Finite structure splitting (FSS) is a bottleneck for quantum dot (QD) based solid state entangled photon pair generator (EPPG) for Quantum Key Distribution (QKD) application. In QD, entangle photon pairs are generated through a cascaded emission process—biexciton to exciton to ground state. The FSS of the excitonic state destroys the entanglement of the photon pairs, hence needs to be eliminated. FSS can be tuned by engineering the crystal growth direction, varying dot shape or size, changing the material composition and/or applying external strain. Numerical investigation of FSS and designing of realistically-sized QD based EPPG demands multiscale-multiphysics many-body simulation efforts. To this end, in this work, we report the coupling of full configuration integration (FCI) method with the atomistic empirical tight-binding (TB) models (10-band sp3s* and 20-band sp3d5s*) to calculate the excitonic energetics and FSS in recently reported multimillion-atom III-V dot-in-nanowire structures. The core of the computational framework comprises two parts: i) NEMO3D, which, using the TB models, can compute single-electron energetics of multimillion-atom structures, and ii) An FCI kernel, which computes the many-particle energetics and wavefunctions using the single-electron outputs as derived from NEMO3D. NEMO3D is a broad platform that handles geometry construction, calculation of strain distributions and built-in potential fields, solving the Schrodinger’s equation and computing optical matrix elements. Three output files from NEMO3D are of particular importance for the FCI toolkit: i) Single-electron energy values, ii) Eigen functions, and iii) Relaxed atom positions of the device. FCI calculates the Coulomb and Exchange matrix elements associated with multi-particles and forms the many-body Hamiltonian. The excitonic states (electron-hole pair) are calculated by solving the many-body Hamiltonian and the value of FSS, if exists, is determined. Recently, nitride-based nanostructured devices have been found to be a promising candidate for single and entangled multi-photon emitter applications. The principal goal of this dissertation is to facilitate the numerical design of InGaN/GaN based dot-in-nanowire EPPG units. To this end, a number of kernels in NEMO3D and FCI packages were augmented. The geometry constructor in NEMO3D was extended for two non-polar planes of wurtzite crystal: m-plane and a-plane. It is found that these two non-polar planes, with much smaller built-in piezoelectric fields, exhibit improved optical transition probabilities than the polar c-plane counterpart. As test cases, light-emitters in dot-in-wire and multiple quantum well (MQW) configurations were simulated and compared in all three (c-plane, m-plane, and a-plane) growth directions. TCAD toolkits are used to simulate the terminal optical characteristics such as internal quantum efficiency (IQE) and spontaneous emission rate. Hexagonal-base truncated-pyramid shaped QD was also added to the NEMO3D geometry constructor as pyramid shaped dots offer directionality and better extraction efficiency of emitted photons, which is important for single or entangled photon generators. The FCI simulator was modified for calculating the excitonic states that involve an electron-hole pair. As for EPPG design, four device structures are considered: i) Disk-in-nanowire on the polar c-plane, ii) pyramid shaped dot-in-nanowire on polar c-plane, iii) Disk-in-nanowire on non-polar m-plane, and iv) Disk-in-nanowire on non-polar a-plane. Simulations are done for different disk thicknesses, material compositions, quantum dot shapes and crystal directions. Results and in-depth analysis are presented on the effects of these design parameters on many-body energetics e.g. binding energy, excitonic bandgaps and FSS. The derivation of excitonic transition probability from single-electron momentum matrix is discussed in detail. Finally, an EPPG design is proposed employing the entangled polarization profiles from two excitonic emissions.

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(工学) / 甲第24621号 / 工博第5127号 / 新制||工||1980(附属図書館) / 京都大学大学院工学研究科電子工学専攻 / (主査)教授 竹内 繁樹, 教授 川上 養一, 教授 木本 恒暢 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

In this thesis, we focus on the generation of entangled photon pair from III-V quantum dots. The achievements mainly consists of two aspects: one is the wavelength tunability of these entangled photon pairs, which is enabled by on-chip strain engineering; the other is the brightness enhancement with an optical-broadband antenna to boost the extraction of entangled photons from the material matrix where quantum dots are embedded in.

[pt] A internet quântica atrai a atenção de muitos pesquisadores e empresas. O elemento essencial para realizá-la é o emaranhamento. A distribuição do emaranhamento permite a transmissão de qubits sem realmente enviá-los pelo canal quântico. Portanto, a fonte que produz esses estados emaranhados deve fazê-lo de forma confiável e com taxa competitiva à de comunicação clássica. Este trabalho apresenta uma ferramenta de simulação para a fonte de pares de fótons emaranhados mais comum, o EPPS baseado em SPDC. Além disso, usando filtros, emulamos o efeito do SPDC dentro de uma cavidade. Otimizando os parâmetros da fonte, obtivemos um ganho de 6dB na taxa de chaves secretas em comparação com um processo SPDC simples. / [en] The quantum internet has dragged the attention of many researchers and companies. The essential element to accomplish it is entanglement. Distributing entanglement allows the transmission of qubits without really sending them through the quantum channel. Therefore, the source that produces these entangled states shall do it reliably and with a competitive rate to classical communication. This work presents a simulation tool for the most common entangled photon pair source, the SPDC-based EPPS. Furthermore, using filters, we can emulate the effect of cavity-enhanced SPDC. Optimizing the parameters of the source, we achieved a 6dB gain on the Secret Key Rate compared to a simple SPDC process.

