Generation and control of entanglement are fundamental tasks in quantum information. In this paper, we propose a novel approach to generating controllable frequency-entangled photons using the concept of synthetic frequency dimension in an optical system. This system consists of a ring resonator made of tailored third-order nonlinear media to induce photon-photon interactions and a periodic modulator to manipulate coupling between different frequency modes. We show that this system provides a unique platform for the exploration of distinct few- or many-body quantum phases including chaos, localization, and integrability in a highly integrable photonics platform. In particular, we develop a proposal to calculate the spectral form factor, which characterizes the degree of chaos in the system and differentiates between these phases based on observable measurements. Then, the switching of the quench dynamics from an intermediate phase between integrable and chaotic to the Stark many-body phase can generate and sustain stable frequency-entangled multiphoton states. This work is the first to explore rich and controllable quantum phases beyond single-particle physics in a synthetic dimension.
Generation and control of entanglement are fundamental tasks in quantum information. In this paper, we propose a novel approach to generating controllable frequency-entangled photons using the concept of synthetic frequency dimension in an optical system. This system consists of a ring resonator made of tailored third-order nonlinear media to induce photon-photon interactions and a periodic modulator to manipulate coupling between different frequency modes. We show that this system provides a unique platform for the exploration of distinct few- or many-body quantum phases including chaos, localization, and integrability in a highly integrable photonics platform. In particular, we develop a proposal to calculate the spectral form factor, which characterizes the degree of chaos in the system and differentiates between these phases based on observable measurements. Then, the switching of the quench dynamics from an intermediate phase between integrable and chaotic to the Stark many-body phase can generate and sustain stable frequency-entangled multiphoton states. This work is the first to explore rich and controllable quantum phases beyond single-particle physics in a synthetic dimension.
The recent emerging field of synthetic dimension in photonics offers a variety of opportunities for manipulating different internal degrees of freedom of photons such as the spectrum of light. While nonlinear optical effects can be incorporated into these photonic systems with synthetic dimensions, these nonlinear effects typically result in long-range interactions along the frequency axis. Thus, it has been difficult to use the synthetic dimension concept to study a large class of Hamiltonians that involves local interactions. Here we show that a Hamiltonian that is locally interacting along the synthetic dimension can be achieved in a dynamically modulated ring resonator incorporating χ ( 3 ) nonlinearity, provided that the group velocity dispersion of the waveguide forming the ring is specifically designed. As a demonstration we numerically implement a Bose–Hubbard model and explore photon blockade effect in the synthetic frequency space. Our work opens new possibilities for studying fundamental many-body physics in the synthetic space in photonics, with potential applications in optical quantum communication and quantum computation.
Complex optical quantum states based on entangled photons are essential for investigations of fundamental physics and are the heart of applications in quantum information science. Recently, integrated photonics has become a leading platform for the compact, cost-efficient, and stable generation and processing of optical quantum states. However, onchip sources are currently limited to basic two-dimensional (qubit) two-photon states, whereas scaling the state complexity requires access to states composed of several (<2) photons and/or exhibiting high photon dimensionality. Here we show that the use of integrated frequency combs (on-chip light sources with a broad spectrum of evenly-spaced frequency modes) based on high-Q nonlinear microring resonators can provide solutions for such scalable complex quantum state sources. In particular, by using spontaneous four-wave mixing within the resonators, we demonstrate the generation of bi- and multi-photon entangled qubit states over a broad comb of channels spanning the S, C, and L telecommunications bands, and control these states coherently to perform quantum interference measurements and state tomography. Furthermore, we demonstrate the on-chip generation of entangled high-dimensional (quDit) states, where the photons are created in a coherent superposition of multiple pure frequency modes. Specifically, we confirm the realization of a quantum system with at least one hundred dimensions. Moreover, using off-the-shelf telecommunications components, we introduce a platform for the coherent manipulation and control of frequencyentangled quDit states. Our results suggest that microcavity-based entangled photon state generation and the coherent control of states using accessible telecommunications infrastructure introduce a powerful and scalable platform for quantum information science.
The investigation of integrated frequency comb sources characterized by equidistant spectral modes was initially driven by considerations toward classical applications, seeking a more practical and miniaturized way to generate stable broadband sources of light. Recently, in the context of scaling the complexity of optical quantum circuits, these on-chip approaches have provided a new framework to address the challenges associated with non-classical state generation and manipulation. For example, multi-photon and high-dimensional states were to date either inaccessible, lacked scalability, or were difficult to manipulate, requiring elaborate approaches. The emerging field of quantum frequency combs studying spectral multimode sources based on the judicious excitation of (typically) third-order nonlinear optical micro-cavities has begun to address these issues. Several quantum sources based on this concept have already been demonstrated, among them are combs of correlated photons, cross-polarized photon pairs, entangled photon pairs, multi-photon states, and high-dimensional entangled states. While sources have achieved increasing complexity, so have coherent state processing operations, demonstrated in a practical manner using standard telecommunications components. Here, we review our recent work in the development of this framework, with a focus on multi-photon and high-dimensional states. The integrated frequency comb platform thus demonstrates significant potential for the development of meaningful quantum optical technologies.
