Topological amplification in driven-dissipative lattices

Abstract

A proper characterization of non-trivial topological phases in dissipative systems is highly non-trivial. However, quantum simulator setups offer us exciting possibilities to implement quantum many-body phases which should show the emergence of topological non-trivial phenomena. This is the case of superconducting circuits, trapped ion crystals or ultra-cold atom setups, where couplings between sites can be controlled to break time-reversal symmetry and induce effective gauge fields. In this work we present a definition of topological invariants for driven dissipative lattices that relies on a formal mapping between a non-Hermitian coupling matrix and an effective band Hamiltonian. In a nutshell, our work allows to extend the formalism of topological band theory to dissipative bosonic lattices. Our formalism shows a link between directional amplification and non-trivial topological phenomena, leading to the concept of >topological amplifier>. We present a proposal to implement our ideas with superconducting circuits.