Integrated Si3N4 Microring Resonator: A Photon-Pair Source for Quantum Communication

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(1)Thesis. Integrated Si3N4 Microring Resonator: A Photon-Pair Source for Quantum Communication. SAMARA, Farid. Abstract Integrated photonics is emerging as a key technology for use in quantum information and communication. Driven by classical communication, which already has a swathe of scalable, efficient, and robust components, integrated photonics promises to transfer quantum science from a mere lab curiosity into a commercial reality. Chip-based quantum light sources are increasingly being recognized as a practical and high-performance alternative to bulky and power-hungry, table-top photon-pair sources. In particular, photon-pair sources based on spontaneous four-wave mixing in microring resonators (MRR) have emerged as a viable integrated photonic solution for quantum information and communication. This thesis relies on silicon nitride (Si3N4) MRR to realize narrowband, telecom photonpair sources. High quality factor MRRs are enabled by the low propagation losses in the Si3N4 platform; in this thesis, they are exploited to realize bright photon-pair sources with heralded spectral purity up to 0.98. Low quality factor MRRs are exploited for a proof-of-concept high-rate sequential time-bin entanglement with net visibilities up to 99.96 [...]. Reference SAMARA, Farid. Integrated Si3N4 Microring Resonator: A Photon-Pair Source for Quantum Communication. Thèse de doctorat : Univ. Genève, 2021, no. Sc. 5573. DOI : 10.13097/archive-ouverte/unige:154134 URN : urn:nbn:ch:unige-1541349. Available at: http://archive-ouverte.unige.ch/unige:154134 Disclaimer: layout of this document may differ from the published version..

(2) U NIVERSITÉ DE G ENÈVE Groupe de Physique Appliquée. FACULTÉ DES S CIENCES Prof. Hugo Z BINDEN Dr. Rob T HEW. Integrated Si3N4 Microring Resonator: A Photon-Pair Source for Quantum Communication Thèse présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention Physique par Farid S AMARA d’Israël Thèse N◦ 5573. G ENÈVE 2021.

(3) UNIVERSITÉ J?1 DE GENÈVE FACULTÉ DES SCIENCES. DOCTORAT ÈS SCIENCES, MENTION PHYSIQUE Thèse de Monsieur Farid SAMARA intitulée :. «Integrated Si3N4 Microring Resonator: A Photon-Pair Source for Quantum Communication». La Faculté des sciences, sur le préavis de Monsieur H. ZBINDEN, professeur associé et directeur de thèse (Département de physique appliquée), Monsieur R. THEW, docteur et codirecteur de thèse (Département de physique appliquée), Monsieur T. KIPPENBERG, professeur (Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne, Lausanne), Monsieur K. SRINIVASAN, professeur (Photonics and Optomechanics Group, National Institute of Standards and Technology. Maryland, United Sates of America) Monsieur N. MARING (Quandela Nanotechnologies. Palaiseau, France), autorise. l’impression de la présente thèse, sans exprimer d’opinion sur les propositions qui y sont énoncées.. Genève, le 30 juin 2021. Thèse - 5573 -. Le Doyen. N.B. -. La thèse doit porter la déclaration précédente et remplir les conditions énumérées dans les "Informations relatives aux thèses de doctorat à l'Université de Genève"..

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(5) Abstract Integrated photonics is emerging as a key technology for use in quantum information and communication. Driven by classical communication, which already has a swathe of scalable, efficient, and robust components, integrated photonics promises to transfer quantum science from a mere lab curiosity into a commercial reality. Chip-based quantum light sources are increasingly being recognized as a practical and high-performance alternative to bulky and power-hungry, table-top photon-pair sources. In particular, photon-pair sources based on spontaneous four-wave mixing in microring resonators (MRR) have emerged as a viable integrated photonic solution for quantum information and communication. This thesis relies on silicon nitride (Si3 N4 ) MRR to realize narrowband, telecom photonpair sources. High quality factor MRRs are enabled by the low propagation losses in the Si3 N4 platform; in this thesis, they are exploited to realize bright photon-pair sources with heralded spectral purity up to 0.98. Low quality factor MRRs are exploited for a proof-of-concept high-rate sequential time-bin entanglement with net visibilities up to 99.96 ± 0.03 %. For the goal of practical, real-world deployment of integrated photon-pair sources, it is not enough to demonstrate the performance of a single source. One also needs to demonstrate their high-performance operation in complex quantum networking protocols, such as entanglement swapping between genuinely independent sources. Here, for the first time, we demonstrate entanglement swapping between two independent, spatially separated, and asynchronously-pumped MRR photon-pair sources. Our sources operate in the continuous-wave regime, and time-resolved detection results in high Hong-Ou-Mandel (93.2 ± 1.6 %) and entanglement swapping (91.2 ± 3.4 %) visibilities. Finally, to further improve our rates while maintaining high visibilities in multi-source interference scenarios, the origin of an on-chip-generated noise must be identified and mitigated. Here, we present our first efforts in the quest for tackling this notorious noise problem.. i.

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(7) Résumé La photonique intégrée est en passe de devenir une technologie incontournable de l’information et des communications quantiques. Les développements conduits dans le cadre des communications classiques ont permis d’avoir à disposition des composants évolutifs, efficaces et robustes qui pourraient permettre aux technologies quantiques de passer d’une curiosité de laboratoire à une réalité commerciale. Les sources de lumières quantiques basées sur des puces photoniques deviennent une alternative pratique et performante aux sources de paires de photons traditionnelles qui sont volumineuses et énergivores. En particulier, les sources de paires de photons basées sur le mélange à quatre ondes spontané dans des résonateurs à micro-anneau (RMA) se sont imposées comme une solution d’optique intégrée viable pour l’information et les communications quantiques. Dans cette thèse, nous utilisons des RMA en nitrure de silicium (Si3 N4 ) pour réaliser des sources de paires de photons à bande étroite aux longueurs d’onde télécom. Les faibles pertes de propagation du Si3 N4 permettent d’obtenir des RMA avec des facteurs de qualité élevés que nous exploitons pour réaliser des sources de paires de photons lumineuses dont la pureté spectrale annoncée atteint 0.98. Nous utilisons également des RMA avec des facteurs de qualité bas pour une preuve de concept d’intrication time-bin à haute cadence avec des visibilités atteignant 99.96 ± 0.03%. Afin d’atteindre l’idéal d’un déploiement en situation réelle de sources de paires de photons intégrées, il ne suffit pas de démontrer la performance d’une unique source. Il faut aussi démontrer leur opérativité dans des protocoles de mise en réseau quantiques complexes, tels que l’échange d’intrication entre des sources véritablement indépendantes. Dans ce travail, nous démontrons pour la première fois, un échange d’intrication entre deux sources de photons à RMA indépendantes, séparées spatialement et pompées de façon asynchrone. Nos sources fonctionnent dans le régime à lumière continue et une détection résolue temporellement permet de mesurer des visibilités Hong-Ou-Mandel (93.2 ± 1.6 %) et d’échange d’intrication (91.2 ± 3.4 %) élevées. Finalement, afin d’améliorer nos taux, tout en maintenant des visibilités élevées dans des scénarios d’interférence à sources multiples, l’origine du bruit généré dans la puce doit être identifiée et réduite. Nous présentons ici nos premiers efforts dans le combat de longue haleine qu’est la réduction du bruit. iii.

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(9) Contents Abstract (English/Français). i. 1. Introduction. 1. 2. General concepts 2.1 Single-photon Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Integrated photon-pair sources . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5 5 7 7. 3. Microring resonator-based photon-pair sources 3.1 Microring resonators . . . . . . . . . . . . . . . . . . . . 3.2 Spontaneous four-wave mixing . . . . . . . . . . . . . . 3.3 Classical regime characterization . . . . . . . . . . . . . 3.3.1 The devices in this work . . . . . . . . . . . . . . 3.3.2 Spectrum transmission scan . . . . . . . . . . . . 3.3.3 Phase-matching . . . . . . . . . . . . . . . . . . . 3.3.4 Thermal effects . . . . . . . . . . . . . . . . . . . 3.4 Photon-pair source . . . . . . . . . . . . . . . . . . . . . 3.4.1 Photon-pair source setup . . . . . . . . . . . . . 3.4.2 Cross-correlation measurement . . . . . . . . . . 3.4.3 Coincidences and singles versus power . . . . . 3.4.4 Coincidences-to-accidentals ratio . . . . . . . . . 3.4.5 Heralding efficiency . . . . . . . . . . . . . . . . 3.4.6 Pair generation rate . . . . . . . . . . . . . . . . . 3.4.7 Spectral purity . . . . . . . . . . . . . . . . . . . 3.4.8 Summary of photon-pair source characterisation 3.5 Entanglement generation . . . . . . . . . . . . . . . . . . 3.5.1 Energy-time entanglement . . . . . . . . . . . . 3.5.2 Time-bin entanglement . . . . . . . . . . . . . . 3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Trade-offs . . . . . . . . . . . . . . . . . . . . . . 3.6.2 How does it compare? . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. 11 11 12 14 14 15 18 19 21 22 24 26 27 29 30 32 38 38 39 41 45 45 46 v.

