On-chip generation of high-dimensional entangled quantum states and their coherent control

Gottesman-Kitaev-Preskill Encoding in Continuous Modal Variables of Single Photons

GKP states, introduced by Gottesman, Kitaev, and Preskill, are continuous variable logical qubits that can be corrected for errors caused by phase space displacements. Their experimental realization is challenging, in particular, using propagating fields, where quantum information is encoded in the quadratures of the electromagnetic field. However, traveling photons are essential in many applications of GKP codes involving the long-distance transmission of quantum information. We introduce a new method for encoding GKP states in propagating fields using single photons, each occupying a distinct auxiliary mode given by the propagation direction. The GKP states are defined as highly correlated states described by collective continuous modes, as time and frequency. We analyze how the error detection and correction protocol scales with the total photon number and the spectral width. We show that the obtained code can be corrected for displacements in time-frequency phase space, which correspond to dephasing, or rotations, in the quadrature phase space and to photon losses. Most importantly, we show that generating two-photon GKP states is relatively simple, and that such states are currently produced and manipulated in several photonic platforms where frequency and time-bin biphoton entangled states can be engineered.

NOON-state interference in the frequency domain

The examination of entanglement across various degrees of freedom has been pivotal in augmenting our understanding of fundamental physics, extending to high dimensional quantum states, and promising the scalability of quantum technologies. In this paper, we demonstrate the photon number path entanglement in the frequency domain by implementing a frequency beam splitter that converts the single-photon frequency to another with 50% probability using Bragg scattering four-wave mixing. The two-photon NOON state in a single-mode fiber is generated in the frequency domain, manifesting the two-photon interference with two-fold enhanced resolution compared to that of single-photon interference, showing the outstanding stability of the interferometer. This successful translation of quantum states in the frequency domain will pave the way toward the discovery of fascinating quantum phenomena and scalable quantum information processing.

Nonlinear Optical Properties of 2D Materials and their Applications

2D materials are a subject of intense research in recent years owing to their exclusive photoelectric properties. With giant nonlinear susceptibility and perfect phase matching, 2D materials have marvelous nonlinear light-matter interactions. The nonlinear optical properties of 2D materials are of great significance to the design and analysis of applied materials and functional devices. Here, the fundamental of nonlinear optics (NLO) for 2D materials is introduced, and the methods for characterizing and measuring second-order and third-order nonlinear susceptibility of 2D materials are reviewed. Furthermore, the theoretical and experimental values of second-order susceptibility χ(2) and third-order susceptibility χ(3) are tabulated. Several applications and possible future research directions of second-harmonic generation (SHG) and third-harmonic generation (THG) for 2D materials are presented.

High-Speed Quantum Radio-Frequency-Over-Light Communication

Quantum dense coding (QDC) means to transmit two classical bits by only transferring one quantum bit, which has enabled high-capacity information transmission and strengthened system security. Continuous-variable QDC offers a promising solution to increase communication rates while achieving seamless integration with classical communication systems. Here, we propose and experimentally demonstrate a high-speed quantum radio-frequency-over-light (RFOL) communication scheme based on QDC with an entangled state, and achieve a practical rate of 20 Mbps through digital modulation and RFOL communication. This scheme bridges the gap between quantum technology and real-world communication systems, which bring QDC closer to practical applications and offer prospects for further enhancement of metropolitan communication networks.

Spatiotemporal Single-Photon Airy Bullets

Uninhibited control of the complex spatiotemporal quantum wave function of a single photon has so far remained elusive even though it can dramatically increase the encoding flexibility and thus the information capacity of a photonic quantum link. By fusing temporal waveform generation in an atomic ensemble and spatial single-photon shaping, we hereby demonstrate for the first time complete spatiotemporal control of a propagation invariant (2+1)D Airy single-photon optical bullet. These correlated photons are not only self-accelerating and impervious to spreading as their classical counterparts, but can be concealed and revealed in the presence of strong classical stray light.

Parity-time symmetry enabled ultra-efficient nonlinear optical signal processing

Nonlinear optical signal processing (NOSP) has the potential to significantly improve the throughput, flexibility, and cost-efficiency of optical communication networks by exploiting the intrinsically ultrafast optical nonlinear wave mixing. It can support digital signal processing speeds of up to terabits per second, far exceeding the line rate of the electronic counterpart. In NOSP, high-intensity light fields are used to generate nonlinear optical responses, which can be used to process optical signals. Great efforts have been devoted to developing new materials and structures for NOSP. However, one of the challenges in implementing NOSP is the requirement of high-intensity light fields, which is difficult to generate and maintain. This has been a major roadblock to realize practical NOSP systems for high-speed, high-capacity optical communications. Here, we propose using a parity-time (PT) symmetric microresonator system to significantly enhance the light intensity and support high-speed operation by relieving the bandwidth-efficiency limit imposed on conventional single resonator systems. The design concept is the co-existence of a PT symmetry broken regime for a narrow-linewidth pump wave and near-exceptional point operation for broadband signal and idler waves. This enables us to achieve a new NOSP system with two orders of magnitude improvement in efficiency compared to a single resonator. With a highly nonlinear AlGaAs-on-Insulator platform, we demonstrate an NOSP at a data rate approaching 40 gigabits per second with a record low pump power of one milliwatt. These findings pave the way for the development of fully chip-scale NOSP devices with pump light sources integrated together, potentially leading to a wide range of applications in optical communication networks and classical or quantum computation. The combination of PT symmetry and NOSP may also open up opportunities for amplification, detection, and sensing, where response speed and efficiency are equally important.

