# Breaking Lorentz reciprocity with frequency conversion and delay

## TL;DR

This paper presents a novel, scalable method to break Lorentz reciprocity using frequency conversion and delay, enabling broadband non-reciprocal circuits without magnetic materials, demonstrated by a circulator with high isolation.

## Contribution

The authors introduce a non-reciprocity technique based on non-commuting frequency conversion and delay, leading to scalable, broadband non-reciprocal devices without resonant or magnetic components.

## Key findings

- Achieved >15 dB isolation in a 5-9 GHz circulator
- Constructed universal gyrators for non-reciprocal circuits
- Method applicable to various platforms including superconducting and semiconducting devices

## Abstract

We introduce a method for breaking Lorentz reciprocity based upon the non-commutation of frequency conversion and delay. The method requires no magnetic materials or resonant physics, allowing for the design of scalable and broadband non-reciprocal circuits. With this approach, two types of gyrators --- universal building blocks for linear, non-reciprocal circuits --- are constructed. Using one of these gyrators, we create a circulator with > 15 dB of isolation across the 5 -- 9 GHz band. Our designs may be readily extended to any platform with suitable frequency conversion elements, including semiconducting devices for telecommunication or an on-chip superconducting implementation for quantum information processing.