(10) Contents 4. 5. 6. Practical entanglement swapping between independent sources 4.1 Introduction to entanglement swapping . . . . . . . . . . . . 4.2 Synchronous and asynchronous entanglement swapping . . 4.3 Related works and motivations . . . . . . . . . . . . . . . . . 4.4 Heralded Hong-Ou-Mandel interference . . . . . . . . . . . . 4.5 Entanglement swapping . . . . . . . . . . . . . . . . . . . . . 4.5.1 Energy-time entanglement swapping: the concept . . 4.5.2 Experimental implementation and results . . . . . . . 4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Explaining the imperfect visibility . . . . . . . . . . . 4.6.2 The visibility/rate trade-off . . . . . . . . . . . . . . . 4.6.3 An insight into the future . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. 49 50 51 52 52 56 56 57 59 59 60 62. Noise in Si3 N4 microring resonators 5.1 Noise characterization . . . . . . . . . . . 5.1.1 Noise spectrum . . . . . . . . . . . 5.1.2 Noise as a function of temperature 5.1.3 Autocorrelation measurement . . 5.2 Discussion and outlook . . . . . . . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 65 66 66 68 69 70. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. Conclusion and outlook. A Appendix A.1 Photon coherence time as a function of the pump power . . . . . . . . . A.2 Spectral indistinguishability . . . . . . . . . . . . . . . . . . . . . . . . . . A.3 Polarization indistinguishability . . . . . . . . . . . . . . . . . . . . . . . Bibliography. 73 77 77 79 81 101. A Peer-reviewed articles 103 A.1 High-rate photon pairs and sequential Time-Bin entanglement with Si3 N4 microring resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 A.2 Entanglement swapping between independent and asynchronous integrated photon-pair sources . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Acknowledgements. vi. 127.

(11) 1 Introduction. The first quantum revolution occurred around a century ago with the discovery of quantum mechanics. It gave us a new set of physical rules that govern our reality and resulted in a wide array of technologies, such as the transistor, GPS, and MRI scanner, all of which are now well integrated into our society. The ongoing second quantum revolution aims to go further, aspiring to invent new quantum technologies by achieving the precise control of the individual quantum system. As with the conception of previous technologies, quantum technology is a field driven by scientists’ curiosity, hoping to bring something valuable to our society. Quantum technology encompasses sub-disciplines such as quantum communication [1], computing [2], metrology [3], and sensing [4], often relying on the quantum analog of the classical information unit: the qubit. Several individual quantum systems, such as ions [5], atoms [6], superconducting circuits [7], and photons [8, 1, 9], can be used to encode qubits. Among these, photons can be argued to be the most well adapted for long-distance fiber or free-space-based information transmission due to their resilience to environmental fluctuations and lack of mutual interactions, making them the preferred qubit carrier for quantum communication. Integrated quantum photonics is born from the encounter between the two developing fields of quantum technology and integrated photonics [10]. In particular, several efforts are being focused on developing robust, scalable, and efficient integrated singlephoton sources [11, 12]. Among other things, quantum communication would require a single-photon source operating at telecom wavelengths (where transmission losses in optical fiber are lowest) and producing photons that have high-quality entanglement. Exploiting the nonlinear processes of spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM), photon-pair sources have been demonstrated in a variety of integrated photonic structures, including periodically poled nonlinear crystals [13, 14], strip waveguides [15, 16], disks [17, 18], and microring resonators (MRR) [19, 20, 21, 22].. 1.

(12) Chapter 1. Introduction In particular, photon-pair sources based on SFWM in MRR are emerging as a viable integrated photonics solution that addresses the requirements of quantum communication. They have the added advantages of frequency multiplexing capability [23, 24] and narrowband photon generation [25], with linewidths compatible with the acceptance bandwidth of quantum memories [26] without the need for lossy spectral filtering. The field enhancement given by the resonant condition in MRRs brings down the pump power from the watt regime, as is commonly used in current table-top sources, and into the milliwatt regime. In recent years, the Si3 N4 platform has gained much interest in many linear and nonlinear fields due to its ultra-low propagation loss (1 dB/m) [27], wide transparency window (0.25 to 8 µm), CMOS compatibility [28], and absence of nonlinear losses [29]. Si3 N4 based MRRs have demonstrated their success for soliton microcombs and supercontinuum generation [30], and are now increasingly being employed for narrowband, highrate photon-pair generation at the telecommunication wavelengths [25, 31, 32, 33, 34, 35]. Quantum communication envisions a future of several quantum nodes working synergistically to resolve an entirely new set of problems. Such vision requires the demonstration of performant integrated single-photon sources, as well as their performance as part of a network. The first step toward such a goal is to demonstrate high-visibility, high-rate quantum interferences between independent integrated single-photon sources. While a significant effort in studying the individual sources can now be found in the literature [12], the demonstrations of their performance in multi-source quantum interference scenarios remain outstanding. Recently, quantum teleportation and entanglement swapping was demonstrated using two MRR photon-pair sources [36]. However, this was realized with both sources integrated on the same chip and pumped with the same laser, thus not addressing many of the challenges associated with real-world quantum communication. In this thesis, we implement, characterize, and discuss the operation of Si3 N4 MRRbased photon-pair sources. We present an in-depth analysis and trade-off discussions of several aspects, such as heralding efficiency, pair generation rate, and heralded spectral purity. In particular, high heralded spectral purities were obtained with the time-resolved detection technique, where the system detection jitter is much smaller than the photons’ coherence time. Additionally, we demonstrate high-visibility energy-time and sequential time-bin entanglement generation. The potential of our sources for real-world quantum communication is demonstrated by realizing an asynchronous continuous-wave-based Hong–Ou–Mandel (HOM) and entanglement swapping schemes between truly independent (spatially separated and autonomously pumped), MRR-based photon-pair sources. Here, the time-resolved technique is again exploited to achieve high photon indistinguishability between the independent sources. Compared to the pulsed scheme, our continuous-wave scheme is 2.

(13) particularly advantageous for long-distance entanglement distribution since it avoids the highly demanding precise synchronization of pulsed systems and overcomes problems due to path length fluctuations and chromatic dispersion in optical fibers [37]. During the course of our study, we determined the presence of an on-chip, on-resonance generated photonic noise. This noise was a significant contributor to limiting our HOM and entanglement swapping rates. Motivated by our quest to further increase the rates for a practical, real-world quantum communications solution, we start our investigation into the origin of this photonic noise.. Outline of the thesis General concepts. In this chapter, we start by giving some basic concepts upon which our entire work is founded. This chapter aims to provide the general context of our work; it does not provide a detailed explanation of basic quantum information concepts. Microring resonator-based photon-pair sources. In this chapter, we develop our MRRbased photon-pair sources. We start with a general introduction to MRR and SFWM. We then discuss several important considerations and parameters based upon classical regime characterizations, such as thermal stability, phase-matching, and intrinsic and external quality factors. The photon-pair source is then introduced, and its various essential metrics and their optimizations are discussed. These are the coincidence-toaccidentals ratio, heralding efficiency, intrinsic and external pair generation rate, and spectral purity. Finally, we provide a synthesized table containing a summary of the characterizations of our devices. Energy-time and sequential time-bin entanglement is then demonstrated. This chapter is then terminated with a discussion on trade-offs and a comparison of our photon-pair sources with similar realizations from the literature. Practical entanglement swapping between independent sources. We start this chapter with a general introduction to entanglement swapping. We then discuss the two entanglement swapping schemes: synchronous and asynchronous entanglement swapping. The HOM and entanglement swapping experiments are then carried out. The asynchronous entanglement swapping scheme starts from a pair of energy-time entangled states and ends by distributing a time-bin entangled state. This concept is further explained in this chapter. Finally, we provide a discussion about the origin of the observed visibility and the visibility/four-fold coincidence rates trade-off. We also provide some further insight into what four-fold coincidence rates we may expect from such experiments after performing future improvements. For a comparison with similar results in the literature, the reader is referred to our accepted paper, which is also attached in the appendix. Noise in Si3 N4 MRR. An important limiting factor to the pump power which could be used, hence the detected entanglement swapping rates, was a noise that is generated 3.