Supplementary Information

The online version contains supplementary material available at 10.1186/s43593-024-00062-w.

Quantum Light Generation Based on GaN Microring toward Fully On-Chip Source

An integrated quantum light source is increasingly desirable in large-scale quantum information processing. Despite recent remarkable advances, a new material platform is constantly being explored for the fully on-chip integration of quantum light generation, active and passive manipulation, and detection. Here, for the first time, we demonstrate a gallium nitride (GaN) microring based quantum light generation in the telecom C-band, which has potential toward the monolithic integration of quantum light source. In our demonstration, the GaN microring has a free spectral range of 330 GHz and a near-zero anomalous dispersion region of over 100 nm. The generation of energy-time entangled photon pair is demonstrated with a typical raw two-photon interference visibility of 95.5±6.5%, which is further configured to generate a heralded single photon with a typical heralded second-order autocorrelation g_{H}^{(2)}(0) of 0.045±0.001. Our results pave the way for developing a chip-scale quantum photonic circuit.

All-optical Stern-Gerlach effect in the time domain

The Stern-Gerlach experiment, a seminal quantum physics experiment, demonstrated the intriguing phenomenon of particle spin quantization, leading to applications in matter-wave interferometry and weak-value measurements. Over the years, several optical experiments have exhibited similar behavior to the Stern-Gerlach experiment, revealing splitting in both spatial and angular domains. Here we show, theoretically and experimentally, that the Stern-Gerlach effect can be extended into the time and frequency domains. By harnessing Kerr nonlinearity in optical fibers, we couple signal and idler pulses using two pump pulses, resulting in the emergence of two distinct eigenstates whereby the signal and idler are either in phase or out of phase. This nonlinear coupling emulates a synthetic magnetization, and by varying it linearly in time, one eigenstate deflects towards a higher frequency, while the other deflects towards a lower frequency. This effect can be utilized to realize an all-optical, phase-sensitive frequency beam splitter, establishing a new paradigm for classical and quantum data processing of frequency-bin superposition states.

Practical high-dimensional quantum key distribution protocol over deployed multicore fiber

Quantum key distribution (QKD) is a secure communication scheme for sharing symmetric cryptographic keys based on the laws of quantum physics, and is considered a key player in the realm of cyber-security. A critical challenge for QKD systems comes from the fact that the ever-increasing rates at which digital data are transmitted require more and more performing sources of quantum keys, primarily in terms of secret key generation rate. High-dimensional QKD based on path encoding has been proposed as a candidate approach to address this challenge. However, while proof-of-principle demonstrations based on lab experiments have been reported in the literature, demonstrations in realistic environments are still missing. Here we report the generation of secret keys in a 4-dimensional hybrid time-path-encoded QKD system over a 52-km deployed multicore fiber link forming by looping back two cores of a 26-km 4-core optical fiber. Our results indicate that robust high-dimensional QKD can be implemented in a realistic environment by combining standard telecom equipment with emerging multicore fiber technology.

Ultra-compact electro-optic phase modulator based on a lithium niobate topological slow light waveguide

Electro-optic modulators (EOMs) are essential devices of optical communications and quantum computing systems. In particular, ultra-compact EOMs are necessary for highly integrated photonic chips. Thin film lithium niobate materials are a promising platform for designing highly efficient EOMs. However, EOMs based on conventional waveguide structures are at a millimeter scale and challenging to scale down further, greatly hindering the capability of on-chip integration. Here, we design an EOM based on lithium niobate valley photonic crystal (VPC) structures for the first time. Due to the high effective refractive index introduced by the strong slow light effect, the EOM can achieve an ultra-compact size of 4 μm×14 μm with a half-wave voltage of 1.4 V. The EOM has a high transmittance of 0.87 in the 1068 nm because of the unique spin-valley locking effect in VPC structures. The design is fully compatible with current nanofabrication technology and immune to fabrication defects. Therefore, it opens a new possibility in designing lithium niobate electro-optic modulators and will find broad applications in optical communication and quantum photonic devices.

