Andreas Nunnenkamp, University of Cambridge, UK

Directional amplification, in which signals are selectively amplified depending on their direction of propagation, has attracted much attention as a key resource for applications, including quantum information processing. Recently, several, physically very different, directional amplifiers have been proposed and realized in the lab. In this work, we present a unifying framework based on topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. More specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the spectrum of the dynamic matrix of the system and the regimes of directional amplification, in which the end-to-end gain grows exponentially with the number of cavities. We compute analytically the scattering matrix, the gain and reverse gain, showing their explicit dependence on the value of the topological invariant. Parameter regimes achieving directional amplification can be elegantly obtained from a topological `phase diagram', which provides a guiding principle for the design of both phase-preserving and phase-sensitive multimode directional amplifiers. Our results are of direct relevance for optomechanical systems, superconducting circuits, and the emerging field of topolectrical circuits.

References: [1] C.C. Wanjura, M. Brunelli, A. Nunnenkamp, arXiv:1909.11647 (2019).