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We model backscatter for electric fields propagating through optical micro-ring resonators, as occurring both in-ring and in-coupler. These provide useful tools for modelling transmission and in-ring fields in these optical devices. We then discuss spontaneous four-wave mixing and use the models to obtain heralding efficiencies and rates. We observe a trade-off between these, which becomes more extreme as the rings become more strongly backscattered., Comment: 8 pages, 8 figures - matches version published in J. Phys. Photonics

Exploiting semiconductor fabrication techniques, natural carriers of quantum information such as atoms, electrons, and photons can be embedded in scalable integrated devices. Integrated optics provides a versatile platform for large-scale quantum information processing and transceiving with photons. Scaling up the integrated devices for quantum applications requires highperformance single-photon generation and photonic qubit-qubit entangling operations. However, previous demonstrations report major challenges in producing multiple bright, pure and identical single-photons, and entangling multiple photonic qubits with high fidelity. Another notable challenge is to noiselessly interface multiphoton sources and multiqubit operators in a single device. Here we demonstrate on-chip genuine multipartite entanglement and quantum teleportation in silicon, by coherently controlling an integrated network of microresonator nonlinear single-photon sources and linear-optic multiqubit entangling circuits. The microresonators are engineered to locally enhance the nonlinearity, producing multiple frequencyuncorrelated and indistinguishable single-photons, without requiring any spectral filtering. The multiqubit states are processed in a programmable linear circuit facilitating Bell-projection and fusion operation in a measurement-based manner. We benchmark key functionalities, such as intra-/inter-chip teleportation of quantum states, and generation of four-photon Greenberger-HorneZeilinger entangled states. The production, control, and transceiving of states are all achieved in micrometer-scale silicon chips, fabricated by complementary metal-oxide-semiconductor processes. Our work lays the groundwork for scalable on-chip multiphoton technologies for quantum computing and communication.

Applied quantum optics stands to revolutionise many aspects of information technology, provided performance can be maintained when scaled up. Silicon quantum photonics satisfies the scaling requirements of miniaturisation and manufacturability, but at 1.55 $\mu$m it suffers from unacceptable linear and nonlinear loss. Here we show that, by translating silicon quantum photonics to the mid-infrared, a new quantum optics platform is created which can simultaneously maximise manufacturability and miniaturisation, while minimising loss. We demonstrate the necessary platform components: photon-pair generation, single-photon detection, and high-visibility quantum interference, all at wavelengths beyond 2 $\mu$m. Across various regimes, we observe a maximum net coincidence rate of 448 $\pm$ 12 Hz, a coincidence-to-accidental ratio of 25.7 $\pm$ 1.1, and, a net two photon quantum interference visibility of 0.993 $\pm$ 0.017. Mid-infrared silicon quantum photonics will bring new quantum applications within reach., Comment: 8 pages, 4 figures; revised figures, updated discussion in section 3, typos corrected, added reference

We measure the temperature dependence of the two-photon absorption and optical Kerr nonlinearity of a silicon waveguide over a range of temperatures from 5.5 to 300 K at a wavelength of 1.55 {\mu}m. The two-photon absorption coefficient is calculated from the power dependent transmission of a 4.9 ps pulse. We observed a nearly two-fold decrease in the two-photon absorption coefficient from 0.76 cm/GW at 300K to 0.42 cm/GW at 5.5 K. The Kerr nonlinearity is inferred from the self-phase modulation induced spectral broadening of the transmitted pulse. A smaller reduction in Kerr nonlinearity from 5.2E-18 m^2/W at 300 K to 3.9E-18 m^2/W at 5.5 K is found. The increased ratio of Kerr to absorptive nonlinearity at low temperatures indicates an improved operation of devices that make use of a nonlinear phase shift, such as optical switches or parametric photon-pair sources. We examine how the heralding efficiency of a photon-pair source will change at low temperature. In addition, the modelling and experimental techniques developed can readily be extended to other wavelengths or materials of interest., Comment: 9 pages, 5 figures

A novel time-domain approach using the momentum operator is used to model spontaneous four-wave mixing in a lossless nonlinear waveguide. The effects of self- and cross-phase modulation on the photon-pair production rate and heralded photon purity are investigated. We show that in the special case where only one half of the photon-pair state is filtered that the generation rate and purity of the heralded photons are unmodified by the presence of self- and cross-phase modulation. The significance of this special case arises when we consider heralded single-photon sources, where future schemes are likely to only filter the herald photon to ensure a high heralding efficiency is maintained.

High visibility on-chip quantum interference among indistinguishable single-photons from multiples sources is a key prerequisite for integrated linear optical quantum computing. Resonant enhancement in micro-ring resonators naturally enables brighter, purer and more indistinguishable single-photon production without any tight spectral filtering. The indistinguishability of heralded single-photons from multiple micro-ring resonators has not been measured in any photonic platform. Here, we report on-chip indistinguishability measurements of heralded single-photons generated from independent micro-ring resonators by using an on-chip Mach-Zehnder interferometer and spectral demultiplexer. We measured the raw heralded two-photon interference fringe visibility as 72 +/- 3%. This result agrees with our model, which includes device imperfections, spectral impurity and multi-pair emissions. We identify multi-pair emissions as the main factor limiting the nonclassical interference visibility, and show a route towards achieving near unity visibility in future experiments.

We derive a cross-Kerr type effective Hamiltonian for the four-level atom interacting with three electromagnetic fields in the N-configuration. When the atom has relaxed into the ground state a cross-Kerr nonlinearity arises between two weak probe fields. As a development on earlier work we show in general that the atom will also display a linear and self-Kerr response. However, if certain resonance conditions are satisfied then the linear and self-Kerr interactions will vanish. The electrical susceptibilities of the probe transitions are also explored and it is shown that a large, pure cross-Kerr nonlinearity can be generated with vanishing absorption of both probe fields., Comment: 7 pages, 4 figures, submitted to Phys. Rev. A, Replacement: added Acknowledgments section

We derive the form of the cross-Kerr interaction in a four-level atomic system in the N-configuration. We use time-independent perturbation theory to calculate the eigenenergies and eigenstates of the Schrodinger equation for the system. The system is considered as a perturbation of a Raman resonant three-level lambda scheme for which exact solutions are known. We show that within the strong control field limit the cross-Kerr interaction can arise between two weak probe fields. The strength of this nonlinear coupling is several orders of magnitude larger than that achievable using optical fibres., Comment: 5 pages, resubmitted to Physical Review A with clarified style and correction to Fig 1