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This experimental work demonstrates multipartite quantum correlation in bright frequency combs out of a microresonator integrated on silicon nitride working above its oscillation threshold. Multipartite features, going beyond so far reported two-mode correlation, naturally arise due to a cascade of non-linear optical processes, making a single-color laser pump sufficient to initiate their generation. Our results show the transition from two-mode to multipartite correlation, witnessed by noise reductions as low as $-2.5$\,dB and $-2$\,dB, respectively, compared to corresponding classical levels. A constant of the movement of the non-linear interaction Hamiltonian is identified and used to asses the multipartite behavior. Reported demonstrations pave the way to next generation on-chip multipartite sources for quantum technologies applications., Comment: 4 figures

In multimode optical systems, the spectral covariance matrix encodes all the information about quantum correlations between the quadratures of Gaussian states. Recent research has revealed that, in scenarios that are more common than previously thought, part of these correlations remain inaccessible to standard homodyne detection scheme. Formally, this effect can be attributed to a non-real spectral covariance matrix. In this work, we provide a systematic framework and explicit criteria for identifying experimental configurations leading to such a behavior. This study will facilitate the proper exploitation and optimal engineering of CV quantum resources., Comment: 13 pages, 11 figures, submitted

Rare-earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare-earth ions ensemble, but only a few studies have focused on its the dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest neighbors nuclear spins in the crystal. The primary non-Kramers rare-earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations., Comment: 20 pages, 14 figures

The frequency comb of a multimode interferometer offers exceptional scalability potential for field-encoded quantum information. However, the staple field detection method, homodyne detection, cannot access quantum information in the whole comb because some spectral quadratures (and their asymmetries with respect to the LO) are out of reach. We present here the first general approach to make arbitrary, one-shot measurements of a multimode quantum optical source, something that is required for photonic quantum computing and is not possible when using homodyne detection with a pulse-shaped LO. This approach uses spectral mode-matching, which can be understood as interferometry with a memory effect. We derive a complete formalism and propose an implementation by microcavity arrays., Comment: 16 pages, 12 figures, submitted

We present a theoretical model of multimode quantum correlations in bright frequency combs generated in continuous-wave regime by microresonators above threshold. Our analysis shows how these correlations emerge from cascading four-wave mixing processes fed by the input pump as well as the generated bright beams. Logarithmic negativity criterion is employed to quantify entanglement between partitions of modes, demonstrating the transition from a bipartite regime just above the oscillation threshold to the multipartite one at higher input pump powers. Due to its generality, our model can be safely used to describe other kinds of non-linear $\chi$ (3) cavities.

In the context of quantum integrated photonics, this work investigates the quantum properties of light generated by silicon and silicon nitride micro-resonators pumped in pulsed regime. The developed theoretical model, performed in terms of the morphing supermodes, provides a comprehensive description of the generated quantum states. Remarkably, it shows that a full measurement of states carrying optimal squeezing levels is not accessible to standard homodyne detection, thus leaving hidden part of generated quantum features. By presenting and discussing this behaviour, as well as possible strategies to amend it, this work proves itself essential to future quantum applications exploiting micro-resonators as sources of multimode states.

This work marks an important progress towards practical quantum optical technologies in the continuous variable regime, as it shows the feasibility of experiments where non-Gaussian state generation entirely relies on plug-&-play components from guided-wave optics technologies. This strategy is demonstrated experimentally with the heralded preparation of low amplitude Schr\"odinger cat states based on single-photon subtraction from a squeezed vacuum. All stages of the experiment are based on off-the-shelf fiber components. This leads to a stable, compact, and easily re-configurable realization, fully compatible with existing fibre networks and, more in general, with future out-of-the-laboratory applications.

This work establishes a versatile theoretical framework that explicitly describes single-photon subtraction from multimode quantum light in the context of non-Gaussian state generation and manipulation. The treatment focuses on easy-to-implement configurations in which no mode-selective operation is available and evaluates features and advantages of scheme where only simple filtering stages are employed on the experiments. Such configuration, by considerably reducing the experimental overheads, makes experiments involving single photon subtraction easier to be implemented. Obtained theoretical framework allows retrieving, given a multimode input state, optimal conditions required to herald and then to detect non-Gaussian states, providing a practical and powerful toolbox for experiments' design. The application of the proposed approach to the case study of Schr\"odinger kitten preparation starting from a frequency multimode squeezed state illustrates the impact of the derived theoretical tools.

