This thesis investigates the world of optics at the sub-wavelength scale, with a focus on understanding the behaviour of singularities that can arise in the electromagnetic field when confined to two dimensions. Predominantly we have investigated random waves, which are the most generic form of wave patterns. By treating these singularities as if they are real particles, we make use of methods from statistical physics to investigate their behaviour, both their spatial correlations, as well as their temporal dynamics through time-resolved measurements. Finally we show that it is possible to measure both infrared and visible light simultaneously, while still retaining sensitivity to amplitude, phase and polarization for both colours.@en

The quest to miniaturize optical and electronic devices has driven significant interest in transition metal dichalcogenides (TMDs) like molybdenum disulfide (MoS₂) due to their remarkable optoelectronic properties. This thesis explores the synthesis, structural control, and advanced characterization of MoS₂, with a focus on vertically-aligned nanosheets for enhanced non-linear optical applications. A novel 4D-STEM framework, StrainMAPPER, is developed to map strain at atomic resolution, revealing critical insights into bandgap modulation. Additionally, convergent beam electron diffraction (CBED) techniques are used to identify crystal domains and grain boundaries. These findings contribute to advancing the fabrication and characterization of TMD nanomaterials, enabling new platforms for tunable nanoelectronics and nanophotonics.@en

Two-dimensional (2D) layered materials are integral to modern condensed matter research due to their remarkable electronic and optical properties. A key feature of these materials is that their properties can be adjusted bymaking small changes to their structure at the nano- and atomic scale. Understanding and linking these electronic and optical properties to structural features at the nanoscale is crucial for unlocking the full potential of 2D layered materials and maximizing their use in advanced devices. This thesis uses electron-based microscopy and spectroscopy to achieve the high spatial and energy resolution required for this goal. These techniques address the limitations of optical and X-ray spectroscopy, which, while offering excellent spectral resolution, lack the spatial precision needed to resolve nanoscale morphologies and atomic structures critical for understanding 2Dmaterials. To achieve this,we employ two advanced electron microscopy methodologies: probe corrected Scanning Transmission Electron Microscopy (STEM) and monochromated Electron Energy-Loss Spectroscopy (EELS). Together, these techniques enable the acquisition of high-quality Spectral Images (SIs) with both exceptional spatial and spectral resolution, providing a powerful platform for the detailed characterization of 2D layered materials. To further enhance the potential of STEM-EELS, we integrate Machine Learning (ML)-based approaches. These approaches introduce innovative solutions such as the removal of the dominant Zero Loss Peak (ZLP) background in the low-loss energy region, peak identification and multivariate techniques to separate overlapping signals and so fully leverage the rich information contained in STEM-EELS SIs Chapter 2 establishes the data processing methodology used in this work. It provides an overview of STEM-EELS SIs, detailing how they are acquired, interpreted, and the challenges involved in processing these high-dimensional datasets. A key focus is on ourML-based approach for image-wide subtraction of the ZLP in SIs. This step is crucial for isolating spatially localized information in the low-loss energy region, which would otherwise be obscured by the ZLP tail. The methodology incorporates ML techniques originally developed in high-energy physics for probing the interior structure of protons, demonstrating the adaptability of these methods to electron microscopy. This analysis framework, named EELSFITTER, serves as the foundation for the remainder of the thesis, where it is applied to the characterization of 2D layered materials. Developed in Python, the framework is open-source and freely available for use by the research community. In Chapter 3, the framework EELSFITTER is applied to investigate Indium Selenide (InSe) nanosheets and Tungsten Disulfide (WS2) flakes with mixed polytipism (2H/3R). The thickness and stacking order of layers are critical structural features that influence the optoelectronic properties of 2D materials, including their band gap. For InSe, the stacking order or crystalline phase determines whether the band gap is direct or indirect and affects its value. In the case of WS2, a member of the Transition Metal Dichalcogenides (TMDs) family, thickness plays a direct role in tuning the band gap, making it an ideal benchmark for validating the ML-based approach. Using robust ZLP subtraction in the SIs of these materials, we achieve nanoscale precision in spatially resolving their band gap and dielectric function. Additionally, we correlate the electronic properties to structural features, with a particular focus on local specimen thickness, demonstrating the effectiveness of this methodology. We extend the data processing techniques and analytical methods to tackle automated feature identification within the energy-loss and energy-gain region of EELS in Chapter 4. The first part of this chapter focuses on one-dimensional (1D) Molybdenum Disulfide (MoS2) nanostructures. As a TMD material similar to WS2, MoS2 in a 1D morphology allows us to study the effects of curvature-induced strain on its optoelectronic properties. We characterise excitonic and plasmonic resonances, revealing how these features are influenced by the 1D geometry. Additionally, we investigate excitonic behaviour and the band gap value in relation to localized curvature-induced strain, comparing the properties at the tips of the 1D structures with those at the body. The second part of the chapter examines the layered topological insulator Bismuth Telluride Bi2Te3. Here, we focus on the energy-gain region, applying ML-based techniques originally developed formodelling the loss region of the ZLP.Using this approach, we extract a well-defined collective excitation at -0.8 eV on the energy-loss axis. By relying on the energy-gain region, we avoid complications from multiple scattering, enabling the characterization of this excitation with enhanced spectral precision. This chapter highlights the versatility of our methods for analyzing diverse materials and morphologies. In Chapter 5, we focus on WS2 nanotriangles, examining localised plasmonic resonances that form along their edges. By employing non-negative matrix factorization (NMF), we identify the spatial distribution of these resonances and successfully separate them from signals originating from overlapping WS2 nanotriangles. The results of the NMF analysis are compared with electrodynamical simulations, which reveal strong agreement with the observed localized plasmonic resonances. Further,we quantify these resonances by analysing their dispersion relation through a 1D Fabry-Perot model. This analysis demonstrates a quadratic dispersion characteristic of surface plasmonic phenomena, offering deeper insights into the optical behaviour of WS2 nanotriangles. This thesis presents the development of novel strategies for processing and interpreting STEM-EELS SIs in both the low energy-loss and energy-gain regions. Through these advancements, we provide valuable insights into the relationship between structural and physical properties across various morphologies and material types of layered materials. Importantly, all computational frameworks developed during this work are open-source and freely available, ensuring that the methodologies and approaches can be easily adopted by other researchers...@en

