We generalize the concept of photonic gauge potential in real space, by introducing an additional "synthetic" frequency dimension in addition to the real space dimensions. As an illustration we consider a one-dimensional array of ring resonators, each supporting a set of resonant modes having a frequency comb with spacing Ω, undergoing a refractive index modulation at the modulation frequency equal to Ω. We show that the modulation phase provides a gauge potential in the synthetic two-dimensional space with the dimensions being the frequency and the spatial axes.Such gauge potential can create a topologically protected one-way edge state in the synthetic space that is useful for high-efficiency generation of higher-order side bands.

The physics of a photonic structure is commonly described in terms of its apparent geometric dimensionality. On the other hand, with the concept of synthetic dimension, it is in fact possible to explore physics in a space with a dimensionality that is higher as compared to the apparent geometrical dimensionality of the structures. In this review, we discuss the basic concepts of synthetic dimension in photonics, and highlighting the various approaches towards demonstrating such synthetic dimension for fundamental physics and potential applications.

Weyl points, as a signature of 3D topological states, have been extensively studied in condensed matter systems. Recently, the physics of Weyl points has also been explored in electromagnetic structures such as photonic crystals and metamaterials. These structures typically have complex three-dimensional geometries, which limits the potential for exploring Weyl point physics in on-chip integrated systems. Here we show that Weyl point physics emerges in a system of two-dimensional arrays of resonators undergoing dynamic modulation of refractive index. In addition, the phase of modulation can be controlled to explore Weyl points under different symmetries. Furthermore, unlike static structures, in this system the non-trivial topology of the Weyl point manifests in terms of surface state arcs in the synthetic space that exhibit one-way frequency conversion. Our system therefore provides a versatile platform to explore and exploit Weyl point physics on chip.

The concept of synthetic dimensions has generated interest in many branches of science, ranging from ultracold atomic physics to photonics, as it provides a versatile platform for realizing effective gauge potentials and topological physics. Previous experiments have augmented the real-space dimensionality by one additional physical synthetic dimension. In this study, we endow a single ring resonator with two independent physical synthetic dimensions. Our system consists of a temporally modulated ring resonator with spatial coupling between the clockwise and counterclockwise modes, creating a synthetic Hall ladder along the frequency and pseudospin degrees of freedom for photons propagating in the ring. We observe a wide variety of physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and signatures of topological chiral one-way edge currents, completely in synthetic dimensions. Our experiments demonstrate that higher-dimensional physics can be studied in simple systems by leveraging the concept of multiple simultaneous synthetic dimensions.

There has been significant recent interest in synthetic dimensions, where internal degrees of freedom of a particle are coupled to form higher-dimensional lattices in lower-dimensional physical structures. For these systems, the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide a direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a resonator at frequencies commensurate with its mode spacing, we create a periodically driven lattice of coupled modes in the frequency dimension. The strength and range of couplings can be dynamically reconfigured by changing the modulation amplitude and frequency. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system provide a direct readout of its band structure. We also realize long-range coupling, gauge potentials and nonreciprocal bands by simply incorporating additional frequency drives, enabling great flexibility in band structure engineering.

We provide a systematic study of non-Hermitian topologically charged systems. Starting from a Hermitian Hamiltonian supporting Weyl points with arbitrary topological charge, adding a non-Hermitian perturbation transforms the Weyl points to one-dimensional exceptional contours. We analytically prove that the topological charge is preserved on the exceptional contours. In contrast to Hermitian systems, the addition of gain and loss allows for a new class of topological phase transition: when two oppositely charged exceptional contours touch, the topological charge can dissipate without opening a gap. These effects can be demonstrated in realistic photonics and acoustics systems.

A laser generates light through stimulated emission of radiation and requires population inversion. Quantum interference can yield lasing without inversion. However, such phase-sensitive quantum amplification still requires some atomic population in the excited state. Here, we present a new kind of quantum amplifier based on collective superradiant emission which does not need any population in the excited state. We show that parametric resonance between the driving (e.g., infrared) field and collective superradiant oscillations of the atomic polarization can yield light amplification at high (e.g., XUV) frequencies. To achieve gain, one must suppress a time-dependent Stark shift caused by the driving field. The resulting superradiant amplifier is many orders of magnitude more efficient than the usual nonlinear multiphoton excitation and holds promise for a new kind of generator of highfrequency coherent radiation. In addition to a detailed analytical analysis, confirmed by numerical simulations, we provide a physically appealing explanation of the quantum amplification by superradiant emission of radiation (QASER) operation in terms of coupled classical oscillators. We also present an experiment that demonstrates the QASER amplification mechanism in an electronic circuit, which, to the best of our knowledge, is the first experimental demonstration of the difference combination resonance.

The ability to control the spectrum of light is of fundamental significance in many applications of light. We consider a dynamically modulated ring resonator that supports a set of resonant modes equally spaced in their resonant frequencies, and is modulated at a frequency that is slightly detuned from the modal frequency spacing. We find that such a system can be mapped into a tight-binding model of photons under a constant effective force, and, as a result, the system exhibits Bloch oscillation along the frequency axis. The sign of the detuning is mapped to the sign of the effective force and hence controls the direction of the Bloch oscillation. We also show that a periodic switching of the detuning can lead to unidirectional transport of light along the frequency axis. Our work points to a new capability for manipulating the frequencies of light using dynamic microcavity structures.