Polarization entangled photon pairs on demand are considered to be an important building block of quantum communication technology. It has been demonstrated that semiconductor quantum dots (QDs), which exhibit a certain spatial symmetry, can be used as a triggered, on-chip source of polarization entangled photon pairs. Due to limitations of the growth, the as-grown QDs usually do not exhibit the required symmetry, making the availability of post-growth tuning techniques essential. In this work first the QD-morphology of hundreds of QDs is correlated with the optical emission of neutral excitons confined in GaAs/AlGaAs QDs. It is presented how elastic anisotropic stress can be used to partially restore the symmetry of self-assembled GaAs/AlGaAs and InGaAs/GaAs QDs, making them as candidate sources of entangled photon pairs. As a consequence of the tuning of the QD-anisotropy we observe a rotation of the polarization of the emitted light. The joint modification of polarization orientation and QD anisotropy can be described by an anticrossing of the so-called bright excitonic states. Furthermore, it is demonstrated that anisotropic stress can be used to tune the purity of the hole states of the QDs by modifying the degree of heavy and light hole mixing. This ability might be interesting for applications using the hole spin as a so-called quantum bit.

Polarization entangled photon pairs on demand are considered to be an important building block of quantum communication technology. It has been demonstrated that semiconductor quantum dots (QDs), which exhibit a certain spatial symmetry, can be used as a triggered, on-chip source of polarization entangled photon pairs. Due to limitations of the growth, the as-grown QDs usually do not exhibit the required symmetry, making the availability of post-growth tuning techniques essential. In this work first the QD-morphology of hundreds of QDs is correlated with the optical emission of neutral excitons confined in GaAs/AlGaAs QDs. It is presented how elastic anisotropic stress can be used to partially restore the symmetry of self-assembled GaAs/AlGaAs and InGaAs/GaAs QDs, making them as candidate sources of entangled photon pairs. As a consequence of the tuning of the QD-anisotropy we observe a rotation of the polarization of the emitted light. The joint modification of polarization orientation and QD anisotropy can be described by an anticrossing of the so-called bright excitonic states. Furthermore, it is demonstrated that anisotropic stress can be used to tune the purity of the hole states of the QDs by modifying the degree of heavy and light hole mixing. This ability might be interesting for applications using the hole spin as a so-called quantum bit.