Superconducting qubits are a leading platform holding potential for realization of fault-tolerant universal quantum computation. However, experimental demonstration of quantum fault tolerance may require scaling up to hundreds of physical qubits (Chapter 1).

The non-linearity of superconducting qubits emerges from current-phase relation in superconducting tunnel junctions, better known as Josephson junctions (Chapter 2). The transmon is a special case of the charge qubit with a large parallel shunt capacitance which results in suppression of charge noise sensitivity at the cost of reduced anharmonicity. The resonance frequency of a transmon depends on the charging energy contributed by the total capacitance of the circuit and the non-linear inductive energy of a Josephson junction. This inductance is in turn directly proportional to the room-temperature conductance of the tunnel junctions, determined by the junction area and thickness of the tunnel barrier. The manipulation of superconducting artificial atoms by strongly coupling to microwave photons is achieved using circuit quantum electrodynamics. In planar superconducting circuits, on­-chip transmission lines based on coplanar waveguide geometry is routinely employed to manipulate and readout the qubit states (Chapter 3).

The QuSurf architecture for a full-stack quantum computer features an extensible surface code comprising flux-tunable qubits with four-port connectivity to nearest neighbours. The first distance-3 logical qubit requires a 2D lattice of 17 qubits to perform quantum error correction. At the hardware level, we concurrently pursue a short-term low-overhead and a long-term high-overhead strategy with lateral and vertical input/output signal routing respectively (Chapter 3). The usefulness of a superconducting quantum processor depends on three main fabrication metrics, the physical yield of individual components, how well it matches the chip design specifications and its susceptibility to environmentally-induced decoherence (Chapter 4). Due to the nanometer-scale of Josephson junctions, it is particularly challenging to reliably target a desired qubit frequency within a margin of 50 MHz.

This thesis outlines the current fabrication bottlenecks which limit scalability with a focus on increasing the precision of qubit frequency targeting. The addition of through-silicon vias for vertical routing of signals and increasing the density of on-chip components add layers of complexity to this problem, which necessitates testing two variants of Josephson junctions with subtle differences in the fabrication process and its geometry. The primary objective is to systematically identify and quantify the sources of deviation affecting fabrication of the two Josephson junctions variants. To determine the causes of spread in Josephson junctions aside from intrinsic variations in the tunnel barrier, room-temperature conductance measurements are compared for thousands of test junction structures fabricated at waferscale. (Chapter 5). We also develop customized fabrication tools and techniques to achieve selective or global tailoring of qubit frequencies (Chapter 6). The thesis concludes with a summary on the factors identified in this work which impacts qubit frequency targeting, a reflection on the limitations of this work and an outlook on specific aspects of scalability of superconducting qubits in the near future (Chapter 7). @en

