Arbitrary linear transformations for photons in the frequency synthetic dimension

TL;DR

This paper introduces a reconfigurable photonic architecture utilizing the synthetic frequency dimension of photons to perform arbitrary linear transformations with high fidelity, enabling advanced applications in classical and quantum photonics.

Contribution

The authors develop a novel photonic structure with dynamically modulated micro-ring resonators that can implement any linear transformation in the frequency domain, using inverse design and automatic differentiation.

Findings

Achieved near-unity fidelity in arbitrary transformations

Demonstrated reconfigurability for multiple photonic manipulations

Scalable and compact design suitable for integrated photonics

Abstract

Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a new photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology.