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We measure the nonlinearity of a telecom-wavelength superconducting nanowire single-photon detector via incoherent beam combination. At typical photon count rates and detector bias current, the observed relative deviation from a perfectly linear response is in the order of 0.1% when the flux is doubled. This arises from a balance between the counteracting nonlinearities of deadtime-induced detector saturation and of multi-photon detections. The observed behaviour is modelled empirically, which suffices for a correction of measured data. In addition, statistical simulations, taking into account the measured recovery of the detection efficiency, provide insight into possible mechanisms of multi-photon detection., Comment: 9 pages, 8 figures

Entanglement and interference are both hallmark effects of quantum physics. Particularly rich dynamics arise when multiple (at least partially) indistinguishable particles are subjected to either of these phenomena. By combining both entanglement and many-particle interference, we propose an interferometric setting through which N-particle interference can be observed, while any interference of lower orders is strictly suppressed. We experimentally demonstrate this effect in a four-photon interferometer, where the interference is nonlocal, in principle, as only pairs of photons interfere at two separate and independent beam splitters. A joint detection of all four photons identifies a high-visibility interference pattern varying as a function of their collective four-particle phase, a genuine four-body property.

The surface of semiconductor nanostructures has a major impact on their electronic and optical properties. Disorder and defects in the surface layer typically cause degradation of charge carrier transport and radiative recombination dynamics. However, surface vicinity is inevitable for many scalable nano-optical applications. Epitaxially grown quantum dots are the best candidate for high-performance single photon emission and show great potential for quantum technologies. Yet, these emitters only reveal their excellent properties if they are deeply embedded in a semiconductor host. Until today, quantum dots close to surfaces yield weak, broad, and unstable emissions. Here, we show the complete restoration of optical properties from quantum dots grown directly on a semiconductor surface. The vanishing luminescence from the as-grown sample turns into bright, ultra-stable, coherent and blinking-free single photon emission after sulphur passivation. Under quasi-resonant excitation, single photons are generated with 98.8% purity, 77% indistinguishability, linewidths down to 4 $\mu$eV and 99.69% persistency across 11 orders of magnitude in time. The emission is stable even after two years and when being subjected to nanomanufacturing processes. Some long-standing stumbling blocks for surface-dominated quantum dots are thereby removed, unveiling new possibilities for hybrid nano-devices and applications in quantum communication or sensing., Comment: New experiments show that the results have to be re-interpreted, most likely leading to a new manuscript

We report on a multi-photon source based on active demultiplexing of single photons emitted from a resonantly excited GaAs quantum dot. Active temporal-to-spatial mode demultipexing is implemented via resonantly enhanced free-space electro-optic modulators, making it possible to route individual photons at high switching rates of 38 MHz. We demonstrate routing into four spatial modes with a high end-to-end efficiency of 79% and measure a four-photon coincidence rate of 0.17 Hz mostly limited by the single-photon source brightness and not by the efficiency of the demultiplexer itself. We use the demultiplexer to characterize the pairwise indistinguishability of consecutively emitted photons from the quantum dot with variable delay time., Comment: The supplementary material is included as ancillary file

Semiconductor-based emitters of pairwise photonic entanglement are a promising constituent of photonic quantum technologies. They are known for the ability to generate discrete photonic states on-demand with low multiphoton emission, near-unity entanglement fidelity, and high single photon indistinguishability. However, quantum dots typically suffer from luminescence blinking, lowering the efficiency of the source and hampering their scalable application in quantum networks. In this paper, we investigate and adjust the intermittence of the neutral exciton emission in a GaAs/AlGaAs quantum dot under two-photon resonant excitation of the neutral biexciton. We investigate the spectral and quantum optical response of the quantum dot emission to an additional wavelength tunable gate laser, revealing blinking caused by the intrinsic Coulomb blockade due to charge capture processes. Our finding demonstrates that the emission quenching can be actively suppressed by controlling the balance of free electrons and holes in the vicinity of the quantum dot and thereby significantly increasing the quantum efficiency by 30%., Comment: 7 pages, 4 figures

