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 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.

Creating boundaries along a synthetic frequency dimension

“…Recent demonstrations on using perturbations to the cross section of the ring [51,52] promise further flexibility in creating such boundaries. Our results also show that the energy of a synthetic lattice can be confined to a finite number of sites by coupling to additional auxiliary resonators, which is critical in efficient implementations of linear transformations or matrix-vector multiplications [28]. Our work should significantly advance the capabilities of synthetic dimensions in both topological photonics and for optical signal processing.…”

“…Creating a boundary in the synthetic dimension is essential for further exploration of such phenomena in synthetic space. In addition, the creation of boundaries in synthetic dimensions is important for applications such as implementing arbitrary linear transformations for frequency conversion, quantum circuits and photonic neural networks [28].…”

“…In this paper we provide an experimental demonstration for constructing boundaries in synthetic frequency dimensions. Previous theoretical works have investigated synthetic-space boundary effects by assuming sharp [4] or gradual [35] changes in the group-velocity dispersion of the waveguide forming the ring resonator, by strongly coupling an auxiliary ring [28], or by including memory elements [36]. Here we experimentally realize the approach of coupling to auxiliary ring resonators.…”

Synthetic dimension band structures on a Si CMOS photonic platform

“…This work opens the path to harnessing the mature and highly scalable silicon integrated photonics fabrication infrastructure to tackle pressing challenges in quantum simulation and topology science. The high integration density attainable on the Si CMOS platform is poised to greatly increase the level of complexity of lattice models that can be realized on a chip, and to even pursue novel applications for designing optical devices such as isolators [14], or enacting arbitrary linear transformations of photon frequencies [30] by using integrated cavities analogous to the one presented here as a foundational building block. Despite a long list of advantages, which includes high integration density, low cost, and a leading level of standardization, the most notable challenge of using a silicon device platform is optical loss that limits the range of observable emergent lattice phenomena through photon decay.…”

Synthetic frequency dimensions in dynamically modulated ring resonators

“…Towards this end, efficient manipulation of high-dimensional quantum entanglement has been proposed in synthetic space by combining frequency and OAM dimensions 81 . Moreover, unitary transformations for photons along the synthetic frequency dimension has been investigated using electro-optic modulation or with time-resolved photon detection, with prospects for frequencyencoded quantum information processing (QIP) [131][132][133] . On the experimental front, rapid progress in frequency-encoded QIP has been reported using both electro-optic modulation as well as nonlinear wave mixing [134][135][136][137][138][139] , but several challenges regarding loss and scalability remain.…”