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Mid infrared integrated quantum photonics is a promising platform for applications in sensing and metrology. However, there are only few examples of on-chip single photon sources at these wavelengths. These have limited performances with respect to their C-band counterparts. In this work, we demonstrate a new approach to generate heralded single photons in the mid infrared on a silicon chip. By using a standard C-band pump, the inter-modal spontaneous four wave mixing enables the generation of the herald idler at 1259.7 nm and the heralded signal at 2015 nm. The idler photon is easily detected with a common infrared single photon detector while the signal photon is upconverted to the visible before its detection. In this way, we are able to operate a mid infrared source without the need of mid infrared detectors and laser sources. By measuring a heralded $g^{(2)}$ of $0.23 \, \pm \, 0.08$ we demonstrate the single photon behaviour of the source as well as the feasibility of multi-photon coincidence measurements beyond 2 $\mu$m with our setup. The source exhibits a high intrinsic heralding efficiency of $(59 \, \pm \,5)\%$, a maximum coincidence to accidental ratio of $40.4 \, \pm \, 0.9$ and a generation probability of $\left( 0.72 \, \pm \, 0.10 \right)$ W$^{-2}$.

We report on the demonstration of an effective, nonlinearity-induced non-reciprocal behavior in a single non-magnetic multi-mode Taiji resonator. Non-reciprocity is achieved by a combination of an intensity-dependent refractive index and of a broken spatial reflection symmetry. Continuous wave power dependent transmission experiments show non-reciprocity and a direction-dependent optical bistability loop. These can be explained in terms of the unidirectional mode coupling that causes an asymmetric power enhancement in the resonator. The observations are quantitatively reproduced by a numerical finite-element theory and physically explained by an analytical coupled-mode theory. This nonlinear Taiji resonator has the potential of being the building block of large arrays where to study topological and/or non-Hermitian physics. This represents an important step towards the miniaturization of nonreciprocal elements for photonic integrated networks., Comment: 10 pages, 7 figures

In single-particle or intraparticle entanglement, two degrees of freedom of a single particle, e.g., momentum and polarization of a single photon, are entangled. Single-particle entanglement (SPE) provides a source of non classical correlations which can be exploited both in quantum communication protocols and in experimental tests of noncontextuality based on the Kochen-Specker theorem. Furthermore, SPE is robust under decoherence phenomena. Here, we show that single-particle entangled states of single photons can be produced from attenuated sources of light, even classical ones. To experimentally certify the entanglement, we perform a Bell test, observing a violation of the Clauser, Horne, Shimony and Holt (CHSH) inequality. On the one hand, we show that this entanglement can be achieved even in a classical light beam, provided that first-order coherence is maintained between the degrees of freedom involved in the entanglement. On the other hand, we prove that filtered and attenuated light sources provide a flux of independent SPE photons that, from a statistical point of view, are indistinguishable from those generated by a single photon source. This has important consequences, since it demonstrates that cheap, compact, and low power entangled photon sources can be used for a range of quantum technology applications.

We theoretically investigate the dispersion relation of small-amplitude optical waves superimposing upon a beam of polarized monochromatic light propagating along a single-mode channel waveguide characterized by an instantaneous and spatially local Kerr nonlinearity. These small luminous fluctuations propagate along the waveguide as Bogoliubov elementary excitations on top of a one-dimensional dilute Bose quantum fluid evolve in time. They consequently display a strongly renormalized dispersion law, of Bogoliubov type. Analytical and numerical results are found in both the absence and the presence of one- and two-photon losses. Silicon and silicon-nitride waveguides are used as examples. We finally propose an experiment to measure this Bogoliubov dispersion relation, based on a stimulated four-wave mixing and interference spectroscopy techniques., Comment: 17 pages, 7 figures