Semiconductor quantum dots are promising building blocks for quantum communication applications. Although deterministic, efficient, and coherent emission of entangled photons has been realized, implementing a practical quantum repeater remains outstanding. Here we explore the statistical limits for entanglement swapping with sources of polarization-entangled photons from the commonly used biexciton-exciton cascade. We stress the necessity of tuning the exciton fine structure, and explain why the often observed time evolution of photonic entanglement in quantum dots is not applicable for large quantum networks. We identify the critical, statistically distributed device parameters for entanglement swapping based on two sources. A numerical model for benchmarking the consequences of device fabrication, dynamic tuning techniques, and statistical effects is developed, in order to bring the realization of semiconductor-based quantum networks one step closer to reality., Comment: 9 pages, 4 figures

We experimentally investigate the suitability of a multi-path waveguide interferometer with mechanical shutters for performing a test for hypercomplex quantum mechanics. Probing the interferometer with coherent light we systematically analyse the influence of experimental imperfections that could lead to a false-positive test result. In particular, we analyse the effects of detector nonlinearity, input-power and phase fluctuations on different timescales, closed-state transmissivity of shutters and crosstalk between different interferometer paths. In our experiment, a seemingly small shutter transmissivity in the order of about $2 \times 10^{-4}$ is the main source of systematic error, which suggests that this is a key imperfection to monitor and mitigate in future experiments., Comment: 23 pages, 7 figures

We investigate, in a four photon interference experiment in a laser-written waveguide structure, how symmetries control the suppression of many-body output events of a $J_x$ unitary. We show that totally destructive interference does not require mutual indistinguishability between all, but only between symmetrically paired particles, in agreement with recent theoretical predictions. The outcome of the experiment is well described by a quantitative simulation which accounts for higher order emission of the photon source, imbalances in the scattering network, partial distinguishability, and photon loss., Comment: 14 pages, 7 figures

We present a first comprehensive study on deterministic spin preparation employing excited state resonances of droplet etched GaAs quantum dots. This achievement facilitates future investigations of spin qubit based quantum memories using the GaAs quantum dot material platform. By observation of excitation spectra for a range of fundamental excitonic transitions the properties of different quantum dot energy levels, i.e. shells, are revealed. The innovative use of polarization resolved excitation and detection in quasi-resonant excitation spectroscopy facilitates determination of $85$ $\%$ maximum spin preparation fidelity - irrespective of the relative orientations of lab and quantum dot polarization eigenbases. Additionally, the characteristic non-radiative decay time is investigated as a function of ground state, excitation resonance and excitation power level, yielding decay times as low as $29$ ps for s-p-shell exited state transitions. Finally, by time resolved correlation spectroscopy it is demonstrated that the employed excitation scheme has a significant impact on the electronic environment of quantum dot transitions thereby influencing its charge and coherence., Comment: 13 pages, 11 figures

High-fidelity polarization-entangled photons are a powerful resource for quantum communication, distributing entanglement and quantum teleportation. The Bell-CHSH inequality $S\leq2$ is violated by bipartite entanglement and only maximally entangled states can achieve $S=2\sqrt{2}$, the Tsirelson bound. Spontaneous parametric down-conversion sources can produce entangled photons with correlations close to the Tsirelson bound. Sagnac configurations offer intrinsic stability, compact footprint and high collection efficiency, however, there is often a trade off between source brightness and entanglement visibility. Here, we present a Sagnac polarization-entangled source with $2\sqrt{2}-S=(5.65\pm0.57)\times10^{-3}$, on-par with the highest values recorded, while generating and detecting $(4660\pm70)$ pairs/s/mW, which is a substantially higher brightness than previously reported for Sagnac sources and around two orders of magnitude brighter than for traditional cone sources with the highest $S$ parameter. Our source records $0.9953\pm0.0003$ concurrence and $0.99743\pm0.00014$ fidelity to an ideal Bell state. By studying systematic errors in Sagnac sources, we identify that the precision of the collection focal point inside the crystal plays the largest role in reducing the $S$ parameter in our experiment. We provide a pathway that could enable the highest $S$ parameter recorded with a Sagnac source to-date while maintaining very high brightness.

Graph representations are a powerful concept for solving complex problems across natural science, as patterns of connectivity can give rise to a multitude of emergent phenomena. Graph-based approaches have proven particularly fruitful in quantum communication and quantum search algorithms in highly branched quantum networks. Here we introduce a new paradigm for the direct experimental realization of excitation dynamics associated with three-dimensional networks by exploiting the hybrid action of spatial and polarization degrees of freedom of photon pairs in complex waveguide circuits with tailored birefringence. This novel testbed for the experimental exploration of multi-particle quantum walks on complex, highly connected graphs paves the way towards exploiting the applicative potential of fermionic dynamics in integrated quantum photonics.

