[8][9][10][11] . Here, we demonstrate on- as schematized in Fig. 1. In particular, we used a spectrally-filtered mode-locked laser to excite a single resonance of the microring at ~1550 nm wavelength, in turn producing pairs of correlated signal and idler photons spectrally-symmetric to the excitation field and which cover multiple resonances, see Fig. 1. The individual photons were intrinsically generated in a superposition of multiple frequency modes and owing the energy conservation of SFWM, this approach leads to the realization of a two-photon high-dimensional frequency-entangled state.We performed two experiments to characterize the dimensionality of the generated state. The large free spectral range (FSR) of the ring cavity (~200 GHz), i.e. the spectral separation between adjacent resonance modes, enabled us to use a commercially available telecommunications programmable filter (see Methods) for individually selecting and manipulating the states in these modes (given the filter's operational bandwidth of 1527.4 to 1567.5 nm, we were able to access 10 signal and 10 idler resonances). We measured the joint spectral intensity, describing the twophoton state's frequency distribution, see Methods. Specifically, we routed different frequency 4 modes of the signal and idler photons to two single photon detectors and counted photon coincidences for all sets of mode combinations. As shown in Fig. 2a, photon coincidences were measured only for mode combinations spectrally-symmetric to the excitation, a characteristic of frequency-entangled states. In addition, we evaluate the Schmidt number of our source. This parameter describes the lowest number of significant orthogonal modes in a bipartite system, and therefore describes its effective dimension. Through a Schmidt mode decomposition of the correlation matrix (see Methods), we extracted the lower bound for the Schmidt number to be 9.4, see Fig. 2b.Due to the narrow spectral linewidth of the photons (~800 MHz) and the related long coherence time (~0.6 ns), the effective time resolution of our full detection system (~100 ps) was sufficient to perform time-domain measurements and extract the maximal dimensionality of the state, seeMethods. Specifically, we measured the second-order coherence of the signal and idler fields using These measurements confirmed that one photon pair simultaneously spans multiple frequency modes, forming a high-dimensional entangled state of the form, with ∑| | 2 = 1 (Eq. 1).Here | ⟩ s and | ⟩ i are pure, single-frequency quantum states of the signal (s) and idler (i) photons, and k=1,2,…,D is the mode number, as indicated in Fig. 3 In general, the exploitation of quDit states for quantum information processing motivates the need for high-dimensional operations that enable access to multiple modes with a minimum number of components. While the individual elements (phase shifters and beam splitters) employed in the framework of spatial-mode quantum information processing usually operate on only one or two modes at a time 1 , the frequency...

Complex optical photon states with entanglement shared among several modes are critical to improving our fundamental understanding of quantum mechanics and have applications for quantum information processing, imaging, and microscopy. We demonstrate that optical integrated Kerr frequency combs can be used to generate several bi- and multiphoton entangled qubits, with direct applications for quantum communication and computation. Our method is compatible with contemporary fiber and quantum memory infrastructures and with chip-scale semiconductor technology, enabling compact, low-cost, and scalable implementations. The exploitation of integrated Kerr frequency combs, with their ability to generate multiple, customizable, and complex quantum states, can provide a scalable, practical, and compact platform for quantum technologies.

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Nonlinear optical processes are one of the most important tools in modern optics with a broad spectrum of applications in, for example, frequency conversion, spectroscopy, signal processing and quantum optics. For practical and ultimately widespread implementation, on-chip devices compatible with electronic integrated circuit technology offer great advantages in terms of low cost, small footprint, high performance and low energy consumption. While many on-chip key components have been realized, to date polarization has not been fully exploited as a degree of freedom for integrated nonlinear devices. In particular, frequency conversion based on orthogonally polarized beams has not yet been demonstrated on chip. Here we show frequency mixing between orthogonal polarization modes in a compact integrated microring resonator and demonstrate a bi-chromatically pumped optical parametric oscillator. Operating the device above and below threshold, we directly generate orthogonally polarized beams, as well as photon pairs, respectively, that can find applications, for example, in optical communication and quantum optics.

