Strong effective photon-photon interactions mediated by atom-photon couplings have been routinely achievable in QED setups for some time now. Recently, there have been several proposals to push the physics of interacting photons into many- body distributed architectures. The essential idea is to coherently couple together arrays of QED resonators, such that photons can hop between resonators while interacting with each other inside each resonator. These proposed structures have attracted intense theoretical attention while simultaneously inspiring experimental efforts to realise this novel regime of strongly-correlated many-body states of light. A central challenge of both theoretical and practical importance is to understand the physics of such coupled resonator arrays (CRAs) beyond equilibrium, when unavoidable (or sometimes even desired) photon loss processes are accounted for. This thesis presents several studies whose purpose can roughly be divided in two aims. The first part studies just what constitutes a valid physical and computational representation of non-equilibrium driven-dissipative CRAs. Addressing these ques- tions constitutes essential groundwork for further investigations of CRA phenomena, as numerical experiments are likely to guide and interpret near-future experimen- tal array observations. The relatively small body of existing work on CRAs out of equilibrium has often truncated their full, rich physics. It is important to establish the effects and validity of these approximations. To this end we introduce powerful numerical algorithms capable of efficiently simulating the full dynamics of CRAs, and use them to characterise the non-equilibrium steady states of arrays reached under the combined influence of dissipation and pumping. Having established the rigour necessary to realistically describe CRAs, we exam- ine two novel phenomena observable in near-future small arrays. Firstly we relate a counter-intuitive ‘super bunching’ in the statistics of photons emitted from arrays engineered to demonstrate strong effective photon-photon repulsion at the single and two-photon level, to an interplay between the underlying eigen-structure and details of the non-equilibrium operation. Secondly we characterise a dynamical phenomenon in which domains of ‘frozen’ photons remain trapped in sufficiently nonlinear arrays. Finally we present a preliminary characterisation of a previously unexplored phase diagram of arrays under coherent two-photon pumping. Com- petition between the coherence injected by the pumping, photon interactions and delocalisation processes lead to interesting new physical signatures.

Light, when reduced to the level of individual quanta, can possess, besides its familiar properties of wavelength, direction, and polarization, a set of correlations irreducible to classical correlations, among other peculiar behaviour. These correlated states are intrinsically interesting, and are also useful for quantum-enhanced information processing. In this thesis, I use a high-bandwidth, far-off-resonant Raman memory to implement two quantum information primitives -- entanglement generation and light storage -- at room temperature and ambient conditions. Specifically, I show, for the first time, the entanglement of two solid-state objects at room temperature and, also, the storage of light in a hollow-core optical fibre. In the first part, I show that the optical phonon modes of two diamonds can be entangled -- the prototypical non-classical correlation -- at room temperature. The entanglement was generated by spontaneous Raman scattering with projective measurements using single-photon detectors. The degree of entanglement was rigorously quantified by measuring the concurrence -- an entanglement monotone -- of the joint state of the scattered optical fields. In the second part, I store light in the coherent superposition of cesium atoms confined within a kagome-structured hollow-core photonic crystal fibre at room temperature using a far-off-resonant stimulated Raman interaction. The storage efficiency of the memory was 27$pm$1% and the noise level was sufficiently low such that single-photon-level pulses could be stored. Taken together, these results highlight the potential of Raman memories for quantum information tasks in noisy systems with short coherence times.

In the ultracold regime, where the interactions between atoms become quantum mechanical in nature, we can investigate the fundamental properties of matter. A natural progression from the catalogue of pioneering experiments using ultracold atoms is to extend the size of our quantum system by producing ultracold molecules in prescribed low-energy internal states. Techniques for cold molecule production are split into two methods: direct and indirect cooling. While direct cooling methods have yet to realize ultracold temperatures, collisional relaxation in the molecules leads to low internal energy states. By contrast, indirect cooling — the association of molecules from pre-cooled atoms—has produced a range of molecules at ultracold temperatures; the challenge with this technique is to control the internal state. This thesis concentrates on a technique that is complementary to those already in existence: ultrafast photoassociation. Key to this technique is the formation of time non-stationary wavepackets in the excited-state in order to improve FranckCondon overlap of the excited state with deeply bound ground-state vibrational levels. A pump-probe experiment was designed and built to demonstrate the formation of bound excited-state dimers. In this work we show that the initial state from which the wavepacket originates is of critical importance to the evolution of excited-state population. We find that the internuclear separation of the wavepacket produced in a rubidium magneto-optical trap is too large to observe coherent oscillations in the excited state. The implications of this are discussed along with recommendations for future ultrafast photoassociation experiments. Consequently, a new ultracold atom apparatus was built utilizing magnetic and dipole-force trapping to increase the density of the atomic sample; this apparatus will enable future experiments combining the exciting fields of ultracold matter and ultrafast light.