(14) Chapter 1. Introduction on-chip and on-resonance. This chapter provides some initial measurements as part of our ongoing quest to identify and mitigate this photonic noise. Conclusion and outlook. This chapter provides our concluding remarks and an outlook on what we should pursue next in our quest to demonstrate MRR photon-pair sources as a serious contender for real-world quantum communication.. 4.

(15) 2 General concepts. This chapter gives an introduction to fundamental elements in quantum communication. As with the rest of this thesis, this introductory chapter assumes the reader’s knowledge of textbook concepts from the fields of quantum information and communication. The purpose of this chapter is to isolate the most relevant basic notions for the present thesis: to set the groundwork and provide context for our experimental work in the following chapters. In Sec. 2.1, we start by introducing single-photon sources in general. From the myriad of single-photon sources which are currently available, integrated photon-pair sources constitute the sub-category of interest for this thesis (Sec. 2.2). Quantum entanglement is then introduced in Sec. 2.3, focusing on energy-time and time-bin (Sec.2.3) as the most relevant form of entanglement for long-distance quantum communication. Although we expected quantum communication to rely mainly on time-bin entanglement, energytime entanglement is especially interesting for us, constituting a fundamental element for our asynchronous entanglement swapping scheme in Ch. 4.. 2.1. Single-photon Sources. A photon is a single excitation of the quantized electromagnetic field [38]. While the concept of a quantized electromagnetic field was first proposed in 1900 by Planck to explain black-body radiation, it was only later in the 1960s that the specific properties of quantum light, including single photons, as opposed to classical light, started to be investigated [39]. Today, single-photon sources have a growing utility in the fields of quantum information and communication, including tests of fundamental physics [40, 41], secure quantum communications [8], and quantum metrology [3]. Consequently, such a wide array of usage has motivated efforts to research and develop single-photon sources, to improve their characteristics, and bridge the gap between their real and ideal properties.. 5.

(16) Chapter 2. General concepts An ideal single-photon source is an abstract concept which is useful as a reference point for comparing realizations of real photon sources. An ideal single-photon source is on-demand and is 100 % efficient; the user can push a button and get a single-photon each time. The photon emission rate is arbitrarily large, and there should be no multiphoton emission events, with a Hanbury-Brown and Twiss (HBT) visibility of zero [42]. For multi-photon applications, the subsequent photons need to be indistinguishable, ensuring a perfect photon bunching effect at the output of a beam splitter [43]. Real single-photon sources can be classified under two main categories; probabilistic and deterministic photon sources. Appertaining to the former are photon-pair sources. These are sources that exploit spontaneous parametric processes like spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM) for producing correlated photon pairs. Such parametric processes are probabilistic by nature, emitting photon-pairs at random intervals. To mitigate this randomness, one can use a photon in a pair to herald the other photon’s presence. Deterministic photon sources, on the other hand, are those emitting single photons. They are based on isolated quantum systems such as single ions [44], single atoms [45], single molecules [46], Quantum Dots [47], or NV color centers [48, 49]. Here, by deterministic, one means that the single-photon emission time is well determined, while on-demand means that it is emitted by request; one can inject an external control sequence which will drive the isolated system into emitting a single photon. While this is an apparent advantage compared to probabilistic sources, the boundary between deterministic and probabilistic photon sources is often blurred; a deterministic photon source becomes probabilistic in practice due to finite collection efficiency. A further contributor to such blurring is that probabilistic photon sources are often operated in the pulsed pump regime and/or part of a multiplexing scheme [50]. Each of the two categories of photon sources has its advantages and disadvantages. Photon-pair sources operate at room temperature and give rise to photons with tunable wavelengths and bandwidths, high indistinguishability [51], and readily generate entangled quantum states. However, multi-pair emission can affect security, reduce the throughput and link lengths of quantum communication channels [8], and affect the visibilities of quantum interferences [52]. Deterministic single-photon sources do not suffer from multi-photon emission. However, they often operate at cold temperatures, lack wavelength and bandwidth tunability, suffer from poor coupling efficiencies (coupling the single-photons into the optical fiber), and limited indistinguishability and fidelity. For example, quantum dots suffer from charge fluctuations [53], and nitrogen-vacancy and other color centers suffer from spectral drifts [54], although there are several efforts to mitigate such drawbacks [55, 56, 57].. 6.

(17) 2.2. Integrated photon-pair sources. 2.2. Integrated photon-pair sources. Integrated photonics is an attractive platform for classical and quantum communication, offering advantages in stability and robustness, with reduced size and cost. The possibility of monolithically integrating several components on a single miniature chip is also desirable for commercial applications. Silicon photonics, in particular, is exciting due to its compatibility with existing electronic foundries. It offers the possibility of monolithically integrating both optical and electronic components on the same chip. The field of integrated quantum photonics is relatively new, with the demonstration by Politi et al. in 2008 [58] generally considered the pioneering work. Today, integrated photonics can produce key devices for quantum technology, from single-photon sources to circuits for quantum state manipulation and single-photon detectors. Integrated parametric photon-pair sources are born from the encounter of non-linear optics with integrated photonics. Integrated SPDC based sources include simple waveguides [59, 60, 61], thin films, and micro-ring resonators (MRR) [62], fabricated in lithium niobate (LiNbO3 ) [59, 61], gallium arsenide (GaAs) [60], and aluminium nitride (AlN) [62] platforms. For silicon and other centrosymmetric materials, the χ(2) component vanishes, making the χ(3) -based process of SFWM the only possible process for photon-pair generation. Depending on the desired application, photon-pairs generated in the same band, as is the case for SFWM sources, could be advantageous. However, this comes with the disadvantage of challenging pump filtering requirements. Integrated SFWM based sources include structures such as simple [63, 64] and spiral [65] waveguides, microring resonators (MRR) [66, 24], and microdisk resonators [18, 17]. They are fabricated in a variety of platforms such as silicon (Si) [65], silicon dioxide (SiO2 ) [64], silicon nitride (Si3 N4 ) [33], as well as hybrid integrations [67, 68].. 2.3. Entanglement. Entanglement [69] is the property of two or more subsystems whose quantum states are undefined; they are describable only jointly by the entire system’s quantum state. Entanglement is one of the most counterintuitive phenomena in quantum mechanics. Two spatially separated but entangled photons appear to be independent, yet they share a quantum correlation; the measurement on one determines the outcome from a measurement of the other. The resulting correlations are deemed quantum because they cannot be understood within the traditional framework of classical physics. Quantum entanglement is so counterintuitive that it was the base of Einstein, Podolsky, and Rosen’s argument about quantum mechanics’ incompleteness (EPR paradox, 1935 [70]), an argument that was considered philosophical until the derivation of Bell’s inequality 7.

