image: Figure | Scheme and experimental setup. a, The dynamics of light with resonator under periodic electro-optic modulation. Each resonant peak of the resonator, separated by the FSR ΩR, hosts a series of frequency-lattice sites selected by low-frequency RF signal ΩR. By coupling the intra-resonant frequency sites of two resonators, complex lattice models can be engineered. The lattice network incorporates three types of couplings: local modulation on the resonator (green), along with DC (yellow) and RF (blue) signals applied to the MZI. b, Schematic of setup for detecting band structures and photon distribution on sites. Three DC+RF signal sets are applied via Bias-Tees to ground-signal-ground (GSG) electrodes, controlling resonators (S1, S3) and MZI (S2). The RF signal is generated by a microwave source or an arbitrary waveform generator (AWG), and is connected to a power amplifier before connected to the Bias-Tees. The letter pairs (A1, A2 ~ F1, F2) denote transmission connections between the panels for electrical circuits and optical paths. Band structure detection employs a Δω -detuned probe laser, with time-resolved transmittance (revealing quasi-momentum slices) captured by a photodetector (PD) and oscilloscope. The top-right figure presents a characteristic band structure reconstructed from temporally stacked transmittance spectra. The acousto-optic modulator (AOM) is used in the heterodyne detection optical path to shift the frequency of a portion of the incident laser, and the site distribution measurements utilize the heterodyne optical path with a PD.
Credit: Yi-Tao Wang et al.
Synthetic dimensions enable the exploration of high-dimensional physical phenomena within low-dimensional platforms and have become a frontier in topological photonics and quantum simulation. In photonics, a widely used approach to constructing synthetic dimensions is based on the frequency domain, where different frequency modes of light are treated as discrete “lattice sites,” and controllable couplings are introduced via external modulations (e.g., electro-optic or acousto-optic modulation). This approach allows the realization of complex lattice models that are difficult to achieve in conventional material systems.Benefiting from the development of thin-film lithium niobate integrated photonic platforms, on-chip synthetic frequency dimensions offer enhanced programmability, scalability, and operational stability. To simulate more complex lattice models, it is essential to engineer higher lattice dimensions and richer coupling types (such as asymmetric couplings), enabling the exploration of diverse topological phases and ultimately the realization of more powerful Hamiltonian simulators.
In a new paper published in Light: Science & Applications, a team of scientists from the Laboratory of Quantum Information, University of Science and Technology of China—including Professors Chuan-Feng Li, Jian-Shun Tang, and Yi-Tao Wang—proposed a hybrid frequency-dimension simulator architecture to address these challenges. Its key innovation lies in combining flexible intra-mode frequency lattice construction with the ability to introduce asymmetric couplings (non-conjugate forward and backward transitions). From the Hamiltonian perspective, this introduces imaginary off-diagonal terms in the k-space Hamiltonian, enabling the simulation of lattice models with richer topological phases—all on a single thin-film lithium niobate chip.
As a demonstration, the architecture was first validated for compatibility with previous methods, realizing Hall ladders, Creutz ladders, and their extensions with long-range couplings. Using the Creutz ladder in the topological flat-band regime, the Aharonov–Bohm cage effect was exploited to demonstrate optical frequency shifting and beam-splitting applications. The SSH model was then constructed to verify the system’s capability for asymmetric couplings, with theoretical, simulated, and experimental band structures confirming accurate model implementation. This work provides a powerful approach for synthesizing large-scale complex lattice models in frequency-dimensional simulators.
The ability to realize richer lattice coupling types is a major research focus in the field of synthetic frequency dimensions. As studies advance, simulating complex models increasingly requires systems with strong capabilities for constructing high-dimensional, complex couplings. This work demonstrates such scalability, highlighting the significance of synthetic frequency dimensions for fundamental physics research. At the same time, synthetic frequency dimensions show broad potential for engineering applications. In optical communications and signal processing, the programmable couplings in the frequency domain can enable efficient frequency conversion, spectral shaping, and optical isolation. Using target-oriented inverse design in the spectral domain, frequency dimensions provide an engineering framework for on-chip optical pulse design.
Journal
Light: Science & Applications
Article Title
A hybrid-frequency programmable synthetic-dimension simulator with rich coupling on a single chip