Semiconductor quantum optics is on the verge of moving from the lab to real world applications. When stepping from basic research to new technologies, device engineers will need new simulation tools for the design and optimization of quantum light sources, which combine classical device physics with cavity quantum electrodynamics. This thesis aims to provide a holistic description of single-photon emitting diodes by bridging the gap between microscopic and macroscopic modeling approaches. The central result is a novel hybrid quantum-classical model system that self-consistently couples semi-classical carrier transport theory with open quantum many-body systems. This allows for a comprehensive description of quantum light emitting diodes on multiple scales: It enables the calculation of the quantum optical figures of merit together with the simulation of the spatially resolved current flow in complex, multi-dimensional semiconductor device geometries out of one box. The hybrid system is shown to be consistent with fundamental laws of (non-)equilibrium thermodynamics and is demonstrated by numerical simulations of realistic devices.

Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.

The outstanding research efforts in quantum information processing over the past two decades reflect the promise this field of physics provides for practical applications in information science as well as for new approaches towards a better understanding of fundamental questions in quantum mechanics. This thesis focuses on the photon as a principal resource to perform quantum information tasks and on schemes to imprint quantum bits onto its various degrees of freedom. Its weak coupling to the environment makes the photon an ideal carrier to securely transmit information by quantum cryptographic protocols. Moreover, efficient implementations of quantum computing using solely linear optics have been proven. Unfortunately, scalability is not easily achieved by a purely photonic approach since the generation of indistinguishable single photons from multiple emitters remains a difficult task. Thus, proposals for more complex quantum networks suggest an architecture with single photons as information carriers between atomic ensembles that act as storage and processing nodes. Computations including a limited number of qubits, however, may be performed by the linear optics scheme. The thesis starts with the generation and characterization of single-photon states, using a source based on a single optically pumped quantum dot. The capability of these states to implement a quantum algorithm using linear optics and single-photon interference is experimentally demonstrated for the first time. Error correction makes the interferometric setup robust against phase-noise. After successful realization of this proof-of-principle experiment, attention is drawn to the need of plug-and-play single-photon sources. Especially quantum key distribution, the most advanced quantum information technology to date which has even found its way into commercial devices, requires compact and low-cost non-classical light sources.Therefore, a single-photon source based on electrically pumped quantum dots is presented that exhibits unmatched spectral purity and single-photon statistics. Results towards the realization of quantum networks are presented in the following chapters, covering the generation of narrow-band single photons which can efficiently couple to atomic resonances. Photons with a spectral width of less than 3 MHz are created by ultra-bright cavity-enhanced spontaneous parametric down-conversion, and their quantum statistics is studied in detail. A setup for time-bin encoding is demonstrated, capable of imprinting quantum information onto these narrow-band single photons. This thesis concludes with slow-light experiments in atomic ensembles as a model system for atom-photon interaction on the single-photon level. The described experiments demonstrate striking features that make the single photon one of the most remarkable physical systems for the field of quantum information.

The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semi-classical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we obtain a new hybrid quantum-classical modeling approach, which enables a comprehensive description of quantum dot devices on multiple scales: It allows the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

This book provides a comprehensive overview of the state-of-the-art in the development of semiconductor nanostructures and nanophotonic devices. It covers epitaxial growth processes for GaAs- and GaN-based quantum dots and quantum wells, describes the fundamental optical, electronic, and vibronic properties of nanomaterials, and addresses the design and realization of various nanophotonic devices. These include energy-efficient and high-speed vertical cavity surface emitting lasers (VCSELs) and ultra-small metal-cavity nano-lasers for applications in multi-terabus systems; silicon photonic I/O engines based on the hybrid integration of VCSELs for highly efficient chip-to-chip communication; electrically driven quantum key systems based on q-bit and entangled photon emitters and their implementation in real information networks; and AlGaN-based deep UV laser diodes for applications in medical diagnostics, gas sensing, spectroscopy, and 3D printing. The experimental results are accompanied by reviews of theoretical models that describe nanophotonic devices and their base materials. The book details how optical transitions in the active materials, such as semiconductor quantum dots and quantum wells, can be described using a quantum approach to the dynamics of solid-state electrons under quantum confinement and their interaction with phonons, as well as their external pumping by electrical currents. With its broad and detailed scope, this book is indeed a cutting-edge resource for researchers, engineers and graduate-level students in the area of semiconductor materials, optoelectronic devices and photonic systems.

This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.