(18) Chapter 2. General concepts in 1964 [71]. Eventually, the EPR paradox was resolved in favor of quantum mechanics by experimentally violating the Bell inequality [72, 73, 74, 75]. Entanglement plays a central role in quantum information and communication. For example, it is used in quantum cryptography [8], permitting fundamentally secure communication, and for quantum teleportation [76] and quantum repeaters [77] to enable efficient quantum state transfers between two distant locations. Quantum entanglement can occur over various degrees of freedom, such as time [78], path [79, 80], and polarization [81].. Energy-time entanglement Energy-time entanglement was first theorized by Franson in 1989 [78] and later demonstrated experimentally by Brendel et al. [82] and Kwiat et al. [83]. In his work, Franson described the phenomena in terms of states generated in a three-level atomic system. Nevertheless, the idea can be extended to photon-pairs generated by a spontaneous parametric process in the continuous-wave regime. The underlying mechanism for energy-time entanglement is a non-classical correlation for the photon-pair energy and time variables. For each photon in a pair, the emission time and the energy are not individually defined, yet the time difference of the two photons and the sum of their energies are well-defined quantities, at least within the photons’ coherence time and the pump’s bandwidth. Such simultaneous energy and time correlation is non-classical by nature; it can violate the classical uncertainty limit on simultaneous energy and time measurements [84]. Direct observation of such energy-time entanglement requires high-resolution time and frequency measurements simultaneously. This is feasible [85] but technically challenging. Alternatively, one can follow Franson’s proposal; the energy-time quantum correlation can be observed by interfering the probability amplitudes of the photon-pair emission times on two unbalanced Mach-Zehnder interferometers. The arm imbalance of both interferometers is identical. The arm imbalance must be much longer than the photons’ coherence time in order to avoid first-order interference, and much smaller than the pump’s coherence time, thus permitting second-order interference. Quantum interference in the photon-pair coincidence events as a function of the sum of the interferometers’ local phase shifts can consequently be observed. Such quantum interference can happen only between the indistinguishable events of photon-pairs generated at an earlier time and taking the long interferometer’s path, and photon-pairs generated at a later time and taking the short interferometer’s path. The interference of photons with classically correlated energies or emission times will result in a maximum visibility of 50% instead of the 100% visibility obtainable with the quantum energy-time correlation.. 8.

(19) 2.3. Entanglement Time-bin entanglement The pulsed version of Franson’s energy-time entanglement scheme is called time-bin entanglement [86, 8, 87]. This implementation works in the pulsed pump regime, and the interference happens between discrete photon-pair emission times. Creating an arbitrary time-bin entanglement state is possible by pumping a non-linear material with a double-pulse of a controllable ratio and relative phase. The controlled double-pulse sequence can be created by passing a pulsed laser through an unbalanced interferometer, with a controllable splitting ratio and relative phase shift [88]. The time-bin degree of freedom is particularly useful for long-distance fiber-based quantum communication due to its insensitivity to polarization fluctuations and robustness to phase shifts in fibers. Indeed, time-bin entanglement and time-bin qubits are typically generated with pulses that are separated by a few ns, a much smaller scale than the time scale for phase drifts in fibers. This makes time-bin the preferred degree of freedom for fiber-based quantum communication and is widely used for quantum cryptography [8], especially in all the record-breaking long-distance quantum key distribution (QKD) experiments [89, 90].. 9.

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(21) 3 Microring resonator-based photonpair sources In this chapter, we develop and characterize MRR-based photon-pair sources. We start with a general introduction to MRR (Sec. 3.1) and the process behind photon-pair creation (Sec. 3.2). Several MRR devices were used, in particular, as the fabrication process evolved, the quality factor (Q-factor) of these devices increased. In Sec. 3.3, we give a list of the devices that we used in this thesis specifying their Q-factors and corresponding linewidths. The section continues with other useful classical regime characterizations and considerations, such as the coupling regime, phase-matching, and thermal stability. In Sec 3.4, we develop our photon-pair source and discuss its important metrics and their optimizations; a summary of the results from the characterization of the devices is provided at the end of this section. Energy-time and sequential time-bin entanglement generation are carried out in Sec. 3.5. Finally, this chapter is concluded with a discussion of some essential trade-offs, and a comparison of our sources with realizations of similar sources in the literature (Sec. 3.6).. 3.1. Microring resonators. A ring resonator is a photonic cavity made by a fiber or a waveguide in a loop-like structure (see Fig. 3.1). The cavity is evanescently coupled to one or two straight waveguides, called bus-waveguides, which serve to couple light into and out of the cavity. The ring geometry can be circular or a racetrack. If the dimensions of such a cavity are on the micrometer scale, we call it a microring resonator (MRR). Depending on the Q-factor, MRRs can give rise to an extremely high field enhancement. This, together with a small effective mode area due to small mode confinement in waveguides, results in a significant increase in the nonlinear interaction strength. MRRs deliver a power-efficient, compact, and stable alternative to what is achieved with bulk optics. Such advantages explain the increasing interest in MRRs for both classical and quantum applications, an interest that has emerged in the last decade and is still growing. 11.

(22) Chapter 3. Microring resonator-based photon-pair sources. Idler Pump Signal F1. F2. Figure 3.1: Schematic representation of MRR. The pump (green) is injected in the buswaveguide and is coupled on-resonance, generating signal (red) and idler (blue) fields. The residual pump is rejected (F1), and signal and idler are separated (F2).. today. As is the case for integrated optics in general, the research field of MRRs for classical applications is more mature than its quantum counterpart. Nevertheless, the quantum optics community is showing an increasing interest in MRRs and their multiple applications to quantum communication: photon-pair generation [91, 92, 20, 24, 93], entanglement generation [19, 22], squeezing [94], frequency conversion [95, 96], and quantum random number generation (QRNG) [97]. MRRs can also be used for highdimensional entanglement generation in the field of quantum computing [98, 33].. 3.2. Spontaneous four-wave mixing. Spontaneous four-wave mixing (SFWM) is a parametric process involving a four-photon interaction mediated by a medium exhibiting a third-order nonlinearity – i.e. a medium in which the χ(3) susceptibility is non-negligible. Like all parametric processes, no transfer of energy happens between the optical fields and the medium; the quantum state of the medium before and after the interaction remains the same. In SFWM, two pump photons are converted into a photon-pair at lower and higher energies (Fig. 3.2a). The converted photons are conventionally called signal (higher energy) and idler (lower energy). The generated photon-pair must conserve the energy and the momentum of the two pump photons (Fig. 3.2b). The energy conservation condition means that the two photons are generated symmetrically around the pump wavelength. Usually, momentum conservation is not naturally satisfied due to material dispersion. However, phase-matching can recover momentum conservation by adequately engineering the geometrical dispersion to compensate for material dispersion. Depending on the polarizations of the photons involved, the SFWM process can be broken into three types. The so-called type-0 SFWM is a process where all the involved 12.

(23) 3.2. Spontaneous four-wave mixing. (b). (a). Energy conservation. Momentum conservation. ωp ωp. χ. ωp. (3). ωp. ωi ωp. Kp. Kp. ωi ωs. ωp. ωs. Ki. Ks. Figure 3.2: The spontaneous four-wave mixing (SFWM) process. (a) A χ(3) nonlinear material mediates the conversion of two pump photons (ω p ) into a photon-pair (ωs , ωi ). The relatively strong pump is also present at the output of the material. (b) The photonpair must conserve the energy and momentum of the pump. photons are co-polarized; it is also the most efficient process among the three types [99]. Type-0 SFWM is usually the process of choice for integrated photonics, where the waveguides often have low transmission losses for only one polarization. The other two types, namely type-I and type-II, involve orthogonally polarized modes. See [100], for example, for further details on these two types. Finally, if the two pump photons are at the same wavelength, the process is called degenerate SFWM; otherwise, we speak of non-degenerate SFWM. The efficiency of the SFWM process scales as ∝ γ2 P2 , where P is the pump power, and γ is the nonlinear parameter defined as γ=. 2πcn2 , λAe f f. (3.1). where λ is the wavelength, Ae f f is the effective mode area, c is the speed of light, and n2 is the Kerr coefficient, i.e. the intensity (I) dependent refractive index (n = n0 + n2 I). From Eq. 3.1, we see that small effective mode areas and high Kerr coefficients are necessary for an efficient SFWM process. The photon-pair generated by the SFWM process is in a two-mode squeezed state [101], †. |ψi = e( βCI I −h.c.) |vaci ,. (3.2). where | β|2 is proportional to the average number of pump photons, and C †I I is the two-photon creation operator given by 1 C †I I = √ 2. Z Z. dωs dωi A(ωs , ωi ) a†s (ωs ) ai† (ωi ) ,. (3.3). such that C †I I |vaci is the normalized two photon-state [102, 101]. a†s and ai† are the 13.