Transferring entangled states between photon pairs is essential for quantum communication technologies. Semiconductor quantum dots are the most promising candidate for generating polarization-entangled photons deterministically. Recent improvements in photonic quality and brightness now make them suited for complex quantum optical purposes in practical devices. Here we demonstrate for the first time swapping of entangled states between two pairs of photons emitted by a single quantum dot. A joint Bell measurement heralds the successful generation of the Bell state $\Psi^+$ with a fidelity of up to $0.81 \pm 0.04$. The state's nonlocal nature is confirmed by violating the CHSH-Bell inequality. Our photon source is compatible with atom-based quantum memories, enabling implementation of hybrid quantum repeaters. This experiment thus is a major step forward for semiconductor based quantum communication technologies.

Several distinct classes of unitary mode transformations have been known to exhibit the strict suppression of a large set of transmission events, as a consequence of totally destructive many-particle interference. In another work [Dittel et al., Phys. Rev. Lett. 120, 240404 (2018)] we unite these cases by identifying a general class of unitary matrices which exhibit such interferences. Here, we provide a detailed theoretical analysis that substantially expands on all aspects of this generalisation: We prove the suppression laws put forward in our other paper, establish how they interrelate with forbidden single-particle transitions, show how all suppression laws hitherto known can be retrieved from our general formalism, and discuss striking differences between bosons and fermions. Furthermore, beyond many-particle Fock states on input, we consider arbitrary pure initial states and derive suppression laws which stem from the wave function's permutation symmetry alone. Finally, we identify conditions for totally destructive interference to persist when the involved particles become partially distinguishable., Comment: 16 pages, 4 figures

In a general, multi-mode scattering setup, we show how the permutation symmetry of a many-particle input state determines those scattering unitaries which exhibit strictly suppressed many-particle transition events. We formulate purely algebraic suppression laws that identify these events and show that the many-particle interference at their origin is robust under weak disorder and imperfect indistinguishability of the interfering particles. Finally, we demonstrate that all suppression laws so far described in the literature are embedded in the general framework that we here introduce., Comment: 6 pages, 2 figures

We employ active feedback to stabilize the frequency of single photons emitted by two separate quantum dots to an atomic standard. The transmission of a single, rubidium-based Faraday filter serves as the error signal for frequency stabilization to less than 1.5% of the emission linewidth. Long-term stability is demonstrated by Hong-Ou-Mandel interference between photons from the two quantum dots. The observed visibility of $V_{\mathrm{lock}}=(41 \pm 5)$% is limited only by internal dephasing of the dots. Our approach facilitates quantum networks with indistinguishable photons from distributed emitters.

We conceive an all-optical representation of the dynamics of two distinct types of interacting bosons in a double well by an array of evanescently coupled photonic waveguides. Many-particle interference effects are probed for various interaction strengths by changing the relative abundance of the particle species and can be readily identified by monitoring the propagation of the light intensity across the waveguide array. In particular, we show that finite inter-particle interaction strengths reduce the many-particle interference contrast by dephasing. A general description of the many-particle dynamics for arbitrary initial states is given in terms of two coupled spins by generalising the Schwinger representation to two particle species.

Semiconductor InAs/GaAs quantum dots grown by the Stranski-Krastanov method are among the leading candidates for the deterministic generation of polarization entangled photon pairs. Despite remarkable progress in the last twenty years, many challenges still remain for this material, such as the extremely low yield (<1% quantum dots can emit entangled photons), the low degree of entanglement, and the large wavelength distribution. Here we show that, with an emerging family of GaAs/AlGaAs quantum dots grown by droplet etching and nanohole infilling, it is possible to obtain a large ensemble (close to 100%) of polarization-entangled photon emitters on a wafer without any post-growth tuning. Under pulsed resonant two-photon excitation, all measured quantum dots emit single pairs of entangled photons with ultra-high purity, high degree of entanglement (fidelity up to F=0.91, with a record high concurrence C=0.90), and ultra-narrow wavelength distribution at rubidium transitions. Therefore, a solid-state quantum repeater - among many other key enabling quantum photonic elements - can be practically implemented with this new material.