Recently, quantum networks have emerged as a focal point of research and discussion due to their promise in overcoming the limitations of classical networks, offering unparalleled capabilities in secure communication, quantum computation, and distributed quantum information processing. Simply speaking, a quantum network is a network in which the nodes are capable of storing and processing quantum information and communicate via quantum channels. Unlike classical computers and networks, in which components at nodes and the interconnections between them are mostly made of electronics circuits, there is not a homogeneous system for all the applications in a quantum network. This in particular, increases the need for implementation of heterogeneous quantum systems. An important milestone in the development of hybrid quantum networks are the interconnections between different components at the nodes, which serve as quantum channels. A quantumchannel is an interconnection between two quantum systems that can route carriers of quantum information, while preserving their coherence over the routing process. Finding such a channel, with carriers having the ability to couple to different quantum systems is not trivial. Although quanta of mechanical vibrations - known as "phonons" - have shown great potential for this task, as they can couple to many different types of quantumsystems.
The aim of this thesis is to design an integrated platform using highly confined GHz phonons, with scalability as a primary consideration. This platform serves as an on-chip phononic quantum channel, enabling the ability to perform on-chip operations directly on single phonons on a chip. Moreover, the designed structures in this thesis are advantageous for advanced quantum acoustics experiments and pave the way towards having full coherent control on phonons on a chip.@en

The behavior of light is well understood and well documented in many different scenarios. Nonetheless the situations can get more complicated. We can easily calculate the electromagnetic field confined to a cubic volume by solving the wave equations. However, this is not so easy for arbitrary geometries of the boundary. The wave equation most likely does not have well defined Eigenmodes for arbitrary shape of the boundary and conditions on this boundary. This complex situation can give a chaotic field. In this bachelor thesis we are going to investigate this situation for a 2-dimensional cavity in the shape of a quarter stadium, in which light can move freely and is reflected on the boundaries. The shape of our cavity is expected to result in a really chaotic field, whose properties will be studied in detail below. We will introduce ergodicity and compare the behaviors of a chaotic and non-chaotic cavity using ergodic properties and looking at the divergence of two neighboring trajectories. Furthermore we will look at the onset of chaos in the wave field inside the cavity and suggest a test to determine if a field is completely chaotic.

In cavity optomechanics, optical fields are coupled to the displacement of mechanical resonators. While it is interesting to study fundamental aspects of this interaction, it is the ability to link this mechanical displacement to various other degrees of freedom that inspires many applications in the field. In these applications, the mechanical resonator can be used as a handle to an external influence for the purpose of sensing, but also as a transducer between two otherwise detached degrees of freedom. The latter approach is the focus of this work. A particularly interesting regime for such a transduction process is between a few-gigahertz microwave tone and optical photons at telecom wavelengths around 1550 nm, connecting the operating regimes of long-range telecommunication with that of superconducting quantum nodes. Bridging the gap between these domains is an essential step towards any size of quantum network based on superconducting nodes, as the losses encountered in microwave transmission lines prohibits the connection of such nodes over length scales extending beyond a few meters. As such, a transducer between the few-gigahertz and optical telecom domains would enable the use of low-loss optical channels to connect remote superconducting nodes, given that the quantum information is preserved throughout the conversion process. One approach of realizing such a converter makes use of a gigahertz-frequency mechanical mode as the transducing element, which is coupled to the optical telecom domain using the optomechanical interaction and to the microwave domain using the electromechanical interaction. In this work, we aim to unify both of these interactions in a single device by designing and fabricating optomechanical devices from the III/V semiconductors, which, alongside their good optical properties, are also piezoelectric. In Chapter 2, we motivate our material choice and introduce the relevant properties of the materials, as well as their impact on the fabrication process. Following the material discussion, we then set out in Chapter 3 to realize a microwave-to-optics converter made of an optomechanical crystal in gallium arsenide, which we resonantly couple to a interdigital transducer using surface-acoustic-waves. With this device, we demonstrate the first microwave-to-optics conversion using a mechanical mode with an average number of thermal excitations below one. As well as verifying the coherence of the conversion process, our experiments also highlight the limitations arising from the material choice due to absorption-induced incoherent heating of the mechanical mode. The material choice itself then becomes the central topic of Chapter 4, where we opt for a gallium phosphide, a relative of gallium arsenide, which prominently features a larger bandgap. With this material we show non-classical correlations between photons an phonons. We enter a a regime that was previously inaccessible to devices made from piezoelectric materials, a promising step towards realizing the noise-requirements for microwave-to-optics converters. In Chapter 5, we use the insights from the two previous chapters to design a new type of electro-opto-mechanical resonator, specifically aimed at microwave-to-optics conversion. We miniaturize the electromechanical interface and use strongly coupled mechanical resonators for the transfer of excitations between the microwave and mechanical mode. We fabricate and characterise initial devices as well as demonstrate the validity of the functioning principle. Finally in Chapter 6, we reflect on the results of the previous chapters and highlight some potential advantages of other approaches. @en