(24) Chapter 3. Microring resonator-based photon-pair sources creation operators for the signal and idler modes, respectively. A(ωs , ωi ) is the joint spectral amplitude (JSA); it is determined by the phase-matching condition, the pump spectral shape, and the third-order nonlinearity. For low pump powers such that | β| 1, the photon-pair state can be approximated as. |ψi ≈ |vaci + βC †I I |vaci .. (3.4). The C †I I |vaci normalization condition requires that Z Z. dωs dωi |A(ωs , ωi )|2 = 1 ,. (3.5). where |A(ωs , ωi )|2 is the joint spectral intensity (JSI). Finally, we would like to anticipate the relevance of the above-presented analysis to our discussion about the photon-pair spectral purity in Sec. 3.4.7.. 3.3. Classical regime characterization. This section provides preliminary MRR characterizations which are important to understand before the photon-pair source experiment. In Sec. 3.3.1, we provide the naming conventions, Q-factors, and linewidths of the devices presented in this thesis. In Sec. 3.3.2, we analyze the spectrum of our resonances and provide the relevant parameters extracted from such a scan. Sec. 3.3.3 is dedicated to discussing some phase-matching considerations and providing a way to predict the number of emitted photon-pair modes. Finally, in Sec. 3.3.4, we discuss the thermal effects which influence our laser to resonance coupling.. 3.3.1. The devices in this work. Our devices are fabricated in the Si3 N4 platform as part of a scientific collaboration with the Kippenberg group (K-Lab at EPFL) [103]. The Si3 N4 platform benefits from ultra-low propagation loss (1 dB/m) [27], wide transparency range, high power handling capability [29], and CMOS and space compatibility [28]. The devices are optimized to work in the classical regime (above threshold), demonstrating several practical applications based on soliton micro-combs and supercontinuum generation [30]. Nevertheless, these samples can readily be used in the single-photon regime, which is the subject of this thesis. The results presented in this work provide a basis for optimizing the device fabrication process and design in order to better address some specific future needs for quantum communication.. 14.

(25) 3.3. Classical regime characterization. Device. Q-factor. ∆v [MHz]. Note. Paper. MRR01. 0.12 × 106. MRR02 MRR03 MRR04 MRR05 MRR06. 1645. Time-bin entanglement. A.1. 0.62 × 106. 309. -. A.1. 0.42 × 106. 462. Swapping Source 1. A.2. 0.62 × 106. 309. Swapping Source 2. A.2. 2.03 × 106. 78. Pigtailed device. -. 4.71 × 106. 46. Pigtailed device. -. Table 3.1: The devices that were used in this thesis. MRR02 and MRR04 are the same device (see footnote a). Table 3.1 reports the devices that were exploited in our worka . We have used devices with different field enhancements; this can be seen from different quality factors (Q-factors) and resonance linewidths, ∆vb . As the research in this thesis evolved, the fabrication process has improved, explaining the different characteristics of the devices in Table 3.1. Nevertheless, the specific experiment being undertaken often determined the choice of the device based on its Q-factor (high or low), as will be shown in the following parts of this thesis.. 3.3.2. Spectrum transmission scan. The resonance comb of each device can be measured by performing a calibrated power transmission scan across the device spectrum (Fig. 3.3). The non-normalized scan illustrates that, generally, the transmission is not uniform across the entire C-band. Indeed, due to the different propagation properties of the light inside the resonator, the different resonances have different widths and contrasts. The differing dip contrasts are best illustrated from the normalized transmission scan (see Fig. 3.3 bottom). To have a resonance at a specific wavelength, the propagating light must acquire an integer number of 2π, allowing it to constructively interfere. The family of resonant modes is therefore given by 2πm = β(ω )2πR ,. (3.6). where β(ω ) is the propagation constant, R is the radius of the ring, and m is the azimuthal a MRR02. and MRR04 are the same device. MRR04 was characterized with a newer setup involving a time-to-digital converter (ID900 IDQ) with better resolution than the one used for MRR02 (ID800 IDQ). b We adopt the convention of indicating the resonance’s linewidth obtained from the transmission scan and cross-correlation measurement by ∆v and Γ, respectively. Unless otherwise specified, the values provided always refer to the specific resonances we consider for pumping and photon-pair collection. Often we provide the resonance values of the signal, idler, and pump separately; however, if only one value is provided, this is taken as the average of the three.. 15.

(26) Chapter 3. Microring resonator-based photon-pair sources. Figure 3.3: The un-normalized (top) and normalized (bottom) spectral transmission scan. The data is taken with device MRR05.. mode number. Fig. 3.4a zooms in on the resonance at 1550.29 nm. The resonance linewidth, ∆v, can be obtained by fitting the dip with a Lorentzian shape. This defines the loaded quality factor (Q) as Q = 2π. f0 intracavity energy ≈ , energy dissipation per roundtrip ∆v. (3.7). where f 0 and ∆v are the resonance’s central frequency and linewidth, respectively. The contrast of the resonance’s dip is defined by the intrinsic (Qint ) and external (Qext ) quality factors. The intrinsic quality factor is the uncoupled cavity’s Q-factor; it is determined by the cavity’s intrinsic losses, such as material absorption and scattering. The external quality factor is determined by the coupling between the bus-waveguide 16.

(27) 3.3. Classical regime characterization. 1.2. 196.5. 0.8. FSR [GHz]. Transmission. 1.0. 0.6 0.4 0.2 0.0. 196.4 196.3 196.2 196.1. −400 −200 0 200 400 Frequency detuning [MHz]. 1500. 1550 1600 Wavelength [nm]. (a). (b). Figure 3.4: (a) The spectral transmission scan of the resonance around 1550.29 nm. The dip is fitted with a Lorentzian shape, providing a linewidth ∆v = 67.85 MHz. (b) The free spectral range (FSR) as a function of the wavelength of the different resonances. The device under consideration is MRR05. The resonance in (a) is different from the one used for photon-pair generation (Table. 3.1).. and the ring resonator. The three quality factors are related by 1 1 1 = + . Q Qint Qext. (3.8). In the absence of other forms of parasitic couplings, such as coupling to higher-order modes, the resonance contrast is given by [104] T = 1−2. Qint Qext. 2. .. (3.9). Depending on the relative values of Qext and Qint , three coupling regimes can be identified: under-coupled regime (Qext > Qint ), critically coupled regime (Qext =Qint ), and over-coupled regime (Qext < Qint ). These coupling regimes directly determine some important photon-pair source metrics such as the heralding efficiency (Sec. 3.4.5) and pair-generation rate (Sec. 3.4.6). The free spectral range (FSR) defines the spectral distance between two adjacent resonances. Since in a photon-pair source one usually needs to isolate a pair of resonances from the rest of the comb, the FSR must be chosen to facilitate the photon-pair collection. This thesis is situated within the framework of quantum communication, for which telecom is the preferred band due to its low transmission losses in optical fibers. Fil17.

(28) Chapter 3. Microring resonator-based photon-pair sources tering at the telecommunication wavelengths can be achieved with off-the-shelf, high performance, and low loss components. We use dense wavelength division multiplexing (DWDM), which are ’standardized’ filters designed to multiplex and demultiplex specific wavelengths defined by the International Telecommunication Union (ITU). They are available with different FSRs, with 200 GHz and 100 GHz being the most common variant. Their insertion loss is below 0.2 dB. Fig. 3.4b reports the FSR for the various resonances from Fig. 3.3. The average FSR of ≈196 GHz gives a good matching with the ITU 200 GHz comb, at least for a pump, signal, and idler in the same spectral region. As seen in Fig. 3.4b, the FSR is not constant, but it changes across the spectrum due to dispersion.. 3.3.3. Phase-matching. Spontaneous four-wave mixing is an energy and momentum conserving process. Energy conservation can be written as ∆ω = 2ω p − ωs − ωi = 0 .. (3.10). That is, the signal and idler frequencies are symmetrically distributed around the pump frequency. The momentum conservation condition, also called the phase-matching condition, is usually a vectorial relation on the K-vectors (Fig. 3.2b). However, for waveguides, the momentum conservation condition becomes a linear momentum conservation condition, which can be expressed in term of the propagation constants as. ∆β = 2β p − β s − β i = 0 .. (3.11). Usually, due to the dispersion, energy and momentum conservation conditions can not be simultaneously satisfied. The solution is to engineer the device’s dispersion so that geometrical dispersion can compensate for material dispersion. The geometrical dispersion of MRRs is completely determined by three parameters: the waveguide width, waveguide thickness, and the MRR’s radius. Due to the resonant condition (Eq. 3.6), the phase-matching condition of MRRs is readily satisfied by considering mode number matched resonances such that ∆m = 2m p − ms − mi = 0 ,. (3.12). where m is the azimuthal mode number. The energy conservation condition is then satisfied by properly engineering the dispersion so that the set of modes that are satisfying ∆m = 0 are also equidistant in frequency.. 18.