We demonstrate supermode-based second harmonic generation in an integrated nonlinear interferometer made of linear and nonlinear directional couplers. We use a fully-fibered pump shaper to demonstrate second harmonic generation pumped by the symmetric or anti-symmetric fundamental spatial modes. The selection of the pumping mode and thus of a specific SHG spectral profile is achieved through the selection of the fundamental wavelength and via a robust phase setting scheme. We use two methods: either post-selecting or actively setting the pumping mode. Such a modal phase matching paves the way for classical and quantum applications of coupled nonlinear photonic circuits, where multimode excitation, encoding and detection are a route for multiplexing and scaling up light-processing., Comment: 14 pages, 7 figures

Photonic quantum technology can be enhanced by monolithic fabrication of both the underpinning quantum hardware and the corresponding electronics for classical readout and control. Together, this enables miniaturisation and mass-manufacture of small quantum devices---such as quantum communication nodes, quantum sensors and sources of randomness---and promises the precision and scale of fabrication required to assemble useful quantum computers. Here we combine CMOS compatible silicon and germanium-on-silicon nano-photonics with silicon-germanium integrated amplification electronics to improve performance of on-chip homodyne detection of quantum light. We observe a 3 dB bandwidth of 1.7 GHz, shot-noise limited performance beyond 9 GHz and minaturise the required footprint to 0.84 mm. We use the device to observe quantum squeezed light, from 100 MHz to 9 GHz, generated in a lithium niobate waveguide. This demonstrates that an all-integrated approach yields faster homodyne detectors for quantum technology than has been achieved to-date and opens the way to full-stack integration of photonic quantum devices., Comment: Nat. Photonics (2020)

Progress in integrated photonics enables combining several elementary functions on single substrates for realizing advanced functionnalized chips. We report a monolithic integrated quantum photonic realization on lithium niobate, where nonlinear optics and electro-optics properties have been harnessed simultaneously for generating heralded configurable, two-photon states. Taking advantage of a picosecond pump laser and telecom components, we demonstrate the production of various path-coded heralded two-photon states, showing 94\% raw visibility for Hong-Ou-Mandel interference. The versatility and performance of such a highly integrated photonic entanglement source enable exploring more complex quantum information processing protocols finding application in communication, metrology and processing tasks.

We investigate the impact of photorefractive effect on lithium niobate integrated quantum photonic circuits dedicated to continuous variable on-chip experiments. The circuit main building blocks, i.e. cavities, directional couplers, and periodically poled nonlinear waveguides are studied. This work demonstrates that, even when the effect of photorefractivity is weaker than spatial mode hopping, they might compromise the success of on-chip quantum photonics experiments. We describe in detail the characterization methods leading to the identification of this possible issue. We also study to which extent device heating represents a viable solution to counter this effect. We focus on photorefractive effect induced by light at 775 nm, in the context of the generation of non-classical light at 1550 nm telecom wavelength.

We propose and experimentally demonstrate a plug-and-play, practical, and enabling method allowing to synchronize the building blocks of a quantum network in an all-optical way. Our scheme relies on mature and reliable classical telecommunication and non-linear optical technologies and can be implemented in a universal way with off-the-shelf components. Compared to already reported solutions, it allows achieving high-quality synchronization compatible with high network-operation rate and is free from opto-electronic jitters affecting servo-loop based configurations. We test our scheme with a genuine quantum optical method in terms of the interference between two photons coming from two remotely synchronized sources spaced by distances of up to 100 km. Measured visibilities well above 90% confirm the validity of our approach. Due its simplicity and high-quality performance, our scheme paves the way for the synchronization of long-distance quantum networks based on fibre, free-space, as well as hybrid solutions.

We propose a scheme for the generation of hybrid states entangling a single-photon time-bin qubit with a coherent-state qubit encoded on phases. Compared to other reported solutions, time-bin encoding makes hybrid entanglement particularly well adapted to applications involving long-distance propagation in optical fibers. This makes our proposal a promising resource for future out-of-the-laboratory quantum communication. In this perspective, we analyze our scheme by taking into account realistic experimental resources and discuss the impact of their imperfections on the quality of the obtained hybrid state.