Quantum transport of high-dimensional spatial information with a nonlinear detector

Information exchange between two distant parties, where information is shared without physically transporting it, is a crucial resource in future quantum networks. Doing so with high-dimensional states offers the promise of higher information capacity and improved resilience to noise, but progress to date has been limited. Here we demonstrate how a nonlinear parametric process allows for arbitrary high-dimensional state projections in the spatial degree of freedom, where a strong coherent field enhances the probability of the process. This allows us to experimentally realise quantum transport of high-dimensional spatial information facilitated by a quantum channel with a single entangled pair and a nonlinear spatial mode detector. Using sum frequency generation we upconvert one of the photons from an entangled pair resulting in high-dimensional spatial information transported to the other. We realise a d = 15 quantum channel for arbitrary photonic spatial modes which we demonstrate by faithfully transferring information encoded into orbital angular momentum, Hermite-Gaussian and arbitrary spatial mode superpositions, without requiring knowledge of the state to be sent. Our demonstration merges the nascent fields of nonlinear control of structured light with quantum processes, offering a new approach to harnessing high-dimensional quantum states, and may be extended to other degrees of freedom too.

Thermo-Optic Response and Optical Bistablility of Integrated High-Index Doped Silica Ring Resonators

The engineering of thermo-optic effects has found broad applications in integrated photonic devices, facilitating efficient light manipulation to achieve various functionalities. Here, we perform both an experimental characterization and a theoretical analysis of these effects in integrated microring resonators made from high-index doped silica, which have had many applications in integrated photonics and nonlinear optics. By fitting the experimental results with theory, we obtain fundamental parameters that characterize their thermo-optic performance, including the thermo-optic coefficient, the efficiency of the optically induced thermo-optic process, and the thermal conductivity. The characteristics of these parameters are compared to those of other materials commonly used for integrated photonic platforms, such as silicon, silicon nitride, and silica. These results offer a comprehensive insight into the thermo-optic properties of doped silica-based devices. Understanding these properties is essential for efficiently controlling and engineering them in many practical applications.

Spectral Hong-Ou-Mandel Effect between a Heralded Single-Photon State and a Thermal Field: Multiphoton Contamination and the Nonclassicality Threshold

The Hong-Ou-Mandel (HOM) effect is crucial for quantum information processing, and its visibility determines the system's quantum-classical characteristics. In an experimental and theoretical study of the spectral HOM effect between a thermal field and a heralded single-photon state, we demonstrate that the HOM visibility varies dependent on the relative photon statistics of the interacting fields. Our findings reveal that multiphoton components in a heralded state get engaged in quantum interference with a thermal field, resulting in improved visibilities at certain mean photon numbers. We derive a theoretical relationship for the HOM visibility as a function of the mean photon number of the thermal field and the thermal part of the heralded state. We show that the nonclassicality degree of a heralded state is reflected in its HOM visibility with a thermal field; our results establish a lower bound of 41.42% for the peak visibility, indicating the minimum assignable degree of nonclassicality to the heralded state. This research enhances our understanding of the HOM effect and its application to high-speed remote secret key sharing, addressing security concerns due to multiphoton contamination in heralded states.

Shaping the spectral correlation of bi-photon quantum frequency combs by multi-frequency excitation of an SOI integrated nonlinear resonator

We reveal the generation of a broadband (> 1.9 THz) bi-photon quantum frequency comb (QFC) in a silicon-on-insulator (SOI) Fabry-Pérot micro-cavity and the control of its spectral correlation properties. Correlated photon pairs are generated through three spontaneous four-wave mixing (SFWM) processes by using a co-polarized bi-chromatic coherent input with power P1 and P2 on adjacent resonances of the nonlinear cavity. Adjusting the spectral power ratio r = P1/(P1 + P2) allows control over the influence of each process leading to an enhancement of the overall photon pair generation rate (PGR) μ(r) by a maximal factor of μ(r = 0.5)/μ(r = 0) ≈ 1.5, compared to the overall PGR provided by a single-pump configuration with the same power budget. We demonstrate that the efficiency aND of the non-degenerate excitation SFWM process (NDP) doubles the efficiency a1 ≈ a2 of the degenerate excitation SFWM processes (DP), showing a good agreement with the provided model.

Resource-Efficient High-Dimensional Entanglement Detection via Symmetric Projections

We introduce two families of criteria for detecting and quantifying the entanglement of a bipartite quantum state of arbitrary local dimension. The first is based on measurements in mutually unbiased bases and the second is based on equiangular measurements. Both criteria give a qualitative result in terms of the state's entanglement dimension and a quantitative result in terms of its fidelity with the maximally entangled state. The criteria are universally applicable since no assumptions on the state are required. Moreover, the experimenter can control the trade-off between resource-efficiency and noise-tolerance by selecting the number of measurements performed. For paradigmatic noise models, we show that only a small number of measurements are necessary to achieve nearly-optimal detection in any dimension. The number of global product projections scales only linearly in the local dimension, thus paving the way for detection and quantification of very high-dimensional entanglement.

Ultra-low time jitter transform-limited dissipative Kerr soliton microcomb

Microresonator soliton frequency combs offer unique flexibility in synthesizing microwaves over a wide range of frequencies. Therefore, it is very important to study the time jitter of soliton microcombs. Here, we fabricate optical microresonators with perfect transmission spectrum that characterizes highly uniform extinction ratio and absence of mode interactions by laser machining high-purity silica fiber preforms. Based on such perfect whispering-gallery-mode cavity, We demonstrate that K-band microwave with ultra-low phase noise (-83 dBc/Hz@100 Hz; -112 dBc/Hz@1kHz; -133 dBc/Hz@10kHz) can be generated by photo-detecting the repetition rate of a soliton microcomb. Also, with the Raman scattering and dispersive wave emission largely restricted, we show that ultra-low time jitter soliton has a wide existence range. Our work illuminates a pathway toward low-noise photonic microwave generation as well as the quantum regime of soliton microcombs.