(29) 3.3. Classical regime characterization. 7 6. 2.0 ∆ω [GHz]. ∆ω [GHz]. 2.5. 1.5 1.0. 5 4 3 2. 0.5. 1. 0.0. 0. 0. 5. 10. 15 20 25 |m − mp | (a). 30. 35. 0. 5. 10. 15 20 25 |m − mp |. 30. 35. (b). Figure 3.5: The energy conservation condition, expressed in ∆ω as a function of the mode number around the pump mode m p . The dashed line corresponds to ∆ω = 4π∆v p . (a) Moderate Q-factor device (MRR04) with Q = 0.610 × 106 and ∆v p = 315 MHz. (b) High Q-factor device (MRR06), with Q = 4.712 × 106 and ∆v p = 46 MHz.. Fig. 3.5 shows ∆ω (Eq. 3.10) for a fixed pump frequency ω p (around 1557 nm), and mode number matched resonances (∆m = 0) for two different devices. From both figures, a and b, we can see that as |m − m p | increases, ∆ω increases, and energy conservation becomes less satisfied; consequently, the photon-pair source conversion efficiency decays. Fig. 3.5a shows a moderate Q-factor device (MRR04), with Q = 0.610 × 106 and ∆v p = 315 MHz; while Fig. 3.5b shows a high Q-factor device (MRR06), with Q = 4.712 × 106 and ∆v p = 46 MHz. ∆v p is the pump’s resonance linewidth. If we assume that our photonpair source can be considered efficient for ∆ω < 4π∆v p , then the difference between the two devices becomes immediately evident. MRR04 emits photon-pairs efficiently over roughly 18 resonance pairs, while MRR06 emits photon-pairs efficiently over only 8 resonance pairs. The above analysis highlights the different dispersion engineering requirements as a function of the Q-factor. A high Q-factor device has more stringent requirements, especially if photon-pair emission is desired from multiple correlated resonance pairs.. 3.3.4. Thermal effects. In the following, we discuss how thermal effects in MRRs affect the on-resonance operation and the possibility to exploit these effects for providing a wavelength tunability. 19.

(30) Chapter 3. Microring resonator-based photon-pair sources Thermal locking By propagating inside the MRR, part of the light gets absorbed due to absorption losses. This results in the cavity heating up and, consequently, a shift of the resonance structure due to thermal effects. According to their origin, these effects are broken mainly into dn two categories; namely, cavity expansion and the thermo-refractive effect ( dT ) [105]. The thermal effects are especially important in MRRs due to the small mode volume and power enhancement given by the cavity [106]. Carmon et al. [105] have shown that, in the steady-state, MRRs can be in three different regimes: stable warm equilibrium, unstable warm equilibrium, and stable cold equilibrium. Warm and cold refer to on- and off-resonance, respectively. The steady-state equilibrium regime is determined by two factors: the pump laser’s detuning from the resonance dip and the scan direction in which the laser pump is brought on-resonance. We are interested in the stable warm equilibrium regime. To achieve this operation regime, the pump must be brought on-resonance by scanning it from higher to lower frequencies. Additionally, the pump must be parked somewhere on the blue-shifted side of the resonance. By doing so, our resonance and the pump laser are self-locked; due to the thermal effects, the cavity resonance follows the laser wavelength, compensating for small fluctuations in the pump laser wavelength. However, the self-locked regime is not enough to compensate for large laser wavelength drifts. A better solution for achieving a long on-resonance operation is to combine the self-locked regime with a feedback control system [107]. This should keep the laser on-resonance by following fast wavelength fluctuations (passive self-locking) as well as slow wavelength drifts (active locking). We implemented such a feedback control system by monitoring the residual pump power at the MRR output and actively tuning a Peltier on which the chip was mounted. In this way, for devices with moderate Q-factors (below 1 × 106 ), we were able to extend the on-resonance operation from several hours to several days.. Wavelength thermal tuning dn The thermo-refractive effect ( dT ) can be exploited in order to tune the MRR resonance wavelengths. Wavelength tuning helps align the resonances with the ITU grid, allowing the use of commercially available, high-performance, and cheap DWDM filters. Additionally, it allows the wavelengths of different MRR photon-pair sources to be aligned, enabling spectral indistinguishably (see Sec. A.2 in the appendix).. Fig. 3.6 shows the change in the resonance wavelength as a function of temperature. Cooling the chip down from room temperature (20◦ C) to -60◦ C, the resonance shifts linearly towards the blue side, with a coefficient of 15.14 pm/◦ C. The fitting in Fig. 3.6 was obtained by excluding the point at -112◦ C. The data point at -112◦ C deviates 20.

(31) 3.4. Photon-pair source. Wavelength [nm]. 1558.0 1557.5 1557.0 1556.5 1556.0 1555.5 −125 −100. −75 −50 −25 Temperature [°C]. 0. 25. Figure 3.6: Wavelength thermal tuning. The wavelength of a certain resonance as a function of temperature. The measurement was performed with a pigtailed device (MRR05) placed inside a Stirling cooler. significantly from the linear behavior. This is expected from Si3 N4 , where the thermooptic coefficient is almost constant only for temperatures above ≈-70◦ C (≈200 K) [108]. Wavelength thermal tunability is achieved by mounting the chip on a Peltier cooling unit controlled by a digital PID system. The system is isolated by a simple cover over the chip, thus increasing its thermal stability. Such a solution permits operation at temperatures from about 50◦ C down to several degrees celsius. However, in operating at low temperatures (below 10◦ C), one must be cautious in avoiding water condensation on the chip. A droplet of water that can occupy the space between the lensed fiberc and the chip can cause a significant degradation or even total loss of the fiber-to-waveguide coupling. To avoid the water condensation problems and allow operation at even lower temperatures, we use a pig-tailed chip with lensed fibers directly glued to the chip’s facet. Such pig-tailed devices can operate at very low or even cryogenic temperatures. The measurement in Fig. 3.6 was obtained by placing a pig-tailed device inside a Stirling cooler (Twinbird SC-UD08).. 3.4. Photon-pair source. In this section, we investigate the MRR as a photon-pair source. Sec. 3.4.1 starts by introducing the general setup for operating the MRR as a photon-pair source. In Sec. 3.4.2, cA. lensed fiber is used to couple the fiber-based setup to the chip (see Sec. 3.4.1).. 21.

(32) Chapter 3. Microring resonator-based photon-pair sources. PC EDFA. PBS. PC. Tunable BP. Signal. Pump CW. DWDM. SiN MMR 99%. 99%. Pump Rejection. x2 1%. PM. TEC Control. x2. DWDM. 1%. Idler. DWDM x2. Coincidences. Pump Preparation. PM. Figure 3.7: Schematic of the experimental setup for photon-pair generation. A continuous-wave CW laser is prepared before injection in the Si3 N4 MRR. EDFA: erbiumdoped fiber amplifier. PC: polarization controller. PBS: fiber polarizing beam-splitter. BP: bandpass filter. PM: power meter. DWDM: dense wavelength division multiplexing.. we introduce the cross-correlation measurement, followed by several photon-pair source metrics that we can extract from such measurements: coincidence (and single) rates (Sec. 3.4.3), coincidences-to-accidentals ratio (Sec. 3.4.4), heralding efficiency (Sec. 3.4.5), and pair generation rate (Sec. 3.4.6). Finally, we finish with an extensive discussion on spectral purity and the autocorrelation measurement (Sec. 3.4.7).. 3.4.1. Photon-pair source setup. Fig. 3.7 provides the setup that we use for operating the MRR as a photon-pair source. The sample is mounted on an X-axis translation stage and is coupled to two antireflection coated (AR) lensed fibers (spot-size diameter of 5 µm, OZ optics) mounted on XYZ-axis translation stages (Eliot MDE122). The lensed fibers, together with the on-chip inverse tapering, provide the necessary mode matching between the photonic integrated circuit (PIC) and the fiber-based setup. The waveguide-fiber coupling transmission can be up to ≈65%. Alternatively, the lensed fiber can be directly pigtailed to the Si3 N4 chip, providing a stable coupling without the alignment stages. Fig. 3.8 shows pictures of the two types of coupling. An external cavity continuous-wave (CW) laser (DL100 Toptica) acts as the pump laser. The pump is then amplified with an erbium-doped fiber amplifier (EDFA, Keopsys KPS-BT-C) to provide sufficient power. Two polarization controllers and a polarizing beam splitter provide a way to control both the pump power and its polarization. The polarization is aligned with the TE mode of the waveguide, providing the maximum transmission. A series of commercially available and low loss (insertion loss, IL < 0.2 dB) dense wavelength division multiplexers (DWDM) reject the amplified spontaneous emission (ASE) from the EDFA. Our DWDMs are designed to work only in the C-band. A tunable bandpass (BP) filter serves to provide spontaneous emission rejection at wavelengths outside the C-band. The DWDMs and tunable bandpass filter provide total 22.

