Arbitrary linear transformations for photons in the frequency synthetic dimension

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 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. Photonic processors that can perform arbitrary tasks are in demand for many applications. Here, the authors present a photonic architecture using waveguide and resonator couplings to perform arbitrary linear transformations, by taking advantage of the frequency synthetic dimension.

Automated summary

Researchers have proposed a photonic architecture for arbitrary linear transformations by utilizing the synthetic frequency dimension, achieving near-unity fidelity with favorable scaling. The structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes, enabling various manipulations and transformations in both classical and quantum domains.