Arbitrary linear transformations for photons in the frequency synthetic dimension

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.

Novel optical neural network architecture with the temporal synthetic dimension

“…Therefore, the concept of synthetic dimensions opens an avenue towards establishing flexible experimental platforms to explore a variety of important physics [43][44][45][46]. Most recently, it has been proposed that the ONN with the concept of synthetic dimensions provides a potential route towards the simple ONN design for complicated functionality [47][48][49].…”

Observation of arbitrary topological windings of a non-Hermitian band

“…Our implementation utilizes the concept of a synthetic dimension [34][35][36][37][38]. In particular, we use a synthetic frequency dimension [39][40][41][42][43][44][45] as formed by multiple frequency modes in a ring resonator under amplitude and phase modulations. Our measurement provides direct visualization of non-trivial topological band winding.…”