diagonalization of an effective Hamiltonian. By means of that mapping we unveil an application of topological band theory to the description of quantum amplification with non-reciprocal systems. We exemplify our ideas with an array of photonic cavities which can be mapped into a topological insulator Hamiltonian in the AIII symmetry class. We investigate stability properties and prove the existence of stable topologically non-trivial steady-state phases. Finally, we show numerically that the topological amplification process is robust against disorder in the lattice parameters.