The observation of the electro-optic effect in strained silicon waveguides has been considered as a direct manifestation of an induced $\chi^{(2)}$ non-linearity in the material. In this work, we perform high frequency measurements on strained silicon racetrack resonators. Strain is controlled by a mechanical deformation of the waveguide. It is shown that any optical modulation vanishes independently of the applied strain when the applied voltage varies much faster than the carrier effective lifetime, and that the DC modulation is also largely independent of the applied strain. This demonstrates that plasma carrier dispersion is responsible for the observed electro-optic effect. After normalizing out free carrier effects, our results set an upper limit of $8\,pm/V$ to the induced high-speed $\chi^{(2)}_{eff,zzz}$ tensor element at an applied stress of $-0.5\,GPa$. This upper limit is about one order of magnitude lower than the previously reported values for static electro-optic measurements.

Microresonator devices which posses ultra-high quality factors are essential for fundamental investigations and applications. Microsphere and microtoroid resonators support remarkably high Q's at optical frequencies, while planarity constrains preclude their integration into functional lightwave circuits. Conventional semiconductor processing can also be used to realize ultra-high-Q's with planar wedge-resonators. Still, their full integration with side-coupled dielectric waveguides remains an issue. Here we show the full monolithic integration of a wedge-resonator/waveguide vertically-coupled system on a silicon chip. In this approach the cavity and the waveguide lay in different planes. This permits to realize the shallow-angle wedge while the waveguide remains intact, allowing therefore to engineer a coupling of arbitrary strength between these two. The precise size-control and the robustness against post-processing operation due to its monolithic integration makes this system a prominent platform for industrial-scale integration of ultra-high-Q devices into planar lightwave chips., Comment: 6 pages, 4 figures

We report on a combined theoretical and experimental study of the optical coupling between a microdisk resonator and a waveguide laying on different planes. While the lateral coupling between a planar resonator and a waveguide is characterized by a unique distance at which the resonant waveguide transmission vanishes because of destructive interference, the vertical coupling geometry exhibits an oscillatory behavior in the coupling amplitude as a function of the vertical gap. This effect manifests experimentally as oscillations in both the waveguide transmission and the mode quality factor. An analytical description based on coupled-mode theory and a two-port beam-splitter model of the waveguide-resonator coupling is developed, which compares successfully both to experimental data and numerical simulations., Comment: 5 pages, 3 figures

We present a numerical analysis and preliminary experimental results on one-dimensional Fabry-Perot micro-cavities in Si$_3$N$_4$ waveguides. The Fabry-Perot micro-cavities are formed by two distributed Bragg reflectors separated by a straight portion of waveguide. The Bragg reflectors are composed by a few air slits produced within the Si$_3$N$_4$ waveguides. In order to increase the quality factor of the micro-cavities, we have minimized, with a multiparametric optimization tool, the insertion loss of the reflectors by varying the length of their first periods (those facing the cavity). To explain the simulation results the coupling of the fundamental waveguide mode with radiative modes in the Fabry-Perot micro-cavities is needed. This effect is described as a recycling of radiative modes in the waveguide. To support the modelling, preliminary experimental results of micro-cavities in Si$_3$N$_4$ waveguides realized with Focused Ion Beam technique are reported., Comment: 5 pages, 5 figures

A simple numerical method to study the effect of an applied magnetic field on the energy spectrum of non-periodic superlattice structures is presented. The magnetic field could be either parallel or perpendicular to the growth direction. Our method is based on the transfer matrix technique and on the effective mass approximation. We discuss the advantages and disadvantages of the proposed approach using several examples. In particular, we study the perturbation to the energy spectrum of periodic superlattice induced by the introduction of an enlarged well. We found that these perturbations are negligible for B//z but relevant for B$\perp $z. Preliminary results for Fibonacci superlattices in magnetic fields are presented as well. In these quasi-periodic structures the energy levels become strongly dispersive in presence of a perpendicular magnetic field., Comment: revtex: 25 pages 9 figures upon request, UTF/22.10.92