We develop a universal approach enabling the study of any multimode quantum optical system evolving under a quadratic Hamiltonian. Our strategy generalizes the standard symplectic analysis and permits the treatment of multimode systems even in situations where traditional theoretical methods cannot be applied. This enables the description and investigation of a broad variety of key-resources for experimental quantum optics, ranging from optical parametric oscillators, to silicon-based micro-ring resonator, as well as opto-mechanical systems.

We demonstrate a squeezing experiment exploiting the association of integrated optics and telecom technology as key features for compact, stable, and practical continuous variable quantum optics. In our setup, squeezed light is generated by single pass spontaneous parametric down conversion on a lithium niobate photonic circuit and detected by an homodyne detector whose interferometric part is directly integrated on the same platform. The remaining parts of the experiment are implemented using commercial plug-and-play devices based on guided-wave technologies. We measure, for a CW pump power of 40\,mW, a squeezing level of $-2.00\pm0.05$\,dB, (antisqueezing $+2.80\pm0.05$\,dB) thus confirming the validity of our approach and opening the way toward miniaturized and easy-to-handle continuous variable based quantum systems.

In the context of ultra-fast quantum communication and random number generation, detection timing-jitters represent a strong limitation as they can introduce major time-tagging errors and affect the quality of time-correlated photon counting or quantum state engineering. Despite their importance in emerging photonic quantum technologies, no detector model including such effects has been developed so far. We propose here an operational theoretical model based on POVM density formalism able to explicitly quantify the effect of timing-jitter for a typical class of single photon detector. We apply our model to some common experimental situations.

In a recent paper [Phys. Rev. A {\bf 96}, 053822 (2017)], we proposed a strategy to generate bipartite and quadripartite continuous-variable entanglement of bright quantum states based on degenerate down-conversion in a pair of evanescently coupled nonlinear $\chi^{(2)}$ waveguides. Here, we show that the resources needed for obtaining these features can be optimized by exploiting the regime of second harmonic generation: the combination of depletion and coupling among pump beams indeed supplies all necessary wavelengths and appropriate phase mismatch along propagation. Our device thus entangles the two fundamental classical input fields without the participation of any harmonic ancilla. Depending on the propagation distance, the generated harmonics are entangled in bright or vacuum modes. We also evidence two-color bipartite and quadripartite entanglement over the interacting modes. The proposed device represents a boost in continuous-variable integrated quantum optics since it enables a broad range of quantum effects in a very simple scheme, which optimizes the resources and can be easily realized with current technology., Comment: 8 pages, 8 figures

We study continuous-variable entanglement of bright quantum states in a pair of evanescently coupled nonlinear $\chi^{(2)}$ waveguides operating in the regime of degenerate down-conversion. We consider the case where only the energy of the nonlinearly generated fields is exchanged between the waveguides while the pump fields stay independently guided in each original waveguide. We show that this device, when operated in the depletion regime, entangles the two non-interacting bright pump modes due to a nonlinear cascade effect. It is also shown that two-colour quadripartite entanglement can be produced when certain system parameters are appropriately set. This device works in the traveling-wave configuration, such that the generated quantum light shows a broad spectrum. The proposed device can be easily realized with current technology and therefore stands as a good candidate for a source of bipartite or multipartite entangled states for the emerging field of optical continuous-variable quantum information processing., Comment: 10 pages, 12 figures

Integrated optical components on lithium niobate play a major role in standard high-speed communication systems. Over the last two decades, after the birth and positioning of quantum information science, lithium niobate waveguide architectures have emerged as one of the key platforms for enabling photonics quantum technologies. Due to mature technological processes for waveguide structure integration, as well as inherent and efficient properties for nonlinear optical effects, lithium niobate devices are nowadays at the heart of many photon-pair or triplet sources, single-photon detectors, coherent wavelength-conversion interfaces, and quantum memories. Consequently, they find applications in advanced and complex quantum communication systems, where compactness, stability, efficiency, and interconnectability with other guided-wave technologies are required. In this review paper, we first introduce the material aspects of lithium niobate, and subsequently discuss all of the above mentioned quantum components, ranging from standard photon-pair sources to more complex and advanced circuits., Comment: To appear as a review paper for Journal of Optics (JOPT)

We demonstrate, for the first time, the realization of an entirely guided-wave squeezing experiment at a telecom wavelength. The state generation relies on waveguide non-linear optics technology while squeezing collection and transmission are implemented by using only telecom fibre components. We observe up to $-1.83\pm0.05$ dB of squeezing emitted at 1542 nm in CW pumping regime. The compactness and stability of the experiment, compared to free-space configurations, represent a significant step towards achieving out-of-the-lab CV quantum communication, fully compatible with existing telecom fibre networks. We believe that this work stands as a promising approach for real applications as well as for "do-it-yourself" experiments, Comment: 4 pages, 3 figures