We report measurements of Hanbury Brown and Twiss correlation of coherent light transmitted through disordered one-dimensional photonic lattices. Although such a lattice exhibits transverse Anderson localization when a single input site is excited, uniform excitation precludes its observation. By examining the Hanbury Brown--Twiss correlation for a uniformly excited disordered lattice, we observe intensity anticorrelations associated with photon antibunching--a signature of non-Gaussian statistics. Although the measured average intensity distribution is uniform, transverse Anderson localization nevertheless underlies the observed anticorrelation., Comment: 4 pages, 4 figures

Beyond the regime of distinguishable particles, many-body quantum interferences influence quantum transport in an intricate manner. However, symmetries of the single-particle transformation matrix alleviate this complexity and even allow the analytic formulation of suppression laws, which predict final states to occur with a vanishing probability due to total destructive interference. Here we investigate the symmetries of hypercube graphs and their generalizations with arbitrary identical subgraphs on all vertices. We find that initial many-particle states, which are invariant under self-inverse symmetries of the hypercube, lead to a large number of suppressed final states. The condition for suppression is determined solely by the initial symmetry, while the fraction of suppressed states is given by the number of independent symmetries of the initial state. Our findings reveal new insights into particle statistics for ensembles of indistinguishable bosons and fermions and may represent a first step towards many-particle quantum protocols in higher-dimensional structures., Comment: 21 pages, 5 figures, accepted in Quantum Science and Technology

We design and realise a hybrid interferometer consisting of three paths based on integrated as well as on bulk optical components. This hybrid construction offers a good compromise between stability and footprint on one side and means of intervention on the other. As experimentally verified by the absence of higher-order interferences, amplitude and phase can be manipulated in all paths independently. In conjunction with single photons, the setup can, therefore, be applied for fundamental investigations on quantum mechanics., Comment: accepted in APL Photonics

The scalability of quantum dot based non-classical light sources relies on the control over their dissimilar emission energies. Electric fields offer a promising route to tune the quantum dot emission energy through the quantum-confined Stark effect. However, electric fields have been mostly used for tuning the energy of single-photon emission from quantum dots, while electrical control over the energy of entangled-photon emission, which is crucial for building a solid-state quantum repeater using indistinguishable entangled photons, has not been realized yet. Here, we present a method to achieve electrical control over the energy of entangled-photon emission from quantum dots. The device consists of an electrically-tunable quantum diode integrated onto a piezoactuator. We find that, through application of a vertical electric field, the critical uniaxial stress used to eliminate the fine-structure-splitting of quantum dots can be linearly tuned. This allows realization of a triggered source of energy-tunable entangled-photon emission, an important step towards a solid-state quantum repeater application., Comment: 12 pages and 6 figures

We present a method of locally inverting the sign of the coupling term in tight-binding systems, by means of inserting a judiciously designed ancillary site and eigenmode matching of the resulting vertex triplet. Our technique can be universally applied to all lattice configurations, as long as the individual sites can be detuned. We experimentally verify this method in laser-written photonic lattices and confirm both the magnitude and the sign of the coupling by interferometric measurements. Based on these findings, we demonstrate how such universal sign-flipped coupling links can be embedded into extended lattice structures to impose a $\mathbb{Z}_2$-gauge transformation. This opens a new avenue for investigations on topological effects arising from magnetic fields with aperiodic flux patterns or in disordered systems., Comment: accepted in Phys. Rev. Lett

We measure the next-nearest-neighbour coupling in an array of coupled optical waveguides directly via an integrated eigenmode interferometer. In contrast to light propagation experiments, the technique is insensitive to nearest-neighbour dynamics. Our results show that second-order coupling in a linear configuration can be suppressed well below the level expected from the exponential decay of the guided modes., Comment: Accepted by Applied Physics Letters. After publication, it will be found at http://scitation.aip.org/content/aip/journal/apl

Within the established theoretical framework of quantum mechanics, interference always occurs between pairs of trajectories. Higher order interferences with multiple constituents are, however, excluded by Born's rule and can only exist in generalized probabilistic theories. Thus, high-precision experiments searching for such higher order interferences are a powerful method to distinguish between quantum mechanics and more general theories. Here, we perform such a test in optical multi-path interferometers. Our results rule out the existence of higher order interference terms to an extent which is more than four orders of magnitude smaller than the expected pairwise interference, refining previous bounds by two orders of magnitude. This establishes the hitherto tightest constraints on generalized interference theories.

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the integrated configuration used in our experiments, the order of the transform is mapped onto the longitudinal coordinate, thus opening up the prospect of simultaneously observing all Transformation orders. In the context of classical optics, we implement discrete fractional Fourier transforms, both integer and fractional, of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to transform separable and highly entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools, such as quantum chemistry and biology, physics and mathematics.