Pushing photon-pair generation rate in microresonators by Q factor manipulation

Photon pairs generated by employing spontaneous nonlinear effects in microresonators are critically essential for integrated optical quantum information technologies, such as quantum computation and quantum cryptography. Microresonators featuring high-quality (Q) factors can offer simple yet power-efficient means to generate photon pairs, thanks to the intracavity field enhancement. In microresonators, it is known that the photon-pair generation rate (PGR) is roughly proportional to the cubic power of the Q factor. However, the upper limit on PGR is also set by the Q factor: a higher Q factor brings a longer photon lifetime, which in turn leads to a lower repetition rate allowing for photon flow emitted from the microresonator, constrained by the Fourier-transform limit. Exceeding this limit will result in the overlap of photon wave packets in the time domain, thus degrading the quantum character of single-photon light beams. To push the limit of PGR in a single resonator, we propose a method by harnessing the resonance linewidth-manipulated microresonators to improve the maximum achievable photon repetition rate while keeping the power efficiency. The maximum achievable PGR and power efficiency are thus balanced by leveraging the combination of low and high-Q resonances.

Hyper-entanglement between pulse modes and frequency bins

Hyper-entanglement between two or more photonic degrees of freedom (DOF) can enhance and enable new quantum protocols by allowing each DOF to perform the task it is optimally suited for. Here we demonstrate the generation of photon pairs hyper-entangled between pulse modes and frequency bins. The pulse modes are generated via parametric downconversion in a domain-engineered crystal and subsequently entangled to two frequency bins via a spectral mapping technique. The resulting hyper-entangled state is characterized and verified via measurement of its joint spectral intensity and non-classical two-photon interference patterns from which we infer its spectral phase. The protocol combines the robustness to loss, intrinsic high dimensionality and compatibility with standard fiber-optic networks of the energy-time DOF with the ability of hyper-entanglement to increase the capacity and efficiency of the quantum channel, already exploited in recent experimental applications in both quantum information and quantum computation.

Extraordinary Five-Wave Mixing in a Zinc Oxide Microwire on a Au Film

Coherent multiwave mixing is in demand for optical frequency conversion, imaging, quantum information science, etc., but has rarely been demonstrated in solid-state systems. Here, we observed three- and five-wave mixing (5WM) in a c-axis growth zinc oxide microwire on a Au film with picosecond pulses in the near-infrared region. An output 5WM of 4.7 × 10-7 μW, only 2-3 orders smaller than the three-wave mixing, is achieved when the excitation power is as low as 1.5 mW and the peak power density as weak as ∼107 W/cm2. The excitation power dependence of 5WM agrees well with the perturbation limit under the low intensity but exhibits a strong deviation at a high pumping power. This extraordinary behavior is attributed to the cooperative resonant enhancement effect when pumping in the near-infrared range. Our study offers a potential solid-state platform for on-chip multiwave mixing and quantum nonlinear optics, such as generating many-photon entangled states or the construction of photon-photon quantum logic gates.

Optical Diffractive Convolutional Neural Networks Implemented in an All-Optical Way

Optical neural networks can effectively address hardware constraints and parallel computing efficiency issues inherent in electronic neural networks. However, the inability to implement convolutional neural networks at the all-optical level remains a hurdle. In this work, we propose an optical diffractive convolutional neural network (ODCNN) that is capable of performing image processing tasks in computer vision at the speed of light. We explore the application of the 4f system and the diffractive deep neural network (D2NN) in neural networks. ODCNN is then simulated by combining the 4f system as an optical convolutional layer and the diffractive networks. We also examine the potential impact of nonlinear optical materials on this network. Numerical simulation results show that the addition of convolutional layers and nonlinear functions improves the classification accuracy of the network. We believe that the proposed ODCNN model can be the basic architecture for building optical convolutional networks.

Direct determination of high-order transverse ligand field parameters via µSQUID-EPR in a Et4N[160GdPc2] SMM

The development of quantum technologies requires a thorough understanding of systems possessing quantum effects that can ultimately be manipulated. In the field of molecular magnetism, one of the main challenges is to measure high-order ligand field parameters, which play an essential role in the relaxation properties of SMMs. The development of highly advanced theoretical calculations has allowed the ab-initio determination of such parameters; however, currently, there is a lack of quantitative assessment of how good the ab-initio parameters are. In our quest for technologies that can allow the extraction of such elusive parameters, we develop an experimental technique that combines the EPR spectroscopy and µSQUID magnetometry. We demonstrate the power of the technique by performing EPR-µSQUID measurement of a magnetically diluted single crystal of Et₄N[GdPc₂], by sweeping the magnetic field and applying a range of multifrequency microwave pulses. As a result, we were able to directly determine the high-order ligand field parameters of the system, enabling us to test theoretical predictions made by state-of-the-art ab-initio methods.

