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arXiv:1809.10494

Engineered photon-pair generation by four-wave mixing in asymmetric coupled waveguides

Robert J. A. Francis-Jones, Wright, Thomas A., Andriy Gorbach, Peter J. Mosley

Published Sep 27, 2018• 1 citation
arXivHTMLPDF

Abstract

Third-order nonlinear processes require phase matching between the interacting fields to achieve high efficiencies. Typically in guided-wave $χ^{(3)}$ platforms this is achieved by engineering the dispersion of the modes through the transverse profile of the device. However, this limits the flexibility of the phase matching that can be achieved. Instead, we analyze four-wave mixing in a pair of asymmetric waveguides and show that phasematching may be achieved in any $χ^{(3)}$ waveguide by coupling of a nondegenerate pump from an adjacent waveguide. We demonstrate the additional flexibility that this approach yields in the case of photon-pair generation by spontaneous FWM, where the supermode dispersion may be modified to produce pure heralded single photons -- a critical capability required for example by silicon platforms for chip-scale quantum photonics.

DOI
10.48550/arxiv.1809.10494

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Third-order nonlinear processes require phase matching between the interacting fields to achieve high efficiencies. Typically in guided-wave χ(3)χ^{(3)}χ(3) platforms this is achieved by engineering the dispersion of the modes through the transverse profile of the device. However, this limits the flexibility of the phase matching that can be achieved. Instead, we analyze four-wave mixing in a pair of asymmetric waveguides and show that phasematching may be achieved in any χ(3)χ^{(3)}χ(3) waveguide by coupling of a nondegenerate pump from an adjacent waveguide. We demonstrate the additional flexibility that this approach yields in the case of photon-pair generation by spontaneous FWM, where the supermode dispersion may be modified to produce pure heralded single photons -- a critical capability required for example by silicon platforms for chip-scale quantum photonics.
The intrinsic third-order nonlinearity in silicon has proven it to be quite useful in the field of quantum optics. Silicon is suitable for producing time-correlated photon pairs that are sources of heralded single-photon states for quantum integrated circuits. A quantum signal source in the form of single photons is an inherent requirement for the principles of quantum key distribution technology for secure communications. Here, we present numerical simulations of a silicon ring with a 6 μ m radius side-coupled with a bus waveguide as the source for the generation of single photons. The photon pairs are generated by exploring the process of degenerate spontaneous four-wave mixing (SFWM). The free spectral range (FSR) of the ring is quite large, simplifying the extraction of the signal/idler pairs. The phase-matching condition is considered by studying relevant parameters like the dispersion and nonlinearity. We optimize the ring for a high quality factor by varying the gap between the bus and the ring waveguide. This is the smallest ring studied for photon pair generation with a quality factor in the order of 10 5 . The width of the waveguides is chosen such that the phase-matching condition is satisfied, allowing for the propagation of fundamental modes only. The bus waveguide is pumped at one of the ring resonances with the minimum dispersion (1543.5 nm in our case) to satisfy the principle of energy conservation. The photon pair generation rate achieved is comparable to the state of the art. The photon pair sources exploiting nonlinear frequency conversion/generation processes is a promising alternative to atom-like single-photon emitters in the field of integrated photonics. Such miniaturized structures will benefit future on-chip architectures where multiple single-photon source devices are required on the same chip.
In this work, we propose and theoretically analyze a new scheme for generation of counterpropagating photon pairs in photonic crystal waveguides through the process of spontaneous four-wave mixing. Using the fundamental properties of periodic Bloch modes in a standard photonic crystal waveguide, we demonstrate how modal phase-matching can be reached between forward-propagating pump modes and counterpropagating signal and idler modes, for generation of degenerate and non-degenerate photon pairs. We then show how this scheme can be used for generation of photon pairs that are nearly uncorrelated in the spectral degree of freedom. Such a source will be highly interesting as a heralded source of single photons, especially as the spectrally separable signal and idler photons are also spatially separated directly at the source. We conduct our investigation based on a design in silicon, yet our design concept is general and can in principle be applied to any nanostructured material platform.
Phase matching lies at the heart of the classical nonlinear process for frequency conversion and all-optical processing, as well as the spontaneous parametric process for the quantum light sources generation. In this work, we experimentally demonstrate the coupled-mode phase-matching (CMPM) engineered by the two-paralleled-coupled waveguides on a silicon-on-insulator (SOI) chip, extending the converted beam and entangled photons to the S band and L band. We measure the spectrum and efficiency of wavelength conversion, which successfully validates the designed CMPM scheme. We further measure the pairs generation rate of the biphoton based on the spontaneous four-wave mixing, which features a narrow bandwidth consistent well with the theoretical simulations. Multiple CMPM conditions can be achieved by exploiting the combinations of even and odd supermodes of the coupled system and tuned by designing a proper coupling gap between the two waveguides. The CMPM can extend the FWM nonlinear process ranging from the O band to the U band and even the midinfrared, enriching the working wavelength to a large extent. In addition, the CMPM features a discrete-band narrow bandwidth, which will greatly enhance the encoding density of frequency and the spectral purity of generated photon. In addition, our methods can be easily extended to a wide range of materials such as silicon nitride, dispensing with the dispersion engineering for phase matching.
On-chip heralded single photon sources are of key importance in the development of chip-scale devices exploiting the quantum properties of light. Single photon states can be produced as single photons heralded from correlated photon pairs generated through spontaneous four wave mixing. On-chip heralded single photon sources based on spontaneous four wave mixing have been already demonstrated. However, the heralded and herald photons are usually generated with wavelengths very close to the pump one, limiting the pump rejection efficiency and the application to the mid infrared. Moreover, the common sources of heralded photons based on spontaneous four wave mixing require spectral post filtering to achieve high purity, limiting the brightness and the integration of these sources. A solution to these problems can be provided by intermodal four wave mixing. In this work, we demonstrate the generation of photon pairs through intermodal four wave mixing in silicon waveguides, measuring the coincidences between the idler at 1.281 μm and the signal at 1.952 μm. We then discuss the application of intermodal four wave mixing to on-chip heralded single photon sources.
Single-photon sources are the cornerstone of the optical quantum information process, including quantum computing, simulation, metrology, etc. The practical application requires these sources to be high purity and indistinguishability. A readily available approach is to use heralded single-photon sources to generate photon pairs via spontaneous parametric down-conversion (SPDC). However, the purity of photon pairs generated by SPDC is usually limited by the spectral correlations because of energy conservation. Extra spectral filters and group velocity matching (GVM) can be used to generate spectral uncorrelated photon pairs on-chip. However, the material dispersion of most materials cannot meet the GVM requirements, and extra components will reduce the integration. In this work, we develop a strategy to generate pure single photon on-chip by mode coupling in heterogeneously coupled waveguides. This strategy can tailor the group velocity directly, or shape biphoton wave function through a new degree of freedom that is the non-constant overlap between interacting modes. This allows the generation of high-purity single photons totally on-chip. Design examples based on lithium niobate waveguide are provided to generate spectrally pure photon pairs. This strategy is generic that it is not limited to any material and waveguide system, providing new possibilities in the generation of quantum photons.
Silicon photonics is rapidly emerging as a promising, scalable platform for quantum information applications. As the technology matures, sources of high-quality quantum-optical states are increasingly important. We discuss the use of intermodal four-wave mixing in silicon waveguides for creating entangled photon pairs. We describe a framework to numerically analyze the state of produced photon pairs and discuss a scheme for generating photon pairs that are purely entangled in their transverse waveguide mode. Using this scheme, we find a theoretical fidelity of 99.6 % to a true Bell state in the transverse mode with no spectral correlations.