(33) 3.4. Photon-pair source. (a). (b). Figure 3.8: Picture of the setup. (a) Waveguide is butt-coupled to a lensed fiber using coupling stages. (b) Pigtail coupling: the lensed fiber is directly glued to the waveguide facet. pump isolation above 135 dB. DWDMs are also used at the chip output to reject the pump and demultiplex the signal and idler into different fibers. The achieved pump rejection and signal-idler isolations are 135 dB and 100 dB, respectively. The coupling is continuously monitored by collecting 1% of the pump power at the chip’s input and output. A typical breakdown of the various contribution to the losses is provided in Table 3.2. MRR03. MRR04. [dB]. 5.3 (5.1). 4.3 (4.1). Waveguide-to-fiber (CL). [dB]. 2.0. 3.0. Fiber components (IL). [dB]. 2.1 (1.8). 2.3 (1.8). SNSPDe. [dB]. Total. [dB]. ≈0.08. ≈0.08. Extraction from cavity. (EL)d. 9.5 (9.0). 9.7 (9). Table 3.2: Representative breakdown of losses. When both signal and idler data are provided, the latter is given in the parentheses.. Photons are detected with in-house-developed molybdenum silicide (MoSi) superconducting nanowire single-photon detectors (SNSPD) with detection efficiencies ηd > 80%, recovery times trec < 35 ns, timing jitters σjit ≈ 35 ps, and dark counts below 500 Hz [109]. The detection events are then analyzed with a time-to-digital converter, either IDQ-ID800 d The e The. extraction from the cavity (EL) is explained in Sec. 3.4.5. It is provided here for completeness. finite detection efficiency of the single-photon detectors ηd is usually provided in percentage.. 23.

(34) Chapter 3. Microring resonator-based photon-pair sources. Coincidence rate Rcc [kcps]. 2.5 2.0 1.5 1.0 0.5 0.0 −2.0 −1.5 −1.0 −0.5 0.0 0.5 Delay τ [ns]. 1.0. 1.5. 2.0. Figure 3.9: Signal-idler coincidence histogram of MRR03 when pumped with 12.5 mW (in-chip). The histogram bin size is 13 ps. The fitting function is given in Eq. 3.15. (bin width tbin = 160 ps) or IDQ-ID900 (bin width tbin = 13 ps).. 3.4.2. Cross-correlation measurement. The generation of correlated photon-pairs can be verified with a signal-idler crosscorrelation measurement. Such a measurement gives a qualitative insight into the photon-pair correlation and provides a way to extract several useful photon-pair source metrics, such as pair generation rate (PGR) and heralding efficiency (ηh ). Fig. 3.9 provides an example of such a histogram obtained by pumping MRR03 onresonance with 12.5 mW of pump power (in-chip) and collecting the photon-pair in the adjacent resonances. Here, as is often the case in this thesis, we detect the photons in a time-resolved manner, where the detection scheme’s temporal resolution is small enough to resolve the photon’s temporal shape. This derives from the fact that our detection system’s temporal jitter (tens of psf ) is about one order of magnitude smaller than the photons’ coherence times (hundreds of ps). In such a regime, we expect the temporal shape of the coincidence histogram to be mainly determined by the photon-pair. Due to the presence of the cavity, the photon-pair temporal shape is described by a double exponential. To be more precise, we also consider a small asymmetry between f In. this thesis, two different time-to-digital converters were used, namely, IDQ-ID800 and IDQ-ID900, with bin sizes of 160 ps and 13 ps, respectively. The time-resolved detection regime is better achieved when the IDQ-ID900 device was used.. 24.

(35) 3.4. Photon-pair source signal and idler temporal shapes, which could originate from a slight difference in their cavity lifetimes. The coincidence histogram, therefore, takes the following form [110, 111]: (. Rcc (0)e2πτΓs ,. if τ < 0 .. Rcc (0)e−2πτΓi ,. if τ ≥ 0 .. (3.13). Here, Rcc (0) is the maximum of the coincidence histogram at zero delay, and Γs and Γi are the signal and idler linewidthsg at full width at half maximum (FWHM). If it is necessary to include the detection system effect in Eq. 3.13, one needs to consider that the temporal jitter has a Gaussian distribution of the form: t jit = q. 1 2 2πσjit. e. 2 ) −t2 /(2σjit. ,. (3.14). where σjit is the standard deviation of the temporal jitter distribution. The coincidence histogram shape is then given by the convolution of Eq. 3.13 with Eq. 3.14, which results in: " ! 2 +τ 2πΓ σ 2 2 s jit 4π Γs (Γs σjit /2+τ ) p Rcc (τ ) = Rcc (∞) + Rcc (0) e erfc 2σjit !# (3.15) 2 −τ 2πΓ σ 2 2 i jit p +e4π Γi (Γi σjit /2−τ ) erfc . 2σjit In this thesis, we use Eq. 3.15 to fit our coincidence histograms, extract the signal’s and idler’s linewidths, Γs and Γi , and the photon’s coherence time τc = 1/πΓ. The detection system jitter, σjit , can also be extracted from Eq. 3.15.. Finally, Eq. 3.15 permitted us to conclude that both the detector’s jitter, σjit , and the photon’s coherence time, τc , increase as a function of the pump power (see Sec. A.1 in the appendix). The first is due to the recovery currents in SNSPDs with high detection rates. Indeed, the jitter depends on the current [109]; it increases at a lower SNSPD bias current. For high detection rates, the probability that the detection happens during the recovery, i.e. when the current is below the settled one, is not negligible. The second happens as a consequence of cross-phase modulation in MRRs [112]; this is better explained in Sec. A.1 in the appendix.. 25.

(36) Chapter 3. Microring resonator-based photon-pair sources. 200 MRR03 MRR04. Coincidences rate [kcps]. Coincidences rate [kcps]. 300. 200. 100. 0 0. 5 10 15 Power in-chip [mW]. 20. MRR02 150 100 50 0. (a). 0. 5. 10 15 20 25 Power in-chip [mW]. 30. (b). Figure 3.10: Coincidences as a function of the pump power. The coincidences scale quadratically, as is expected from SFWM (a), and saturate at high pump power due to the detectors’ finite recovery time (b).. 3.4.3. Coincidences and singles versus power. Fig. 3.10 shows the coincidence counts as a function of the pump power. Here the coincidences are taken as the total counts inside the entire coincidence peak (6×FWHM) minus the accidental coincidences obtained at an equal window outside the correlation peak. As seen in Fig. 3.10a, the coincidences scale quadratically with the pump power, as is expected from the SFWM process. However, if the pump power is further increased, the high number of photon counts impinging on the detectors reduces the single-photon detector efficiency (ηd ), thus saturating and even reducing the coincidence counts (Fig. 3.10b). The detection efficiency reduction happens because the SNSPDs have a recovery cycle which they must undergo after each photon detection event. The recovery time of our SNSPDs is on the order of 100 ns, limited mainly by the electronic circuitry. Fig. 3.11 shows the singles as a function of the pump power. The singles here are taken as the net singles obtained by subtracting the off-resonant from the on-resonant singles. As for the coincidences, the singles are expected to scale quadratically with the pump power; nevertheless, we observed the presence of a significant linear component Rn . Such a linear component indicates the presence of photonic noise; this is especially true since there is no linear component appearing in the coincidence counts (Fig. 3.10), indicating that the Rn singles contributing to the linear component are actually uncorrelated photons. It is worth confirming that this photonic noise is resonantly generated; it will be shown in Ch. 5 that the off-resonance photonic noise is more than one order of magnitude should be distinguished from ∆v where the linewidth is directly obtained from the resonance’s transmission scan. The two values are usually very similar. g This. 26.