Frequency-domain engineering of bright squeezed vacuum for continuous-variable quantum information

Multimode bright squeezed vacuum is a non-classical state of light hosting a macroscopic photon number while offering promising capacity for encoding quantum information in its spectral degree of freedom. Here, we employ an accurate model for parametric down-conversion in the high-gain regime and use nonlinear holography to design quantum correlations of bright squeezed vacuum in the frequency domain. We propose the design of quantum correlations over two-dimensional lattice geometries that are all-optically controlled, paving the way toward continuous-variable cluster state generation on an ultrafast timescale. Specifically, we investigate the generation of a square cluster state in the frequency domain and calculate its covariance matrix and the quantum nullifier uncertainties, that exhibit squeezing below the vacuum noise level.

Linear Optical Quantum Computation with Frequency-Comb Qubits and Passive Devices

We propose a linear optical quantum computation scheme using time-frequency degrees of freedom. In this scheme, a qubit is encoded in single-photon frequency combs, and manipulation of the qubits is performed using time-resolving detectors, beam splitters, and optical interleavers. This scheme does not require active devices such as high-speed switches and electro-optic modulators and is robust against temporal and spectral errors, which are mainly caused by the detectors' finite resolution. We show that current technologies almost meet the requirements for fault-tolerant quantum computation.

Spatial-spectral mapping to prepare frequency entangled qudits

Entangled qudits, the high-dimensional entangled states, play an important role in the study of quantum information. How to prepare entangled qudits in an efficient and easy-to-operate manner is still a challenge in quantum technology. Here, we demonstrate a method to engineer frequency entangled qudits in a spontaneous parametric downconversion process. The proposal employs an angle-dependent phase-matching condition in a nonlinear crystal, which forms a classical-quantum mapping between the spatial (pump) and spectral (biphotons) degrees of freedom. In particular, the pump profile is separated into several bins in the spatial domain, and thus shapes the down-converted biphotons into discrete frequency modes in the joint spectral space. Our approach provides a feasible and efficient method to prepare a high-dimensional frequency entangled state. As an experimental demonstration, we generate a three-dimensional entangled state by using a homemade variable slit mask.

Simple and accurate dispersion measurement of GaN microresonators with a fiber ring

The dispersion characteristics of a microresonator are important for applications in nonlinear optics, and precise measurement of the dispersion profile is crucial to device design and optimization. Here we demonstrate the dispersion measurement of high-quality-factor gallium nitride (GaN) microrings by a single-mode fiber ring, which is simple and convenient to access. Once the dispersion parameters of the fiber ring have been determined by the opto-electric modulation method, the dispersion can be obtained from the microresonator dispersion profile by polynomial fitting. To further verify the accuracy of the proposed method, the dispersion of the GaN microrings is also evaluated with frequency comb-based spectroscopy. Dispersion profiles obtained with both methods are in good agreement with simulations based on the finite element method.

All-fibre phase filters with 1-GHz resolution for high-speed passive optical logic processing

Photonic-based implementation of advanced computing tasks is a potential alternative to mitigate the bandwidth limitations of electronics. Despite the inherent advantage of a large bandwidth, photonic systems are generally bulky and power-hungry. In this respect, all-pass spectral phase filters enable simultaneous ultrahigh speed operation and minimal power consumption for a wide range of signal processing functionalities. Yet, phase filters offering GHz to sub-GHz frequency resolution in practical, integrated platforms have remained elusive. We report a fibre Bragg grating-based phase filter with a record frequency resolution of 1 GHz, at least 10× improvement compared to a conventional optical waveshaper. The all-fibre phase filter is employed to experimentally realize high-speed fully passive NOT and XNOR logic operations. We demonstrate inversion of a 45-Gbps 127-bit random sequence with an energy consumption of ~34 fJ/bit, and XNOR logic at a bit rate of 10.25 Gbps consuming ~425 fJ/bit. The scalable implementation of phase filters provides a promising path towards widespread deployment of compact, low-energy-consuming signal processors.

Low-loss fiber-to-chip edge coupler for silicon nitride integrated circuits

Silicon nitride (SiN) integrated optical waveguides have found a wide range of applications due to their low loss, broad wavelength transmission band and high nonlinearity. However, the large mode mismatch between the single-mode fiber and the SiN waveguide creates a challenge of fiber coupling to these waveguides. Here, we propose a coupling approach between fiber and SiN waveguides by utilizing the high-index doped silica glass (HDSG) waveguide as the intermediary to smooth out the mode transition. We achieved fiber-to-SiN waveguide coupling efficiency of lower than 0.8 dB/facet across the full C and L bands with high fabrication and alignment tolerances.

