Arbitrary linear transformations for photons in the frequency synthetic dimension

An optoacoustic field-programmable perceptron for recurrent neural networks

Recurrent neural networks (RNNs) can process contextual information such as time series signals and language. But their tracking of internal states is a limiting factor, motivating research on analog implementations in photonics. While photonic unidirectional feedforward neural networks (NNs) have demonstrated big leaps, bi-directional optical RNNs present a challenge: the need for a short-term memory that (i) programmable and coherently computes optical inputs, (ii) minimizes added noise, and (iii) allows scalability. Here, we experimentally demonstrate an optoacoustic recurrent operator (OREO) which meets (i, ii, iii). OREO contextualizes the information of an optical pulse sequence via acoustic waves. The acoustic waves link different optical pulses, capturing their information and using it to manipulate subsequent operations. OREO's all-optical control on a pulse-by-pulse basis offers simple reconfigurability and is used to implement a recurrent drop-out and pattern recognition of 27 optical pulse patterns. Finally, we introduce OREO as bi-directional perceptron for new classes of optical NNs.

Programmable Photonic Time Circuits for Highly Scalable Universal Unitaries

Programmable photonic circuits (PPCs) have garnered substantial interest for their potential in facilitating deep learning accelerations and universal quantum computations. Although photonic computation using PPCs offers ultrafast operation, energy-efficient matrix calculations, and room-temperature quantum states, its poor scalability hinders integration. This challenge arises from the temporally one-shot operation of propagating light in conventional PPCs, resulting in a light-speed increase in device footprints. Here we propose the concept of programmable photonic time circuits, utilizing time-cycle-based computations analogous to gate cycling in the von Neumann architecture and quantum computation. Our building block is a reconfigurable SU(2) time gate, consisting of two resonators with tunable resonances, and coupled via time-coded dual-channel gauge fields. We demonstrate universal U(N) operations with high fidelity using an assembly of the SU(2) time gates, substantially improving scalability from O(N^{2}) to O(N) in terms of both the footprint and the number of gates. This result paves the way for PPC implementation in very large-scale integration.

Interferometer for Dispersive Measurements

We suggest the use of broadband frequency modulation to construct a novel type of optical interferometer. This interferometer is insensitive to optical phase and allows measurement of the group velocity and group velocity dispersion without the need for short pulse apparatus.

Photonic Topological Spin Pump in Synthetic Frequency Dimensions

Reducing geometrical complexity while preserving desired wave properties is critical for proof-of-concept studies in wave physics, as evidenced by recent efforts to realize photonic synthetic dimensions, isospectrality, and hyperbolic lattices. Laughlin's topological pump, which elucidates quantum Hall states in cylindrical geometry with a radial magnetic field and a time-varying axial magnetic flux, is a prime example of these efforts. Here we propose a two-dimensional dynamical photonic system for the topological pumping of pseudospin modes by exploiting synthetic frequency dimensions. The system provides the independent control of pseudomagnetic fields and electromotive forces achieved by the interplay between mode-dependent and mode-independent gauge fields. To address the axial open boundaries and azimuthal periodicity of the system, we define the adjusted local Chern marker with rotating azimuthal coordinates, proving the nontrivial topology of the system. We demonstrate the adiabatic pumping for crosstalk-free frequency conversion with wave front molding. Our approach allows for reproducing Laughlin's thought experiment at room temperature with a scalable setup.

Experimental realization of convolution processing in photonic synthetic frequency dimensions

Convolution is an essential operation in signal and image processing and consumes most of the computing power in convolutional neural networks. Photonic convolution has the promise of addressing computational bottlenecks and outperforming electronic implementations. Performing photonic convolution in the synthetic frequency dimension, which harnesses the dynamics of light in the spectral degrees of freedom for photons, can lead to highly compact devices. Here, we experimentally realize convolution operations in the synthetic frequency dimension. Using a modulated ring resonator, we synthesize arbitrary convolution kernels using a predetermined modulation waveform with high accuracy. We demonstrate the convolution computation between input frequency combs and synthesized kernels. We also introduce the idea of an additive offset to broaden the kinds of kernels that can be implemented experimentally when the modulation strength is limited. Our work demonstrate the use of synthetic frequency dimension to efficiently encode data and implement computation tasks, leading to a compact and scalable photonic computation architecture.