The exploitation of quantum mechanics has the potential to solve important challenges and \nintroduce novel technologies enabling, among others, powerful computation (which can solve \ncertain problems exponentially faster than classical computers), perfectly secure communications, \nas well as sensing and imaging with precision and resolutions not achievable by classical means. \nIn order to make use of the unique properties of quantum physics, experimental platforms \nthat provide access to, and allow the control of quantum states, need to be developed. In \nparticular, quantum systems composed of multiple parties are required, where each party is in a \ncoherent superposition of states, and where multiples of such parties are in a coherent \nsuperposition with each other (e.g. being entangled). Additionally, in order to make use of such \nentangled quantum systems, it is required that each individual party can be coherently controlled \nand measured. The usability and available quantum resources of the entangled system is related \nto its size, which is proportional to the number of entangled parties, as well as the dimensionality \nof the superposition each party is in. For this reason, there is a imminent demand to achieve, \ninvestigate, and improve the generation and control of large quantum systems, comprised of as \nmany entangled parties as possible, where each party is in an ideally high-dimensional \nsuperposition. \nMany quantum platforms are currently subject to extensive research, such as trapped ions, \nsuperconducting circuits, defect centers in solid-state crystals, mechanical oscillators, and optical \nquantum states (i.e. photons). While all platforms provide distinct advantages (as well as \nchallenges), optical photon states are of particular interest, because they can interact with other \nquantum systems, and can be transmitted over long distances while preserving their quantum \ncoherence without the need for extensive shielding. A large variety of sources for optical \nquantum states has been demonstrated, however most such implementations suffer from high \ncomplexity, ultimately limiting their scalability. Integrated photonics has recently become a \nleading platform for the compact, cost-efficient, and stable generation and processing of optical \nquantum states. However, to date, integrated quantum sources have only been able to generate \nphoton pairs, which operated on single channels, and single polarization modes. Furthermore, in \nthe few realizations of on-chip entanglement, they were limited to two entangled parties, where \neach party was in a two-dimensional superposition. These limitations of current integrated photon sources arise in large part from the concepts currently exploited to generate and control these \nstates. In particular, path-entangled sources are the most commonly used, but increasing the \nquantum state complexity requires a significant, and very challenging, increase in device \ncomplexity. There is therefore an urgent need to develop new concepts that can achieve the onchip \ngeneration of large and complex photon states without increasing source complexity, while \nstill enabling coherent quantum state control and detection. \nIn this work, we aim to address these limitations by making use of multiple frequency and \ntemporal modes within a single spatial waveguide mode (therefore readily compatible with \nstandard optical fibers) of an on-chip microring resonator. This approach is in contrast to more \ncommonly used techniques relying on path entanglement, which exploits multiple spatial modes \nand generates entanglement by means of complex waveguide structures. Working within a single \nspatial mode, we achieve the first demonstration of pure heralded single photons and entangled \nphoton pairs, which are emitted on multiple frequency modes from a single source. We then \ndemonstrate the first generation of multi-photon entangled quantum states on a photonic chip. \nFinally, by making use of the spectral multi-mode nature of optical frequency combs, we achieve \nthe generation of photon pairs in a coherent superposition of multiple frequency modes, \nrepresenting the first generation of high-dimensional entangled states on a photonic chip. \nOur work represents a significant step forward in the generation of complex quantum \nstates on a photonic chip and in a single spatial mode compatible with standard optical fibers. In \naddition, we demonstrated coherent quantum state control and manipulation for all generated \nstates by means of standard telecommunications components, which could in the future be also \nintegrated on single, monolithic chip. Our results indicate that the exploitation of integrated \noptical frequency comb sources for the generation of optical quantum states can provide a \nscalable and practical platform for quantum technologies.
Abstract Based on a coupled resonator array, we theoretically construct and numerically simulate a nonlinear quantum optics platform to dynamically control the Bloch wavevector. By scanning the modulation parameters ( α , k y ), we reproduce the Hofstadter’s butterfly structure in the biphoton energy spectrum and reveal clear correspondences among the eigenenergy spectrum, transmission spectrum, and biphoton joint spectral intensity (JSI). Further research demonstrates that screening the pump wavelength can effectively tailor the JSI profile and the Schmidt number of the quantum state, enabling flexible manipulation of frequency entanglement characteristics. This work provides a theoretical framework for exploring quantum state generation and manipulation in nonlinear topological photonic systems and demonstrates the potential for realizing programmable quantum light sources in integrated quantum photonic circuits.
Synthetic frequency dimension offers a powerful approach to simulate lattice models and control photon dynamics. However, extending this concept into the quantum regime, particularly at the single-photon level, has remained challenging in photonic platforms. Here, we demonstrate quantum-state initialization and detection of single-photon evolutions within a synthetic frequency lattice by integrating a superconducting qubit with a 16-meter aluminum coaxial cable. A tunable superconducting quantum interference device (SQUID)-based modulator is employed to synthesize lattice couplings and artificial gauge fields. We observe single-photon quantum random walks and Bloch oscillations, as well as nonadiabatic, unidirectional frequency conversion under rapid temporal modulation of the lattice Hamiltonian, together with band-structure measurements. The lattice connectivity can be readily reconfigured to construct higher-dimensional lattices using multiple drive tones. Our results establish superconducting quantum circuits as a versatile platform for programmable Hamiltonians and extensible synthetic lattices with flexible single-photon control.