Hyperparametric Oscillation via Bound States in the Continuum

Optical hyperparametric oscillation based on the third-order nonlinearity is one of the most significant mechanisms to generate coherent electromagnetic radiation and produce quantum states of light. Advances in dispersion-engineered high-Q microresonators allow for generating signal waves far from the pump and decrease the oscillation power threshold to submilliwatt levels. However, the pump-to-signal conversion efficiency and absolute signal power are low, fundamentally limited by parasitic mode competition and attainable cavity intrinsic Q to coupling Q ratio, i.e., Q_{i}/Q_{c}. Here, we use Friedrich-Wintgen bound states in the continuum (BICs) to overcome the physical challenges in an integrated microresonator-waveguide system. As a result, on-chip coherent hyperparametric oscillation is generated in BICs with unprecedented conversion efficiency and absolute signal power. This work not only opens a path to generate high-power and efficient continuous-wave electromagnetic radiation in Kerr nonlinear media but also enhances the understanding of a microresonator-waveguide system-an elementary unit of modern photonics.

Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover's Algorithm with Qudits

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states-qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems-so-called ququints-that use ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.

Two-Measurement Tomography of High-Dimensional Orbital Angular Momentum Entanglement

High-dimensional (HD) entanglement enables an encoding of more bits than in the two-dimensional case and promises to increase communication capacity over quantum channels and to improve robustness to noise. In practice, however, one of the central challenges is to devise efficient methods to quantify the HD entanglement explicitly. Full quantum state tomography is a standard technology to obtain all the information about the quantum state, but it becomes impractical because the required measurements increase exponentially with the dimension in HD systems. Hence, it is highly anticipated that a new method will be found for characterizing the HD entanglement with as few measurements as possible and without introducing unwarranted assumptions. Here, we present and demonstrate a scan-free tomography method independent of dimension, which only requires two measurements for the characterization of two-photon HD orbital angular momentum (OAM) entanglement. Taking Laguerre-Gaussian modes of photons as an example, the density matrices of OAM entangled states are experimentally reconstructed with very high fidelity. Our method is also generalized to the mixed HD OAM entanglement. Our results provide realistic approaches for quantifying more complex OAM entanglement in many scientific and engineering fields such as multiphoton HD quantum systems and quantum process tomography.

Third-Order Optical Nonlinearities of 2D Materials at Telecommunications Wavelengths

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and distinctive properties have opened up new avenues for nonlinear optics and the fabrication of related devices with high performance. This paper reviews the recent advances in research on third-order optical nonlinearities of 2D materials, focusing on all-optical processing applications in the optical telecommunications band near 1550 nm. First, we provide an overview of the material properties of different 2D materials. Next, we review different methods for characterizing the third-order optical nonlinearities of 2D materials, including the Z-scan technique, third-harmonic generation (THG) measurement, and hybrid device characterization, together with a summary of the measured n₂ values in the telecommunications band. Finally, the current challenges and future perspectives are discussed.

Graphene oxide for photonics, electronics and optoelectronics

Graphene oxide (GO) was initially developed to emulate graphene, but it was soon recognized as a functional material in its own right, addressing an application space that is not accessible to graphene and other carbon materials. Over the past decade, research on GO has made tremendous advances in material synthesis and property tailoring. These, in turn, have led to rapid progress in GO-based photonics, electronics and optoelectronics, paving the way for technological breakthroughs with exceptional performance. In this Review, we provide an overview of the optical, electrical and optoelectronic properties of GO and reduced GO on the basis of their chemical structures and fabrication approaches, together with their applications in key technologies such as solar energy harvesting, energy storage, medical diagnosis, image display and optical communications. We also discuss the challenges of this field, together with exciting opportunities for future technological advances.

Programmable frequency-bin quantum states in a nano-engineered silicon device

Photonic qubits should be controllable on-chip and noise-tolerant when transmitted over optical networks for practical applications. Furthermore, qubit sources should be programmable and have high brightness to be useful for quantum algorithms and grant resilience to losses. However, widespread encoding schemes only combine at most two of these properties. Here, we overcome this hurdle by demonstrating a programmable silicon nano-photonic chip generating frequency-bin entangled photons, an encoding scheme compatible with long-range transmission over optical links. The emitted quantum states can be manipulated using existing telecommunication components, including active devices that can be integrated in silicon photonics. As a demonstration, we show our chip can be programmed to generate the four computational basis states, and the four maximally-entangled Bell states, of a two-qubits system. Our device combines all the key properties of on-chip state reconfigurability and dense integration, while ensuring high brightness, fidelity, and purity.

Prospects and applications of on-chip lasers

Integrated silicon photonics has sparked a significant ramp-up of investment in both academia and industry as a scalable, power-efficient, and eco-friendly solution. At the heart of this platform is the light source, which in itself, has been the focus of research and development extensively. This paper sheds light and conveys our perspective on the current state-of-the-art in different aspects of application-driven on-chip silicon lasers. We tackle this from two perspectives: device-level and system-wide points of view. In the former, the different routes taken in integrating on-chip lasers are explored from different material systems to the chosen integration methodologies. Then, the discussion focus is shifted towards system-wide applications that show great prospects in incorporating photonic integrated circuits (PIC) with on-chip lasers and active devices, namely, optical communications and interconnects, optical phased array-based LiDAR, sensors for chemical and biological analysis, integrated quantum technologies, and finally, optical computing. By leveraging the myriad inherent attractive features of integrated silicon photonics, this paper aims to inspire further development in incorporating PICs with on-chip lasers in, but not limited to, these applications for substantial performance gains, green solutions, and mass production.