The realization of an ultra-fast source of heralded single photons emitted at the wavelength of 1540 nm is reported. The presented strategy is based on state-of-the-art telecom technology, combined with off-the-shelf fiber components and waveguide non-linear stages pumped by a 10 GHz repetition rate laser. The single photons are heralded at a rate as high as 2.1 MHz with a heralding efficiency of 42%. Single photon character of the source is inferred by measuring the second-order autocorrelation function. For the highest heralding rate, a value as low as 0.023 is found. This not only proves negligible multi-photon contributions but also represents the best measured value reported to date for heralding rates in the MHz regime. These prime performances, associated with a device-like configuration, are key ingredients for both fast and secure quantum communication protocols., Comment: 5 pages, 2 figures

Using a continuous-wave type-II optical parametric oscillator below threshold, we have demonstrated a novel source of heralded single-photons with high-fidelity. The generated state is characterized by homodyne detection and exhibits a 79% fidelity with a single-photon Fock state (91% after correction of detection loss). The low admixture of vacuum and the well-defined spatiotemporal mode are critical requirements for their subsequent use in quantum information processing.

Single-photon entangled states, i.e. states describing two optical paths sharing a single photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness allowing one not only to say whether a given state is path-entangled but also that entanglement lies in the subspace where the optical paths are each filled with one photon at most, i.e. refers to single-photon entanglement. It uses local homodyning only and relies on no assumption about the Hilbert space dimension of the measured system. Our work provides a simple and trustful method for verifying the proper functioning of future quantum networks., Comment: published version

Single-photons play an important role in emerging quantum technologies and information processing. An efficient generation technique consists in preparing such states via a conditional measurement on photon-number correlated beams: the detection of a single-photon on one of the beam can herald the generation of a single-photon state on the other one. Such scheme strongly depends on the heralding detector properties, such as its quantum efficiency, noise or photon-number resolution ability. These parameters affect the preparation rate and the fidelity of the generated state. After reviewing the theoretical description of optical detectors and conditional measurements, and how both are here connected, we evaluate the effects of these properties and compare two kind of devices, a conventional on/off detector and a two-channel detector with photon-number resolution ability.

The interaction of a quantum system with the environment leads to the so-called quantum decoherence. Beyond its fundamental significance, the understanding and the possible control of this dynamics in various scenarios is a key element for mastering quantum information processing. Here we report the quantitative probing of what can be called the quantum decoherence of detectors, a process reminiscent of the decoherence of quantum states in the presence of coupling with a reservoir. We demonstrate how the quantum features of two single-photon counters vanish under the influence of a noisy environment. We thereby experimentally witness the transition between the full-quantum operation of the measurement device to the "semi-classical regime", described by a positive Wigner function. The exact border between these two regimes is explicitely determined and measured experimentally.

Quantum states with non-Gaussian statistics generated by optical parametric oscillators (OPO) with fluctuating parameters are studied by means of the Kurtosis excess of the external field quadratures. The field generated is viewed as the response of a nonlinear device to the fluctuations of laser pump amplitude and frequency, crystal temperature and cavity detuning, in addition to quantum noise sources. The Kurtosis excess has been evaluated perturbatively up to the third order in the strength of the crystal nonlinear coupling factor and the second order in the classical fluctuating parameters. Applied to the device described in Opt. Expr. 13, 948-956 (2005) the model has given values of the Kurtosi excess in good agreement with the measured ones., Comment: 10 pages, new figure added

We report the first experimental observation of bright EPR beams produced by a type-II optical parametric oscillator operating above threshold at frequency degeneracy. The degenerate operation is obtained by introducing a birefringent plate inside the cavity resulting in phase locking. After filtering the pump noise, which plays a critical role, continuous-variable EPR correlations between the orthogonally polarized signal and idler beams are demonstrated.

We suggest a scheme to reconstruct the covariance matrix of a two-mode state using a single homodyne detector plus a polarizing beam splitter and a polarization rotator. It can be used to fully characterize bipartite Gaussian states and to extract relevant informations on generic states., Comment: 7 pages, 1 figure