Creating boundaries along a synthetic frequency dimension

Observing non-Hermiticity induced chirality breaking in a synthetic Hall ladder

Non-Hermitian topological photonics plays a key role in bridging topological matter with gain and loss engineering in optics. Here we report the experimental observation of the break of chiral currents in a Hall ladder from the non-Hermiticity by constructing synthetic frequency dimension in two rings, where currents on both legs of the ladder co-propagate in the same direction. The origin of such phenomena is resulted from the interplay between the effective magnetic flux and the on-site gain and loss. Such non-Hermitian co-propagating currents exhibit characteristics of unidirectional frequency conversion in both rings, and moreover, different from the counterpart in Hermitian systems, can provide a method to probe the signatures of the non-Hermitian skin effect from steady-state bulk dynamics. Our model is further extended to models including next-nearest-neighbor couplings, pointing to a way for observing the non-Hermitian signature with higher winding number, and provides a new control knob for light manipulation with the topological dissipation engineering.

Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions

Non-Abelian gauge fields1 provide a conceptual framework to describe particles having spins, underlying many phenomena in electrodynamics, condensed-matter physics2,3 and particle physics4,5. Lattice models6 of non-Abelian gauge fields allow us to understand their physical implications in extended systems. The theoretical importance of non-Abelian lattice gauge fields motivates their experimental synthesis and explorations7-9. Photons are fundamental particles for which artificial gauge fields can be synthesized10-30, yet the demonstration of non-Abelian lattice gauge fields for photons has not been achieved. Here we demonstrate SU(2) lattice gauge fields for photons in the synthetic frequency dimensions31,32, a playground to study lattice physics in a scalable and programmable way. In our lattice model, we theoretically observe that homogeneous non-Abelian lattice gauge potentials induce Dirac cones at time-reversal-invariant momenta in the Brillouin zone. We experimentally confirm the presence of non-Abelian lattice gauge fields by two signatures: linear band crossings at the Dirac cones, and the associated direction reversal of eigenstate trajectories. We further demonstrate a non-Abelian scalar lattice gauge potential that lifts the degeneracies of the Dirac cones. Our results highlight the implications of non-Abelian lattice gauge fields in topological physics, and provide a starting point for demonstrations of emerging non-Abelian physics in the photonic synthetic dimensions. Our results may also benefit photonic technologies by providing controls of photon spins and pseudo-spins in topologically non-trivial ways33.

On-Chip Photonic Simulating Band Structures toward Arbitrary-Range Coupled Frequency Lattices

Photonic simulators are increasingly used to study physical systems for their affluent manipulable degrees of freedom. The advent of photonic chips offers a promising path towards compact and configurable simulators. Thin-film lithium niobate chips are particularly well suited for this purpose due to the high electro-optic coefficient, which allows for the creation of lattices in the frequency domain. Here, we fabricate and periodically modulate an on-chip resonator to observe band structures. The employed modulation rates are lower than the resonator linewidth, resulting in the inclusion of multiple lattice points within one resonant peak. This alleviates the difficulty of applying and detecting multiharmonic signals which are conventionally of ultrahigh frequency on chips and enables us to simulate structures with arbitrary-range coupling. As examples, we showcase the simulation of nanotubes along several directions where the required frequencies are reduced by more than 3 orders of magnitude (up to reduce near 100 GHz to around 10 MHz in our examples). Encompassing various models equipped with a gauge potential, our experiments demonstrate an effective and technically feasible scenario which may bolster the development of on-chip photonic simulators complementing existing techniques.

Efficient microresonator frequency combs

The rapid development of optical frequency combs from their table-top origins towards chip-scale platforms has opened up exciting possibilities for comb functionalities outside laboratories. Enhanced nonlinear processes in microresonators have emerged as a mainstream comb-generating mechanism with compelling advantages in size, weight, and power consumption. The established understanding of gain and loss in nonlinear microresonators, along with recently developed ultralow-loss nonlinear photonic circuitry, has boosted the optical energy conversion efficiency of microresonator frequency comb (microcomb) devices from below a few percent to above 50%. This review summarizes the latest advances in novel photonic devices and pumping strategies that contribute to these milestones of microcomb efficiency. The resulting benefits for high-performance integration of comb applications are also discussed before summarizing the remaining challenges.

Wave-Function Tomography of Topological Dimer Chains with Long-Range Couplings

The ability to tailor with a high accuracy the intersite connectivity in a lattice is a crucial tool for realizing novel topological phases of matter. Here, we report the experimental realization of photonic dimer chains with long-range hopping terms of arbitrary strength and phase, providing a rich generalization of the Su-Schrieffer-Heeger model which, in its conventional form, is limited to nearest-neighbor couplings only. Our experiment is based on a synthetic dimension scheme involving the frequency modes of an optical fiber loop platform. This setup provides direct access to both the band dispersion and the geometry of the Bloch wave functions throughout the entire Brillouin zone allowing us to extract the winding number for any possible configuration. Finally, we highlight a topological phase transition solely driven by a time-reversal-breaking synthetic gauge field associated with the phase of the long-range hopping, providing a route for engineering topological bands in photonic lattices belonging to the AIII symmetry class.