Silicon source of frequency-bin entangled photons

We demonstrate an integrated source of frequency-entangled photon pairs on a silicon photonics chip. The emitter has a coincidence-to-accidental ratio exceeding 10³. We prove entanglement by showing two-photon frequency interference with a visibility of 94.6% ± 1.1%. This result opens the possibility of on-chip integration of frequency-bin sources with modulators and the other active and passive devices available in the silicon photonics platform.

Quantum interference of multidimensional quantum states via space-division multiplexing of a long-coherent single photon from a warm 87Rb atomic ensemble

The high-dimensional encoding of single photons can offer various possibilities for enhancing quantum information processing. This work experimentally demonstrates the quantum interference of an engineered multidimensional quantum state through the space-division multiplexing of a heralded single-photon state with a spatial light modulator (SLM) and spatial-mode mixing of a single photon through a long multimode fiber (MMF). In our experiment, the heralded single photon generated from a warm ⁸⁷Rb atomic ensemble was bright, robust, and long-coherent. The multidimensional spatial quantum state of the long-coherent single photon was transported through a 4-m-long MMF and arbitrarily controlled using the SLM. We observed the quantum interference of a single-photon multidimensional spatial quantum state with a visibility of >95%. These results may have potential applications in quantum information processing, for example, in photonic variational quantum eigensolve with high-dimensional single photons and realizing high information capacity per photon for quantum communication.

Spectral control of nonclassical light pulses using an integrated thin-film lithium niobate modulator

Manipulating the frequency and bandwidth of nonclassical light is essential for implementing frequency-encoded/multiplexed quantum computation, communication, and networking protocols, and for bridging spectral mismatch among various quantum systems. However, quantum spectral control requires a strong nonlinearity mediated by light, microwave, or acoustics, which is challenging to realize with high efficiency, low noise, and on an integrated chip. Here, we demonstrate both frequency shifting and bandwidth compression of heralded single-photon pulses using an integrated thin-film lithium niobate (TFLN) phase modulator. We achieve record-high electro-optic frequency shearing of telecom single photons over terahertz range (±641 GHz or ±5.2 nm), enabling high visibility quantum interference between frequency-nondegenerate photon pairs. We further operate the modulator as a time lens and demonstrate over eighteen-fold (6.55 nm to 0.35 nm) bandwidth compression of single photons. Our results showcase the viability and promise of on-chip quantum spectral control for scalable photonic quantum information processing.

Chip-Based High-Dimensional Optical Neural Network

Parallel multi-thread processing in advanced intelligent processors is the core to realize high-speed and high-capacity signal processing systems. Optical neural network (ONN) has the native advantages of high parallelization, large bandwidth, and low power consumption to meet the demand of big data. Here, we demonstrate the dual-layer ONN with Mach-Zehnder interferometer (MZI) network and nonlinear layer, while the nonlinear activation function is achieved by optical-electronic signal conversion. Two frequency components from the microcomb source carrying digit datasets are simultaneously imposed and intelligently recognized through the ONN. We successfully achieve the digit classification of different frequency components by demultiplexing the output signal and testing power distribution. Efficient parallelization feasibility with wavelength division multiplexing is demonstrated in our high-dimensional ONN. This work provides a high-performance architecture for future parallel high-capacity optical analog computing.

Thermo-Optic Phase Shifter with Interleaved Suspended Design for Power Efficiency and Speed Adjustment

Conventional thermo-optic devices-which can be broadly categorized to that with and without a thermal isolation trench-typically come with a tradeoff between thermal tuning efficiency and tuning speed. Here, we propose a method that allows us to directly define the tradeoff using a specially designed thermo-optic phase shifter with an interleaved isolation trench. With the design, the tuning efficiency and speed can be precisely tailored simply by controlling the duty ratio (suspended length over total heater length) of the suspended design. Phase shifters are one of the main components in photonic-integrated circuits, and having phase shifters with a flexible design approach may enable the wide adoption of photonic applications such as an optical neural network and LiDAR.

Advances in Chip-Based Quantum Key Distribution

Quantum key distribution (QKD), guaranteed by the principles of quantum mechanics, is one of the most promising solutions for the future of secure communication. Integrated quantum photonics provides a stable, compact, and robust platform for the implementation of complex photonic circuits amenable to mass manufacture, and also allows for the generation, detection, and processing of quantum states of light at a growing system’s scale, functionality, and complexity. Integrated quantum photonics provides a compelling technology for the integration of QKD systems. In this review, we summarize the advances in integrated QKD systems, including integrated photon sources, detectors, and encoding and decoding components for QKD implements. Complete demonstrations of various QKD schemes based on integrated photonic chips are also discussed.

