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

Carlos Vega; Alberto Muñoz de las Heras; Diego Porras; Alejandro González-Tudela

doi:10.22331/q-2025-09-18-1861

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

Carlos Vega, Alberto Muñoz de las Heras, Diego Porras, and Alejandro González-Tudela

Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain.

Published:	2025-09-18, volume 9, page 1861
Editor:	Carlo Beenakker
Eprint:	arXiv:2405.10176v4
Doi:	https://doi.org/10.22331/q-2025-09-18-1861
Citation:	Quantum 9, 1861 (2025).

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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, multi-mode 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, multi-mode 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.

Featured image: Driven dissipative bosonic lattice coupled to chiral, multi-mode waveguide giving rise to topological multi-mode amplification.

Popular summary

Amplification—making signals stronger without adding much noise—is essential for technologies ranging from radio astronomy to quantum computing. A key challenge is achieving amplification that works only in one direction, avoiding unwanted feedback that disrupts delicate quantum systems. This article explores a new mechanism for such directional amplification by engineering unusual, long-range, and one-way couplings between light fields. These couplings emerge when arrays of photonic cavities interact with special waveguides that allow excitations to move only in one direction, similar to how edge states behave in topological insulators. The authors show that these arrangements can give rise to amplification channels protected by the system’s topology, meaning they are robust against imperfections.

What makes the work stand out is the discovery that, unlike previously studied cases, these systems can host multiple simultaneous amplification channels. This leads not only to stronger amplification but also to new dynamical behaviors, such as metastable states where signals linger in unusual ways before stabilizing. The study also proposes how such effects could be realized experimentally using photonic lattices and topological insulators made of microwave resonators. In the long term, this approach could open new routes for designing noise-resilient amplifiers and signal routers for quantum technologies, where controlling light and information with stability and precision is crucial.

► BibTeX data

@article{Vega2025topologicalmulti,
  doi = {10.22331/q-2025-09-18-1861},
  url = {https://doi.org/10.22331/q-2025-09-18-1861},
  title = {Topological, multi-mode amplification induced by non-reciprocal, long-range dissipative couplings},
  author = {Vega, Carlos and Heras, Alberto Mu{\~{n}}oz de las and Porras, Diego and Gonz{\'{a}}lez-Tudela, Alejandro},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1861},
  month = sep,
  year = {2025}
}

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[6] Mauro Cirio, Pengfei Liang, and Neill Lambert, "Input-output hierarchical equations of motion", Physical Review A 112 1, 012211 (2025).

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