Enabling scalable optical computing in synthetic frequency dimension using integrated cavity acousto-optics

Optical computing with integrated photonics brings a pivotal paradigm shift to data-intensive computing technologies. However, the scaling of on-chip photonic architectures using spatially distributed schemes faces the challenge imposed by the fundamental limit of integration density. Synthetic dimensions of light offer the opportunity to extend the length of operand vectors within a single photonic component. Here, we show that large-scale, complex-valued matrix-vector multiplications on synthetic frequency lattices can be performed using an ultra-efficient, silicon-based nanophotonic cavity acousto-optic modulator. By harnessing the resonantly enhanced strong electro-optomechanical coupling, we achieve, in a single such modulator, the full-range phase-coherent frequency conversions across the entire synthetic lattice, which constitute a fully connected linear computing layer. Our demonstrations open up the route toward the experimental realizations of frequency-domain integrated optical computing systems simultaneously featuring very large-scale data processing and small device footprints.

Creating boundaries along a synthetic frequency dimension

Synthetic dimensions have garnered widespread interest for implementing high dimensional classical and quantum dynamics on low-dimensional geometries. Synthetic frequency dimensions, in particular, have been used to experimentally realize a plethora of bulk physics effects. However, in synthetic frequency dimension there has not been a demonstration of a boundary which is of paramount importance in topological physics due to the bulk-edge correspondence. Here we construct boundaries in the frequency dimension of dynamically modulated ring resonators by strongly coupling an auxiliary ring. We explore various effects associated with such boundaries, including confinement of the spectrum of light, discretization of the band structure, and the interaction of boundaries with one-way chiral modes in a quantum Hall ladder, which exhibits topologically robust spectral transport. Our demonstration of sharp boundaries fundamentally expands the capability of exploring topological physics, and has applications in classical and quantum information processing in synthetic frequency dimensions.

Meta-programmable analog differentiator

We present wave-based signal differentiation with unprecedented fidelity and flexibility by purposefully perturbing overmoded random scattering systems such that zeros of their scattering matrices lie exactly at the desired locations on the real frequency axis. Our technique overcomes limitations of hitherto existing approaches based on few-mode systems, both regarding their extreme vulnerability to fabrication inaccuracies or environmental perturbations and their inability to maintain high fidelity under in-situ adaptability. We demonstrate our technique experimentally by placing a programmable metasurface with hundreds of degrees of freedom inside a 3D disordered metallic box. Regarding the integrability of wave processors, such repurposing of existing enclosures is an enticing alternative to fabricating miniaturized devices. Our over-the-air differentiator can process in parallel multiple signals on distinct carriers and maintains high fidelity when reprogrammed to different carriers. We also perform programmable higher-order differentiation. Conceivable applications include segmentation or compression of communication or radar signals and machine vision.

Synthetic dimension band structures on a Si CMOS photonic platform

Synthetic dimensions, which simulate spatial coordinates using nonspatial degrees of freedom, are drawing interest in topological science and other fields for modeling higher-dimensional phenomena on simple structures. We present the first realization of a synthetic frequency dimension on a silicon ring resonator integrated photonic device fabricated using a CMOS process. We confirm that its coupled modes correspond to a one-dimensional tight-binding model through acquisition of up to 280-GHz bandwidth optical frequency comb-like spectra and by measuring synthetic band structures. Furthermore, we realized two types of gauge potentials along the frequency dimension and probed their effects through the associated band structures. An electric field analog was produced via modulation detuning, whereas effective magnetic fields were induced using synchronized nearest- and second nearest-neighbor couplings. Creation of coupled mode lattices and two effective forces on a monolithic Si CMOS device represents a key step toward wider adoption of topological principles.

Topological complex-energy braiding of non-Hermitian bands

Effects connected with the mathematical theory of knots¹ emerge in many areas of science, from physics^2,3 to biology⁴. Recent theoretical work discovered that the braid group characterizes the topology of non-Hermitian periodic systems⁵, where the complex band energies can braid in momentum space. However, such braids of complex-energy bands have not been realized or controlled experimentally. Here, we introduce a tight-binding lattice model that can achieve arbitrary elements in the braid group of two strands 𝔹₂. We experimentally demonstrate such topological complex-energy braiding of non-Hermitian bands in a synthetic dimension^6,7. Our experiments utilize frequency modes in two coupled ring resonators, one of which undergoes simultaneous phase and amplitude modulation. We observe a wide variety of two-band braiding structures that constitute representative instances of links and knots, including the unlink, the unknot, the Hopf link and the trefoil. We also show that the handedness of braids can be changed. Our results provide a direct demonstration of the braid-group characterization of non-Hermitian topology and open a pathway for designing and realizing topologically robust phases in open classical and quantum systems.