The concept of synthetic dimensions in photonics has attracted rapidly growing interest in the past few years. Among a variety of photonic systems, the ring resonator system under dynamic modulation has been investigated in depth both in theory and e
xperiment, and has proven to be a powerful way to build synthetic frequency dimensions. In this tutorial, we start with a pedagogical introduction to the theoretical approaches in describing the dynamically modulated ring resonator system, and then review experimental methods in building such a system. Moreover, we discuss important physical phenomena in synthetic dimensions, including nontrivial topological physics. Our tutorial provides a pathway towards studying the dynamically modulated ring resonator system, understanding synthetic dimensions in photonics, and discusses future prospects for both fundamental research and practical applications using synthetic dimensions.
Topological phases feature robust edge states that are protected against the effects of defects and disorder. The robustness of these states presents opportunities to design technologies that are tolerant to fabrication errors and resilient to enviro
nmental fluctuations. While most topological phases rely on conservative, or Hermitian, couplings, recent theoretical efforts have combined conservative and dissipative couplings to propose new topological phases for ultracold atoms and for photonics. However, the topological phases that arise due to purely dissipative couplings remain largely unexplored. Here we realize dissipatively coupl
Frequency encoding of quantum information together with fiber and integrated photonic technologies can significantly reduce the complexity and resource requirements for realizing all-photonic quantum networks. The key challenge for such frequency dom
ain processing of single photons is to realize coherent and selective interactions between quantum optical fields of different frequencies over a range of bandwidths. Here, we report frequency-domain Hong-Ou-Mandel interference with spectrally distinct photons generated from a chip-based microresonator. We use four-wave mixing to implement an active frequency beam-splitter and achieve interference visibilities of $0.95 pm 0.02$. Our work establishes four-wave mixing as a tool for selective high-fidelity two-photon operations in the frequency domain which, combined with integrated single-photon sources, provides a building block for frequency-multiplexed photonic quantum networks.
We present a chip-scale scanning dual-comb spectroscopy (SDCS) approach for broadband ultrahigh-resolution spectral acquisition. SDCS uses Si3N4 microring resonators that generate two single soliton micro-combs spanning 37 THz (300 nm) on the same ch
ip from a single 1550-nm laser, forming a high-mutual-coherence dual-comb. We realize continuous tuning of the dual-comb system over the entire optical span of 37.5 THz with high precision using integrated microheater-based wavelength trackers. This continuous wavelength tuning is enabled by simultaneous tuning of the laser frequency and the two single soliton micro-combs over a full free spectral range of the microrings. We measure the SDCS resolution to be 319+-4.6 kHz. Using this SDCS system, we perform the molecular absorption spectroscopy of H13C14N over its 2.3 THz (18 nm)-wide overtone band, and show that the massively parallel heterodyning offered by the dual-comb expands the effective spectroscopic tuning speed of the laser by one order of magnitude. Our chip-scale SDCS opens the door to broadband spectrometry and massively parallel sensing with ultrahigh spectral resolution.
Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order topological insu
lators have been proposed as a way of realizing topological states that are two or more dimensions lower than the bulk, due to the quantization of bulk quadrupole or octupole moments. However, all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here we construct photonic higher-order topological insulators (PHOTI) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension, where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacently coupled photonic molecules, we predict a dynamical topological phase transition in the PHOTI. Furthermore, we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a 4th order hexadecapole (16-pole) insulator, supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.
The concept of synthetic dimensions, which has enabled the study of higher-dimensional physics on lower-dimensional physical structures, has generated significant recent interest in many branches of science ranging from ultracold-atomic physics to ph
otonics, since such a concept provides a versatile platform for realizing effective gauge potentials and novel topological physics. Previous experiments demonstrating this concept have augmented the real-space dimensionality by one additional physical synthetic dimension. Here 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 experimentally observe a wide variety of rich physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and chiral 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.
Modulated optical cavities have been proposed and demonstrated for applications in communications, laser frequency stabilization, microwave-to-optical conversion and frequency comb generation. However, most studies are restricted to the adiabatic reg
ime, where either the maximum excursion of the modulation or the modulation frequency itself is below the linewidth of the cavity. Here, using a fiber ring resonator with an embedded electro-optic phase modulator, we investigate the nonadiabatic regime. By strongly driving the modulator at frequencies that are significantly smaller than the free-spectral range of the ring resonator, but well beyond the linewidth of the resonator, we experimentally observe counterintuitive behavior predicted in a recent theoretical study by Minkov et al. [APL Photonics 2, 076101 (2017)], such as the complete suppression of drop-port transmission even when the input laser wavelength is on resonance with the optical cavity. This can be understood as dynamical isolation of the cavity from the input light. We also show qualitative differences in the steady-state responses of the system between the adiabatic and nonadiabatic limits. Our experiments probe a seldom explored regime of operation that is promising for applications in integrated photonic systems with current state-of-the-art technology.
Dual-comb spectroscopy is a powerful technique for real-time, broadband optical sampling of molecular spectra which requires no moving components. Recent developments with microresonator-based platforms have enabled frequency combs at the chip scale.
However, the need to precisely match the resonance wavelengths of distinct high-quality-factor microcavities has hindered the development of an on-chip dual comb source. Here, we report the first simultaneous generation of two microresonator combs on the same chip from a single laser. The combs span a broad bandwidth of 51 THz around a wavelength of 1.56 $mu$m. We demonstrate low-noise operation of both frequency combs by deterministically tuning into soliton mode-locked states using integrated microheaters, resulting in narrow ($<$ 10 kHz) microwave beatnotes. We further use one mode-locked comb as a reference to probe the formation dynamics of the other comb, thus introducing a technique to investigate comb evolution without auxiliary lasers or microwave oscillators. We demonstrate broadband high-SNR absorption spectroscopy of dichloromethane spanning 170 nm using the dual comb source over a 20 $mu$s acquisition time. Our device paves the way for compact and robust dual-comb spectrometers at nanosecond timescales.
We demonstrate continuous tuning of the squeezing level generated in a double-ring optical parametric oscillator by externally controlling the coupling condition using electrically controlled integrated microheaters. We accomplish this by utilizing t
he avoided crossing exhibited by a pair of coupled silicon nitride microring resonators. We directly detect a change in the squeezing level from 0.5 dB in the undercoupled regime to 2 dB in the overcoupled regime, which corresponds to a change in the generated on-chip squeezing factor from 0.9 dB to 3.9 dB. Such wide tunability in the squeezing level can be harnessed for on-chip quantum enhanced sensing protocols which require an optimal degree of squeezing.
We present the first demonstration of all-optical squeezing in an on-chip monolithically integrated CMOS-compatible platform. Our device consists of a low loss silicon nitride microring optical parametric oscillator (OPO) with a gigahertz cavity line
width. We measure 1.7 dB (5 dB corrected for losses) of sub-shot noise quantum correlations between bright twin beams generated in the microring four-wave-mixing OPO pumped above threshold. This experiment demonstrates a compact, robust, and scalable platform for quantum optics and quantum information experiments on-chip.