Recent developments in quantum photonics have initiated the process of bringing photonic-quantumbased systems out-of-the-lab and into real-world applications. As an example, devices to enable the exchange of a cryptographic key secured by the laws of quantum mechanics are already commercially available. In order to further boost this process, the next step is to transfer the results achieved by means of bulky and expensive setups into miniaturized and affordable devices. Integrated quantum photonics is exactly addressing this issue. In this paper, we briefly review the most recent advancements in the generation of quantum states of light on-chip. In particular, we focus on optical microcavities, as they can offer a solution to the problem of low efficiency that is characteristic of the materials typically used in integrated platforms. In addition, we show that specifically designed microcavities can also offer further advantages, such as compatibility with telecom standards (for exploiting existing fibre networks) and quantum memories (necessary to extend the communication distance), as well as giving a longitudinal multimode character for larger information transfer and processing. This last property (i.e., the increased dimensionality of the photon quantum state) is achieved through the ability to generate multiple photon pairs on a frequency comb, corresponding to the microcavity resonances. Further achievements include the possibility of fully exploiting the polarization degree of freedom, even for integrated devices. These results pave the way for the generation of integrated quantum frequency combs that, in turn, may find important applications toward the realization of a compact quantum-computing platform.

Abstract:The on-chip generation of large and complex optical quantum states will enable low-cost and accessible advances for quantum technologies, such as secure communications and quantum computation. Integrated frequency combs are on-chip light sources with a broad spectrum of evenly-spaced frequency modes, commonly generated by four-wave mixing in optically-excited nonlinear micro-cavities, whose recent use for quantum state generation has provided a solution for scalable and multi-mode quantum light sources. Pulsed quantum frequency combs are of particular interest, since they allow the generation of singlefrequency-mode photons, required for scaling state complexity towards, e.g., multi-photon states, and for quantum information applications. However, generation schemes for such pulsed combs have, to date, relied on micro-cavity excitation via lasers external to the sources, being neither versatile nor power-efficient, and impractical for scalable realizations of quantum technologies. Here, we introduce an actively-modulated, nested-cavity configuration that exploits the resonance pass-band characteristic of the micro-cavity to enable a mode-locked and energy-efficient excitation. We demonstrate that the scheme allows the generation of high-purity photons at large coincidence-to-accidental ratios (CAR). Furthermore, by increasing the repetition rate of the excitation field via harmonic modelocking (i.e. driving the cavity modulation at harmonics of the fundamental repetition rate), we managed to increase the pair production rates (i.e. source efficiency), while maintaining a high CAR and photon purity. Our approach represents a significant step towards the realization of fully on-chip, stable, and versatile sources of pulsed quantum frequency combs, crucial for the development of accessible quantum technologies.

17 18 19Most mode-locking techniques introduced in the past 1,2 focused mainly on increasing the 20 spectral bandwidth to achieve ultra-short, sub-picosecond-long coherent light pulses. By 21 contrast, little importance seemed to be given to mode-locked lasers generating Fourier-22 transform-limited nanosecond pulses, which feature the narrow spectral bandwidths 23 required for applications in spectroscopy 3 , efficient excitation of molecules 4 , sensing, and 24 quantum optics 5 . Here we demonstrate a passively mode-locked laser system that relies on 25 simultaneous nested-cavity filtering and cavity-enhanced nonlinear interactions within an 26 integrated microring resonator. This allows us to produce transform-limited optical pulses 27 in the nanosecond regime (4.3 nanoseconds in duration), with an overall spectral bandwidth 28 of 104.9 MHz -more than two orders of magnitude smaller than previous realizations. The 29 very narrow bandwidth of our laser makes it possible to fully characterize its spectral 30 properties in the radiofrequency-domain using widely available GHz-bandwidth 31 optoelectronic components. In turn, this characterization reveals the strong coherence of 32 the generated pulse train. 33

Induced photon correlations are directly demonstrated by exploring two coupled nonlinear processes in an integrated device. Using orthogonally polarized modes within an integrated microring cavity, phase matching of two different nonlinear four‐wave mixing processes is achieved simultaneously, wherein both processes share one target frequency mode, while their other frequency modes differ. The overlap of these modes leads to the coupling of both nonlinear processes, producing photon correlations. The nature of this process is confirmed by means of time‐ and power‐dependent photon correlation measurements. These findings are relevant to the fundamental understanding of spontaneous parametric effects as well as single‐photon‐induced processes, and their effect on optical quantum state generation and control.