Sources of single and polarization-entangled photons are an essential component in a variety of potential quantum information applications. Suitable emitters need to generate photons deterministically and at fast repetition rates, with highest degrees of single-photon purity, entanglement and indistinguishability. Semiconductor quantum dots are among the leading candidates for this task, offering entangled-photon pair emission on-demand, challenging current state-of-the-art sources based on the probabilistic spontaneous parametric down-conversion (SPDC). Unfortunately, their susceptibility to perturbations from the solid-state environment significantly affects the photon coherence and entanglement degree. Furthermore, most quantum dot types suffer from poor wavelength control and emitter yield, due to a random growth process. This thesis investigates the emerging family of GaAs/AlGaAs quantum dots obtained by in-situ Al droplet etching and nanohole infilling. Particular focus is laid on the interplay of growth parameters, quantum dot morphology and optical properties. An unprecedented emission wavelength control with distributions as narrow as ± 1 nm is achieved, using four independent growth parameters: The GaAs infilling amount, the deposition sequence, the migration time and the Al concentration in the barrier material. This enables the generation of large emitter ensembles tailored to match the optical transitions of rubidium, a leading quantum memory candidate. The photon coherence is enhanced by an optimized As flux during the growth process using the GaAs surface reconstruction. With these improvements, we demonstrate for the first time two-photon interference from separate, frequency-stabilized quantum dots using a rubidium-based Faraday filter as frequency reference. Two-photon resonant excitation of the biexciton state is employed for the coherent and deterministic generation of photon pairs with negligible multi-photon emission probability. The GaAs/AlGaAs quantum dots exhibit a very small average fine structure of (4.8 ±2.4) µeV and short average radiative lifetimes of 200 ps, enabling entanglement fidelities up to F = 0.94, which are among the highest reported for any entangled-photon source to date. Furthermore, almost all fabricated emitters on a single wafer exhibit fidelities beyond the classical limit - without any post-growth tuning. By embedding the quantum dots into a broadband-optical antenna we enhance the photon collection efficiency significantly without impairing the high degrees of entanglement. Thus, for the first time, quantum dots are able to compete with SPDC sources, paving the way towards the realization of a semiconductor-based quantum repeater - among many other key enabling quantum photonic elements.:Contents List of Figures ix List of Tables xiii 1 Introduction 1 1.1 Researchmotivation ...................1 1.1.1 Structure of this thesis ................. 3 1.2 Applications based on entangled photons ............. 4 1.2.1 Quantum bits ...................4 1.2.2 Quantum key distribution ................ 5 1.2.3 Qubit teleportation .................. 7 1.2.4 Teleportation of entanglement ..............9 1.2.5 The photonic quantumrepeater .............. 10 1.3 Generation of entangled photons ...............12 1.3.1 The ideal entangled-photon source ............. 12 1.3.2 Non-deterministic photon sources ............. 13 1.3.3 Deterministic photon sources ..............14 2 Fundamentals 17 2.1 Semiconductor quantumdots ................17 2.1.1 Introduction to semiconductor quantum dots .......... 17 2.1.2 Formation of confined excitonic states ............ 19 2.1.3 Energy hierarchy of excitonic states ............. 21 2.2 Entangled photons from semiconductor quantumdots ......... 22 2.2.1 The concept of entanglement ............... 22 2.2.2 Polarization-entangled photon pairs fromthe biexciton radiative decay .. 23 2.2.3 Origin and impact of the exciton fine structure splitting ....... 25 2.2.4 Impact of spin-scattering, dephasing and background photons on the degree of entanglement ..................29 2.3 Quantum dot entangled-photon sources - State of the art ........32 2.4 Exciton radiative lifetime .................. 34 2.4.1 The concept of radiative lifetime .............. 34 2.4.2 Measurement of the radiative lifetime ............35 2.5 Single-photon purity ...................37 2.5.1 Photon number distributions ............... 37 2.5.2 Second-order correlation function .............38 2.5.3 Measurement of the second-order correlation function ....... 40 2.6 Measurement of entanglement ................42 2.6.1 Quantum state tomography ...............43 2.7 Photon coherence and spectral linewidth .............46 2.7.1 The concept of coherence ................ 46 2.7.2 First-order coherence ................. 46 2.7.3 Relation between coherence and spectral linewidth ........ 49 2.7.4 homogeneous vs. inhomogeneous broadening in single quantumdots ..50 2.8 Photon indistinguishability .................51 2.8.1 Hong-Ou-Mandel interference ..............51 2.8.2 Hong-Ou-Mandel interference between photons fromseparate sources .. 52 2.8.3 The Bell state measurement with linear optics .......... 53 3 Experimentalmethods 55 3.1 The GaAs and AlAs material system ............... 55 3.2 Molecular beam epitaxy ..................56 3.2.1 The Concept of molecular beam epitaxy ...........56 3.2.2 Layout and components of the III-V Omicron MBE ........58 3.2.3 Growth parameters .................. 59 3.2.4 Reflection high-energy electron diffraction (RHEED) ........ 60 3.2.5 Growth rate determination using RHEED oscillations .......61 3.3 Optical setups .....................63 4 Results 67 4.1 Growth of GaAs/AlGaAs quantum dots by in-situ Al droplet etching .....68 4.1.1 Motivation for the study of GaAs / AlGaAs quantum dots ......68 4.1.2 GaAs / AlGaAs quantum dot growth process ..........69 4.1.3 Interplay between growth parameters, quantumdot morphology and optical properties ................. 71 4.1.4 Nanohole morphology and quantumdot formation ........ 73 4.1.5 Optical characterization ................75 4.1.6 Deterministic wavelength control .............77 4.1.7 Photon coherence and radiative lifetime ...........84 4.1.8 Decoherence processes in semiconductor quantum dots ......86 4.1.9 Chamber conditioning and growth process optimization ......87 4.1.10 Arsenic flux calibration using the GaAs surface reconstruction ..... 88 4.1.11 Enhanced photon coherence after growth process adjustments ....92 4.2 Two-photon interference from frequency-stabilized GaAs/AlGaAs quantum dots .................94 4.2.1 Frequency tuning of semiconductor quantumdots ........95 4.2.2 Experimental setup .................. 95 4.2.3 Optical characterization of the separate GaAs/AlGaAs quantum dots ... 98 4.2.4 Faraday anomalous dispersion optical filter and frequency feedback ... 99 4.2.5 Two-photon interference between remote, frequency-stabilized quantum dots 100 4.3 Solid-state ensemble of highly entangled photon sources at rubidiumatomic transitions ........................102 4.3.1 Fine-structure splitting ................103 4.3.2 Resonant excitation of the biexciton state ...........105 4.3.3 Single photon purity and radiative lifetime ........... 107 4.3.4 Radiative lifetime of GaAs/AlGaAs quantumdots - comparison to other quantumdot types ...................108 4.3.5 Degree of entanglement ................109 4.3.6 Highly-efficient extraction of the obtained entangled photons ..... 116 5 Conclusions 119 5.1 Summary ....................... 119 5.2 Discussion and outlook ..................122 Bibliography 127 Publications and scientific presentations 150 Acknowledgments 154 Selbstständigkeitserklärung 157 Curriculum vitae 157