Harnessing deep reinforcement learning to construct time-dependent optimal fields for quantum control dynamics

We present an efficient deep reinforcement learning (DRL) approach to automatically construct time-dependent optimal control fields that enable desired transitions in dynamical chemical systems. Our DRL approach gives impressive performance in constructing optimal control fields, even for cases that are difficult to converge with existing gradient-based approaches. We provide a detailed description of the algorithms and hyperparameters as well as performance metrics for our DRL-based approach. Our results demonstrate that DRL can be employed as an effective artificial intelligence approach to efficiently and autonomously design control fields in quantum dynamical chemical systems.

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.

Synthetic frequency dimension from light modulation enables scalable optical computing. The authors show an efficient silicon-based acousto-optic modulator that generates large synthetic frequency lattices and performs matrix-vector multiplications.

Experimental Investigation of Quantum Correlations in a Two-Qutrit Spin System

We report an experimental investigation of quantum correlations in a two-qutrit spin system in a single nitrogen-vacancy center in diamond at room temperatures. Quantum entanglement between two qutrits was observed at room temperature, and the existence of nonclassical correlations beyond entanglement in the qutrit case has been revealed. Our work demonstrates the potential of the NV centers as the multiqutrit system to execute quantum information tasks and provides a powerful experimental platform for studying the fundamental physics of high-dimensional quantum systems in the future.

Self-emergence of robust solitons in a microcavity

In many disciplines, states that emerge in open systems far from equilibrium are determined by a few global parameters^1,2. These states can often mimic thermodynamic equilibrium, a classic example being the oscillation threshold of a laser³ that resembles a phase transition in condensed matter. However, many classes of states cannot form spontaneously in dissipative systems, and this is the case for cavity solitons² that generally need to be induced by external perturbations, as in the case of optical memories^4,5. In the past decade, these highly localized states have enabled important advancements in microresonator-based optical frequency combs^6,7. However, the very advantages that make cavity solitons attractive for memories-their inability to form spontaneously from noise-have created fundamental challenges. As sources, microcombs require spontaneous and reliable initiation into a desired state that is intrinsically robust^8-20. Here we show that the slow non-linearities of a free-running microresonator-filtered fibre laser²¹ can transform temporal cavity solitons into the system's dominant attractor. This phenomenon leads to reliable self-starting oscillation of microcavity solitons that are naturally robust to perturbations, recovering spontaneously even after complete disruption. These emerge repeatably and controllably into a large region of the global system parameter space in which specific states, highly stable over long timeframes, can be achieved.

Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements

Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si₃N₄ microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.

Full tomography of biphoton frequency comb states requires frequency mixing operations which are hard to scale. Here, the authors propose and demonstrate a protocol exploiting advanced Bayesian statistical methods and randomized measurements coming from complex mode mixing in electro-optic phase modulators.

Gaussian Amplitude Amplification for Quantum Pathfinding

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding the minimum or maximum solutions on a weighted directed graph. We focus on the geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by Gaussian distributions. We then demonstrate how an oracle that encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases that are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem.

Integrable Atomtronic Interferometry

High sensitivity quantum interferometry requires more than just access to entangled states. It is achieved through the deep understanding of quantum correlations in a system. Integrable models offer the framework to develop this understanding. We communicate the design of interferometric protocols for an integrable model that describes the interaction of bosons in a four-site configuration. Analytic formulas for the quantum dynamics of certain observables are computed. These expose the system's functionality as both an interferometric identifier, and producer, of NOON states. Being equivalent to a controlled-phase gate acting on 2 hybrid qudits, this system also highlights an equivalence between Heisenberg-limited interferometry and quantum information. These results are expected to open new avenues for integrability-enhanced atomtronic technologies.

Nonreciprocity in Photon Pair Correlations of Classically Reciprocal Systems

Nonreciprocal optical systems have found many applications altering the linear transmission of light as a function of its propagation direction. Here, we consider a new class of nonreciprocity which appears in photon pair correlations and not in linear transmission. We experimentally demonstrate and theoretically verify this nonreciprocity in the second-order coherence functions of photon pairs produced by spontaneous four-wave mixing in a silicon microdisk. Reversal of the pump propagation direction can result in substantial extinction of the coherence functions without altering pump transmission.

Massive-mode polarization entangled biphoton frequency comb

A frequency-multiplexed entangled photon pair and a high-dimensional hyperentangled photon pair are useful to realize a high-capacity quantum communication. A biphoton frequency comb (BFC) with entanglement can be used to prepare both states. We demonstrate polarization entangled BFCs with over 1400 frequency modes, which is approximately two orders of magnitude larger than those of earlier entangled BFCs, by placing a singly resonant periodically poled LiNbO₃ waveguide resonator within a Sagnac loop. The BFCs are demonstrated by measuring the joint spectral intensity, cross-correlation, and autocorrelation. Moreover, the polarization entanglement at representative groups of frequency modes is verified by quantum state tomography, where each fidelity is over 0.7. The efficient generation of a massive-mode entangled BFC is expected to accelerate the increase of capacity in quantum communication.