Topological, multi-mode amplification induced by non-reciprocal, long-range dissipative couplings

TL;DR

This paper explores how non-reciprocal, long-range dissipative couplings in bosonic systems can induce topological, multimode amplification and metastability, with potential realizations in 2D topological insulators.

Contribution

It demonstrates the emergence of unconventional non-reciprocal couplings from a chiral multimode channel and their role in topological amplification phenomena.

Findings

Couplings can produce topological invariants greater than one.

These couplings lead to topological, multimode amplification.

Stable, topological amplifying phases can occur with local parametric drivings.

Abstract

Non-reciprocal couplings or drivings are known to induce steady-state, directional, amplification in driven-dissipative bosonic lattices. This amplification phenomenon has been recently linked to the existence of a non-zero topological invariant defined with the system's dynamical matrix, and thus, it depends critically on the couplings' structure. In this work, we demonstrate the emergence of unconventional, non-reciprocal, long-range dissipative couplings induced by the interaction of the bosonic chain with a chiral, multimode channel, and then study their impact on topological amplification phenomena. We show that these couplings can lead to topological invariant values greater than one which induce topological, multimode amplification and metastability behaviour. Besides, we also show how these couplings can also display topological amplifying phases that are dynamically stable in the presence of local parametric drivings. Finally, we conclude by showing how such phenomena can be naturally obtained in two-dimensional topological insulators hosting multiple edge modes.