We demonstrate quantum walks of correlated photons in a 2D network of directly laser written waveguides coupled in a 'swiss cross' arrangement. The correlated detection events show high-visibility quantum interference and unique composite behaviour: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal non-classical behaviour in a non-planar structure., Comment: 5 pages, 5 figures

We describe theoretically and observe experimentally the formation of a surface state in a semi-infnite waveguide array with side-coupled waveguide, designed to simultaneously achieve Fano and Fabry-Perot resonances. We demonstrate that the surface mode is compact, with all energy concentrated in few waveguides at the edge and no field penetration beyond the side-coupled waveguide position. Furthermore, we show that by broadening the spectral band in the rest of the waveguide array it is possible to suppress exponentially localized modes, whereas the Fano state having the eigenvalue embedded in the continuum is preserved.

Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a lattice, thereby demonstrating the general concept of trans- porting arbitrary quantum information with high fidelity. Coherent transfer over 19 sites is realized by utilizing judiciously designed optical structures consisting of evanescently coupled waveguide ele- ments. We provide unequivocal evidence that such an approach is applicable in the quantum regime, for both bosons and fermions, as well as in the classical limit. Our results illustrate the potential of the perfect state transfer protocol as a promising route towards integrated quantum computing on a chip.

Quantum entanglement, the non-separability of a multipartite wave function, became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. With the discovery of spontaneous parametric down-conversion (SPDC) in nonlinear crystals, an efficient source for entangled photon pairs, so-called biphotons, became available. It has recently been shown that SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional spatial dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional (1D) arrays can be simulated through classical optical beam propagation in a two-dimensional (2D) photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-type inequality.

We demonstrate that single-photon as well as biphoton revivals are possible in a new class of dynamic optical systems-the so-called Glauber-Fock oscillator lattices. In these arrays, both Bloch-like oscillations and dynamic delocalization can occur which can be described in closed form. The bunching and anti-bunching response of path-entangled photons can be pre-engineered in such coupled optical arrangements and the possibility of emulating Fermionic behavior in this family of lattices is also considered. We elucidate these effects via pertinent examples and we discuss the prospect of experimentally observing these quantum interactions., Comment: 5 pages, 5 figures

We show that the geometrically-induced potential existing in undulated slab waveguides dramatically affects the properties of solitons. In particular, whereas solitons residing in the potential maxima do not feature power thresholds and are stable, their counterparts residing in the potential minima are unstable and may exhibit a power threshold for their existence. Additionally, the geometric potential is shown to supports stable multipole solitons that cannot be supported by straight waveguides. Finally, the geometric potential results in the appearance of the effective barriers that prevent transverse soliton motion., Comment: 3 pages, 4 figures, to appear in Optics Letters

Coherent states and their generalisations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space. Theoretical calculations and analogue classical experiments show that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlations not encountered in uniform arrays. Due to the broken shift-invariance of the lattice, these correlations strongly depend on the transverse position. Consequently, quantum random walks with this extra degree of freedom may be realised in Glauber-Fock lattices., Comment: 5 pages, 4 figures

We present, theoretically and experimentally, amorphous photonic lattices exhibiting a band-gap yet completely lacking Bragg diffraction: 2D waveguides distributed randomly according to a liquid-like model responsible for the absence of Bragg peaks as opposed to ordered lattices containing disorder, which always exhibit Bragg peaks. In amorphous lattices the bands are comprised of localized states, but we find that defect states residing in the gap are more localized than the Anderson localization length. Finally, we show how the concept of effective mass carries over to amorphous lattices.

We study experimentally light localization at phase-slip waveguides and at the intersection of phase-slips in a two-dimensional (2D) square photonic lattice. Such system allows to observe a variety of effects, including the existence of spatially localized modes for low powers, the generation of strongly localized states in the form of discrete bulk and surface solitons, as well as a crossover between one-dimensional (1D) and 2D localization., Comment: 4 double-column pages, 6 figures, submitted for publication

We report on the experimental realization of an optical analogue of a quantum geometric potential for light wave packets constrained on thin dielectric guiding layers fabricated in silica by the femtosecond laser writing technology. We further demonstrate the optical version of a topological crystal, with the observation of Bloch oscillations and Zener tunneling of purely geometric nature.