(37) 3.4. Photon-pair source. MRR03 MRR03 MRR04 MRR04. 3. signal idler signal idler. 2 1. 10 Signal MRR02 Idler MRR02. 8 Singles [Mcps]. Singles [Mcps]. 4. 6 4 2. 0 0. 5 10 15 Power in-chip [mW]. 20. (a). 0. 0. 5. 10 15 20 25 Power in-chip [mW]. 30. (b). Figure 3.11: Singles rates as a function of the pump power. The experimental data are 2 + R P – where P is the pump power, R is the linear photonic noise fitted with Rs Pin n in n in term, and Rs is the quadratic SFWM term.. lower than the resonantly generated noise. To put some numbers into perspective, the rate of singles due to SFWM in the idler mode of MRR04 is Rs = 35 kcps/mW2 , while due to noise is Rn = 120 kcps/mW. Finally, note that the singles scale as ηd , while the coincidences scale as ηd2 . This explains why, at high pump power, the coincidences decrease while the singles continue to increase. Due to below threshold pumping and the wide bandgap of Si3 N4 , the coincidence (and single) counts saturation observed here is not due to nonlinear losses or the onset of optical parametric oscillation (OPO), contrary to what is often observed in MRR literature [34, 20, 113]. A proof of this is provided by the fact that the coherence time of our photons increases as a function of the pump power; see Sec. A.1 in the appendix for further explanations.. 3.4.4. Coincidences-to-accidentals ratio. The coincidences-to-accidentals ratio (CAR) is the photon-pair source metric quantifying the quality of the signal-idler cross-correlation. The CAR carries the significance of the signal-to-noise ratio; it is defined as the ratio between the wanted cross-correlations at zero-delay (τ = 0), with the unwanted coincidences at T∞ (τ 0). The unwanted coincidences arise from double-pair contributions, photonic noise, and dark counts from the detectors. By definition, the CAR depends on the temporal window that one considers for calculating the ratio. In this thesis, the CAR’s temporal window is taken to be equal to the 27.

(38) Chapter 3. Microring resonator-based photon-pair sources. 500 MRR03 MRR04. MRR02. 400 CAR. CAR. 1500 1000 500. 300 200 100 0. 0 0. 5 10 15 Power in-chip [mW]. −20 −15 −10 −5 0 5 Power in-chip [dBm]. 20. (a). 10. 15. (b). Figure 3.12: Coincidences-to-accidentals ratio (CAR). The measurement data is compared against predictions (solid line) given by Eq. 3.18. photons’ coherence time τc (average signal and idler). Formally, we define the CAR as CAR =. R +τc /2 −τc /2. Rcc (t) dt − R T∞ +τc /2 T∞ −τc /2. R T∞ +τc /2 T∞ −τc /2. Rcc (t) dt. Rcc (t) dt. .. (3.16). Comparing CAR values from different studies, one needs to pay special attention to the CAR’s exact definition. For example, in some studies, the CAR is defined as CAR =. Rcc (0) − Rcc (∞) , Rcc (∞). (3.17). which makes it artificially high when compared with Eq. 3.16, especially if time-resolved detection is involved. Fig. 3.12 shows the CAR as a function of the pump power. The double-pair contributions reduce the CAR values at high pump power. Due to the different power scalings, linear versus quadratic, when the power is stepped down, the photonic noise replaces the double-pair contributions as the CAR’s limiting factor. At even lower pump powers, the detectors’ dark counts become the limiting factor. To confirm the above description, the measured CAR can be compared against estimation as CAR ≈. pηh2 ηd2 , (( p + pn )ηh ηd + pd )(( p + pn )ηh ηd + pd ). (3.18). where p and pn are the probabilities to generate a photon-pair and a noise photon, respectively, and pd is the probability to have a dark count event. The probabilities, as 28.

(39) 3.4. Photon-pair source the CAR, are defined within the photons’ coherence time. ηh and ηd are the heralding (see Sec. 3.4.5) and the detectors’ efficiencies, respectively. The probabilities in Eq. 3.18 as a function of the pump power can be obtained from the detectors’ parameters (dark count rates and detection efficiency ηd ) along with the parameters of a fully characterized photon-pair source; namely, pair generation rate, photonic noise rate, total losses, and photons’ coherence times. Note that here we have assumed equal heralding efficiencies and detector parameters for both the signal and idler modes. The predicted CARs in Fig. 3.12 are in good agreement with the measured values, thus confirming the limiting factors in each power regime. Finally, note that there is a trade-off between the CAR and the coincidence rates. For example, looking at the devices in Fig. 3.10 and Fig. 3.12, the highest CAR value of 1545 corresponds to a coincidence rateh of 46 cps, while the highest coincidence rate of 127 kcps corresponds to a CAR of 31. The choice of the CAR/coincidence rate trade-off depends on the specific application at hand.. 3.4.5. Heralding efficiency. The heralding efficiency is another crucial parameter for photon-pair sources. It is defined as the probability of detecting the heralded photon once the heralding photon has been detected. The heralding efficiency is directly related to the losses in the system. In the case of resonant photon-pair sources, the finite extraction efficiency, ηex , gives a significant contribution to the losses; the generated photon-pairs must be coupled out of the cavity into the bus waveguide. The extraction efficiency ηex is governed by the ratio Qext /Qint ; it is the penalty to pay for using resonantly enhanced photon-pair sources. The heralding efficiency can be easily estimated from the measured singles (Rs ) and coincidence (Rcc ) rates by considering the following relations: Rs,i = ηh,i ηd PGR ,. (3.19a). Rs,s = ηh,s ηd PGR ,. (3.19b). Rcc = ηh,s ηh,i ηd2 PGR ,. (3.19c). where PGR is the intracavity pair generation rate (see Sec. 3.4.6), ηd is the detection efficiencyi , and ηh,s (ηh,i ) and Rs,s (Rs,i ) are the heralding efficiency and the singles rate for the signal (idler), respectively. By extracting the coincidence and single rates as a function of the pump power from the fit performed in Fig. 3.11 and Fig. 3.10 (the. h Here. we give the coincidence rate in the same histogram window as the CAR, i.e. Tw = τc . The data in Fig. 3.10 is given for Tw = 6× FWHM. i Assumed here equal for the signal and idler detectors.. 29.

(40) Chapter 3. Microring resonator-based photon-pair sources quadratic terms only), the heralding efficiencies are estimated as ηh,i =. Rcc , Rs,s ηd. (3.20a). ηh,s =. Rcc . Rs,i ηd. (3.20b). The highest heralding efficiency was obtained for MRR03, with ηh,i = 14% (ηh,s = 11%). This value can be broken down as follows: 31% extraction efficiency (ηex )j , 68% waveguide to fiber coupling, 66% fiber transmission after the chip, including the filtering stage for pump rejection and signal-idler de-multiplexing. Special attention was made to obtain high heralding efficiencies, yet further improvement is still possible. For example, our filters are based on low loss DWDMs, intraconnected via fiber-to-fiber connectors; a higher transmission is expected by splicing all the DWDMs together. Most importantly, one can further increase the relatively low extraction efficiency value by working in the over-coupled regime. The heralding efficiency improvement due to over-coupling can be better appreciated by recalling that the rate of coupling from the ring into the bus waveguide or to the scattering modes is nothing more than the external (∆vext ) and intrinsic (∆vint ) linewidths, respectively. It follows that the heralding efficiency is proportional to the parameters above as ηh ∝ ηex =. ∆vext 1 = . ∆vext + ∆vint 1 + Qext /Qint. (3.21). Eq. 3.21 shows that ηex → 1 for Qext /Qint → 0. MRR03 is under-coupled, with Qext /Qint = 1.28 × 106 /0.58 × 106 = 2.21. However, we have other devices with strongly over-coupled resonances, e.g. for a particular resonance in MRR06 Qext /Qint = 2.6 × 105 /5.8 × 106 = 0.044, resulting in an extraction efficiency ηex = 95.8%. To show what could be expected from our MRR-based photon-pair sources, we assume, hypothetically, that MRR03 has a similar ηex ; we would then get a heralding efficiency of ηh = 43%.. 3.4.6. Pair generation rate. The pair generation rate, brightness, and pair generation probability are all important photon-pair source metrics. These quantities measure the amount of photon-pair generation, each emphasizing a different aspect. j Other. 30. devices’ ηex values are provided in Table 3.3..