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Photon-pair generation in photonic crystal waveguides

Sina Saravi

Published Jan 1, 2018• 1 citation
Publisher

Abstract

In this thesis, I overcome the challenges and fill the gaps in knowledge for the design and analysis of photonic crystal slab waveguides (PCSWs) as spontaneous parametric down-conversion (SPDC) sources of photon-pairs, as well as to investigate their potential for engineering the properties of the photon-pair quantum state. I have developed the required formalism for analyzing both the quantum process of SPDC and its classical counterpart of second-harmonic generation (SHG). In studying SHG, I verified my formalism through comparing its results with direct nonlinear simulations. In these formulations, special attention was given to treating lossy modes, as they prove to be an inherent part of the SPDC designs in PCSWs. Moreover, I have found a practical set of PCSW designs, phase-matched for three-wave-mixing processes, while demonstrating that PCSWs can offer a strong control over the phase-matching configuration. This includes reaching phase-matching between modes of different propagation directions, reaching simultaneous phase-matching between multiple processes, and controlling the group velocity of the modes at the point of phase-matching. These capabilities proved to be the key to discovering the unique strength of PCSWs for the SPDC application. Through the use of various phase-matching configurations, I showed how compact SPDC sources can be designed using PCSWs that are capable of creating entanglement and tuning its extent in different degrees of freedom, with specific examples for path and spectral degrees of entanglement, all in a fully integrated way and directly at the generation step. This work also includes my experimental results on characterizing lithium niobate nanostructured ridge waveguides, demonstrating phase-matched SHG. Finally, I propose the concept of atom-mediated SPDC, for interfacing a single-emitter source with a photon-pair source, relying on the bandgap evanescent modes of a periodic waveguide.

DOI
10.22032/dbt.38074

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This thesis describes various methods for producing photon pairs from waveguides. It covers relevant topics such as waveguide coupling and phase matching, along with the relevant measurement techniques used to infer photon pair production. A new proposal to solve the phase matching problem is described along with two conceptual methods for generating entangled photon pairs. Photon pairs are also experimentally demonstrated from a third novel structure called a Bragg Reflection Waveguide (BRW). \n \nThe new proposal to solve the phase matching problem is called Directional Quasi-Phase Matching (DQPM). It is a technique that exploits the directional dependence of the non-linear susceptiblity (chi(2)\\chi^{(2)}chi(2)) tensor. It is aimed at those materials that do not allow birefringent phase-matching or periodic poling. In particular, it focuses on waveguides in which the interplay between the propagation direction, electric field polarizations and the nonlinearity can change the strength and sign of the nonlinear interaction periodically to achieve quasi-phasematching. \n \nOne of the new conceptual methods for generating entangled photon pairs involves a new technique that sandwiches two waveguides from two differently oriented but similar crystals together. The idea stems from the design of a Michelson interferometer which interferes the paths over which two unique photon pair processes can occur, thereby creating entanglement in any pair of photons created in the interferometer. By forcing or sandwiching the two waveguides together, the physical space that exists in the standard Micheleson type interferometer is made non-existent, and the interferometer is effectively squashed. The result is that the two unique photon pair processes actually occupy the same physical path. This benefits the stability of the interferometer in addition to miniaturizing it. The technical challenges involved in sandwiching the two waveguides are briefly discussed. \n \nThe main result of this thesis is the observation of photon pairs from the BRW. By analyzing the time correlation between two single photon detection events, spontaneous parametric down conversion (SPDC) of a picosecond pulsed ti:sapph laser is demonstrated. The process is mediated by a ridge BRW. The results show evidence for type-0, type-I and type-II phase matching of pump light at 783nm, 786nm and 789nm to down converted light that is strongly degenerate at 1566nm, 1572nm, and 1578nm respectively. The inferred efficiency of the BRW was 9.8$\\cdot101010^{-9}$ photon pairs per pump photon. This contrasts with the predicted type-0 efficiency of 2.65$\\cdot101010^{-11}$. This data is presented for the first time in such waveguides, and represents significant advances towards the integration of sources of quantum information into the existing telecommunications infrastructure.
Spontaneous parametric down-conversion (SPDC) has become a key method for generating entangled photon pairs. Periodically poled thin-film lithium niobate (TFLN) waveguides induce strong SPDC but require complex fabrication processes. In this work, we experimentally demonstrate efficient SPDC and second harmonic generation using modal phase matching methods. This is achieved with inverse-designed optical mode converters and low-loss optical waveguides in a single nanofabrication process. Inverse design methods provide enhanced functionalities and compact footprints for the converter. Despite the extensive achievements in inverse-designed photonic integrated circuits, the potential of inverse-designed TFLN quantum photonic devices has been seldom explored. The device shows an on-chip conversion efficiency of 3.95% W−1 cm−2 in second harmonic generation measurements and a coincidence count rate up to 21.2 kHz in SPDC experiments. This work highlights the potential of the inverse-designed TFLN photonic devices and paves the way for their applications in on-chip nonlinear or quantum optics.
The aim of this thesis is to explore nonlinear nanostructures – photonic systems with one or more dimension with nanoscale feature size – as new platforms for parametric photon-pair generation. This is motivated by the need for photon-pair sources in many technological applications of quantum optics, such as quantum communication, imaging and computing. The initial hypothesis is that nonlinear nanostructures are a promising platform to complement established photon-pair source schemes based on bulk crystals or photonic integrated circuits in terms of quantum state-engineering, footprint, functional density etc. However, nonlinear pair generation, e.g. via spontaneous parametric down-conversion (SPDC), is a new subfield in nanophotonics with a very limited number of studies existing. This constitutes the knowledge-gap addressed in this thesis. Therefore, the objective is to provide first experimental demonstrations of SPDC in subwavelength-scale and nonlinear nanostructures. We investigate the ability of such systems to control the properties of two-photon quantum states such as frequency and angular spectrum or polarization entanglement. To this end we analyze nanostructures with different degrees of complexity, starting with an unstructured thin crystal with one nanoscale dimension, leading up to a 3D nano-scale resonator with subwavelength-sized features in all dimensions. Furthermore, we test different types of nonlinear materials such as lithium niobate, group III-V semiconductors and emerging, highly nonlinear materials such as molybdenum disulfide. Additionally, we also advance the theoretical understanding by developing a comprehensive model of the quantum process of nonlinear parametric pair-generation in photonic nanostructures.
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.
We propose the use of nonlinear periodic waveguides for direct and fully integrated generation of counterpropagating photon pairs by spontaneous parametric down-conversion. Using the unique properties of Bloch modes in such periodic structures, we furthermore show that two counterpropagating phase-matching conditions can be fulfilled simultaneously, allowing for the generation of path-entangled Bell states in a single periodic waveguide. To demonstrate the feasibility of our proposal, we design a photonic crystal slab waveguide made of lithium niobate and numerically demonstrate Bell-state generation.