Semiconductor quantum dots (QDs) are fascinating systems for potential applications in quantum information processing and communication, since they can emit single photons and polarisation entangled photons pairs on demand. The asymmetry and inhomogeneity of real QDs has driven the development of a universal and fine post-growth tuning technique. In parallel, new growth methods are desired to create QDs with high emission efficiency and to control combinations of closely-spaced QDs, so-called "QD molecules" (QDMs). These systems are crucial for the realisation of a scalable information processing device after a tuning of their interaction energies. In this work, GaAs/AlGaAs QDs with low surface densities, high optical quality and widely tuneable emission wavelength are demonstrated, by infilling nanoholes fabricated by droplet etching epitaxy with different GaAs amounts. A tuning over a spectral range exceeding 10 meV is obtained by inducing strain in the dot layer. These results allow a fine tuning of the QD emission to the rubidium absorption lines, increasing the yield of single photons that can be used as hybrid semiconductor-atomic-interface. By embedding InGaAs/GaAs QDs into diode-like nanomembranes integrated onto piezoelectric actuators, the first device allowing the QD emission properties to be engineered by large electroelastic fields is presented. The two external fields reshape the QD electronic properties and allow the universal recovery of the QD symmetry and the generation of entangled photons, featuring the highest degree of entanglement reported to date for QD-based photon sources. A method for controlling the lateral QDM formation over randomly distributed nanoholes, created by droplet etching epitaxy, is demonstrated by depositing a thin GaAs buffer over the nanoholes. The effect on the nanohole occupancy of the growth parameters, such as InAs amount, substrate temperature and arsenic overpressure, is investigated as well. The QD pairs show good optical quality and selective etching post-growth is used for a better characterisation of the system. For the first time, the active tuning of the hole tunnelling rates in vertically aligned InGaAs/GaAs QDM is demonstrated, by the simultaneous application of electric and strain fields, optimising the device concept developed for the single QDs. This result is relevant for the creation and control of entangled states in optically active QDs. The modification of the electronic properties of QDMs, obtained by the combination of the two external fields, may enable controlled quantum operations.

Semiconductor quantum dots (QDs) are fascinating systems for potential applications in quantum information processing and communication, since they can emit single photons and polarisation entangled photons pairs on demand. The asymmetry and inhomogeneity of real QDs has driven the development of a universal and fine post-growth tuning technique. In parallel, new growth methods are desired to create QDs with high emission efficiency and to control combinations of closely-spaced QDs, so-called "QD molecules" (QDMs). These systems are crucial for the realisation of a scalable information processing device after a tuning of their interaction energies. In this work, GaAs/AlGaAs QDs with low surface densities, high optical quality and widely tuneable emission wavelength are demonstrated, by infilling nanoholes fabricated by droplet etching epitaxy with different GaAs amounts. A tuning over a spectral range exceeding 10 meV is obtained by inducing strain in the dot layer. These results allow a fine tuning of the QD emission to the rubidium absorption lines, increasing the yield of single photons that can be used as hybrid semiconductor-atomic-interface. By embedding InGaAs/GaAs QDs into diode-like nanomembranes integrated onto piezoelectric actuators, the first device allowing the QD emission properties to be engineered by large electroelastic fields is presented. The two external fields reshape the QD electronic properties and allow the universal recovery of the QD symmetry and the generation of entangled photons, featuring the highest degree of entanglement reported to date for QD-based photon sources. A method for controlling the lateral QDM formation over randomly distributed nanoholes, created by droplet etching epitaxy, is demonstrated by depositing a thin GaAs buffer over the nanoholes. The effect on the nanohole occupancy of the growth parameters, such as InAs amount, substrate temperature and arsenic overpressure, is investigated as well. The QD pairs show good optical quality and selective etching post-growth is used for a better characterisation of the system. For the first time, the active tuning of the hole tunnelling rates in vertically aligned InGaAs/GaAs QDM is demonstrated, by the simultaneous application of electric and strain fields, optimising the device concept developed for the single QDs. This result is relevant for the creation and control of entangled states in optically active QDs. The modification of the electronic properties of QDMs, obtained by the combination of the two external fields, may enable controlled quantum operations.