Spectral Engineering of Optical Microresonators in Anisotropic Lithium Niobate Crystal

On-chip optical microresonators are essential building blocks in integrated optics. The ability to arbitrarily engineer their resonant frequencies is crucial for exploring novel physics in synthetic frequency dimensions and practical applications like nonlinear optical parametric processes and dispersion-engineered frequency comb generation. Photonic crystal ring (PhCR) resonators are a versatile tool for such arbitrary frequency engineering, by controllably creating mode splitting at selected resonances. To date, these PhCRs have mostly been demonstrated in isotropic photonic materials, while such engineering can be significantly more complicated in anisotropic platforms that often offer more fruitful optical properties. Here, the spectral engineering of chip-scale optical microresonators is realized in the anisotropic lithium niobate (LN) crystal by a gradient design that precisely compensates for variations in both refractive index and perturbation strength. Controllable frequency splitting is experimentally demonstrated at single and multiple selected resonances in LN PhCR resonators with different sizes, while maintaining high quality-factors up to 1 × 106. Moreover, a sharp boundary is experimentally constructed in the synthetic frequency dimension based on an actively modulated x-cut LN gradient-PhCR, opening up new paths toward the arbitrary control of electro-optic comb spectral shapes and exploration of novel physics in the frequency degree of freedom.

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.

Artificial gauge fields in the t-z mapping for optical pulses: Spatiotemporal wave packet control and quantum Hall physics

We extend the t-z mapping of time-dependent paraxial optics by engineering a synthetic magnetic vector potential, leading to a nontrivial band topology. We consider an inhomogeneous 1D array of coupled optical waveguides and show that the wave equation describing paraxial propagation of optical pulses can be recast as a Schrödinger equation, including a synthetic magnetic field whose strength can be controlled via the spatial gradient of the waveguide properties across the array. We use an experimentally motivated model of a laser-written array to demonstrate that this synthetic magnetic field can be engineered in realistic setups and can produce interesting physics such as cyclotron motion, a controllable Hall drift of the pulse in space or time, and propagation in chiral edge states. These results substantially extend the physics that can be explored within propagating geometries and pave the way for higher-dimensional topological physics and strongly correlated fluids of light.

Topological degeneracy breaking in synthetic frequency lattice by Floquet engineering

Synthetic frequency dimensions provide important opportunities to investigate novel topological phenomena. Previously, many theoretical proposals have been studied and relevant experiments have been performed very recently. However, all these works consider models in the weak modulation regime, where static lattice models are constructed. Here we explore a Floquet Su-Schrieffer-Heeger (SSH) model with time-dependent hoppings in the frequency dimension by dynamically modulating ring resonators ultrastrongly, and find that the topological states, originally degenerate in conventional SSH lattices, are separated in eigenenergies. There exists a series of edge states from band folding at the 0 and π energy bandgaps, which exhibit complex multi-frequency oscillations due to the inclusion of counter-rotating terms with higher order oscillation frequencies. Such a system with stronger modulations can widen the bandgap and therefore it provides an effective way to localize pulses in synthetic frequency dimensions. Our work shows a photonic platform with the synthetic dimension in exploring exotic Floquet topological phenomena and shows potential applications in optical storage and communications.

Multi-dimensional band structure spectroscopy in the synthetic frequency dimension

The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method, we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.

Multidimensional synthetic frequency lattice in the dynamically modulated waveguides

Here we propose an effective method to construct a higher-dimensional synthetic frequency lattice with an optical waveguide under dynamic modulation. By applying the traveling-wave modulation of refractive index modulation with two different frequencies that are not mutually commensurable, a two-dimensional frequency lattice could be formed. The Bloch oscillations (BOs) in the frequency lattice is demonstrated by introducing a wave vector mismatch of the modulation. We show that the BOs are reversible only as the amounts of wave vector mismatch in orthogonal directions are mutually commensurable. Finally, by employing an array of waveguides with each under traveling-wave modulation, a 3D frequency lattice is formed and its topological effect of one-way frequency conversion is revealed. The study offers a versatile platform for exploring higher-dimensional physics in concise optical systems and may find great application in optical frequency manipulations.

Artificial Non-Abelian Lattice Gauge Fields for Photons in the Synthetic Frequency Dimension

Non-Abelian gauge fields give rise to nontrivial topological physics. Here we develop a scheme to create an arbitrary SU(2) lattice gauge field for photons in the synthetic frequency dimension using an array of dynamically modulated ring resonators. The photon polarization is taken as the spin basis to implement the matrix-valued gauge fields. Using a non-Abelian generalization of the Harper-Hofstadter Hamiltonian as a specific example, we show that the measurement of the steady-state photon amplitudes inside the resonators can reveal the band structures of the Hamiltonian, which show signatures of the underlying non-Abelian gauge field. These results provide opportunities to explore novel topological phenomena associated with non-Abelian lattice gauge fields in photonic systems.

Mirror-induced reflection in the frequency domain

Mirrors are ubiquitous in optics and are used to control the propagation of optical signals in space. Here we propose and demonstrate frequency domain mirrors that provide reflections of the optical energy in a frequency synthetic dimension, using electro-optic modulation. First, we theoretically explore the concept of frequency mirrors with the investigation of propagation loss, and reflectivity in the frequency domain. Next, we explore the mirror formed through polarization mode-splitting in a thin-film lithium niobate micro-resonator. By exciting the Bloch waves of the synthetic frequency crystal with different wave vectors, we show various states formed by the interference between forward propagating and reflected waves. Finally, we expand on this idea, and generate tunable frequency mirrors as well as demonstrate trapped states formed by these mirrors using coupled lithium niobate micro-resonators. The ability to control the flow of light in the frequency domain could enable a wide range of applications, including the study of random walks, boson sampling, frequency comb sources, optical computation, and topological photonics. Furthermore, demonstration of optical elements such as cavities, lasers, and photonic crystals in the frequency domain, may be possible.