This thesis is concerned with describing a novel technique for characterizing the (spectrally resolved) spatial properties of light. The new approach, known as Scanning Interference Method for Integrated Transverse Analysis of Radiation (SCIMITAR), is a specific implementation of a variable-separation two-pinhole interferometer. Evaluation of the series of interference patterns produced by a SCIMITAR measurement allows the transverse profiles of intensity and spatial phase to be retrieved, while at the same time characterizing the spatial coherence of light. Including a diffraction grating in the simple experimental arrangement permits the spectral dependence of the aforementioned quantities to be measured. The SCIMITAR technique was demonstrated by characterizing the spatial properties of high harmonic generation (HHG). Excellent agreement with an alternate characterization technique known as SWORD was observed. The spectral dependence of the harmonic spatial properties was also investigated. Evidence suggesting absorption may play a role in shaping the harmonic intensity and spatial coherence was presented. Treating the harmonic radiation as either a fully coherent or partially coherent beam allowed the intensity width, spatial phase curvature and coherence width of the harmonic radiation source to be deduced. Measurement of the fine variation of the harmonic complex coherence factor (CCF) with pinhole separation revealed distinctive modulations. The Van Cittert-Zernike theorem was modified by including a Gerchberg-Saxton inspired improvement, allowing data missing from the SCIMITAR measurement to be inferred. The harmonic equivalent incoherent source intensity profile was found to be asymmetric with low intensity features isolated away from the optical axis. Calculations of the diffraction pattern produced by illumination of a non-redundant array of pinholes showed that the modulated harmonic properties could adversely influence lensless imaging-type experiments.

This thesis describes the experimental realisation and characterisation of three non-trivial trapping geometries for ultracold atoms. The double-well, ring and to some degree shell trap are examples of a highly versatile class of traps called time-averaged adiabatic potentials (TAAPs). In this experiment the TAAPs arise from the combination of three independent magnetic fields; a static quadrupole field dressed by a uniform radio-frequency field is time-averaged by a bias field oscillating at in the kHz regime. The result is a very smooth potential, within which ultracold atoms can be evaporatively cooled to quantum degeneracy, and subsequently manipulated into new geometries without destroying the quantum coherence. The vertically offset double-well potential provided the first example of ultracold atoms confined in a TAAP. The same potential is used to demonstrate efficient evaporative cooling across the Bose-Einstein condensate (BEC) phase transition using only the Landau-Zener loss mechanism. Switching off the time-averaging fields loads atoms from the double-well TAAP into the rf-dressed shell trap. A characterisation of this potential measured low heating rates and lifetimes of up to 58s. With efforts ongoing to increase the trap anisotropy, this potential shows promise for research into the static and rapidly rotating 2D systems. In the presence of a single time-averaging field, the shell geometry is transformed into a ring-shaped trap with an adjustable radius. The ring trap can be controllably tilted and progress towards multiply connected condensates is being made. A rotation scheme to spin up atoms in the ring trap has been demonstrated, presenting the opportunity to investigate the dynamics of superflow in degenerate quantum gases.

The possibility of creating a scaleable quantum network by interconverting photonic and atomic qubits shows great promise. The fundamental requirement for such a network is deterministic control over the emission and absorption of photons from single atoms. This thesis reports on the experi-mental construction of a photon source that can emit single-photons with arbitrary spatio-temporal shape, phase, and frequency. The photon source itself is a strongly-coupled atom cavity system based on a single ⁸⁷ Rb atom within a macroscopic high-finesse Fabry-Perot cavity. It operates intermittently for periods of up to 100µs, with single-photon repetition rates of 1.0 MHz and an efficiency of almost 80%. Atoms are loaded into the cavity using an atomic fountain, with the upper turning point near the centre of the cavity mode. This ensures long interaction times without any disturbances introduced by trapping potentials. The photons’ indistinguishability was tested, with a two-photon Hong-Ou-Mandel visibility of 87%. This ability to both generate, and control, the photons’ properties, for example producing photons with symmetric or multi-peaked spatio-temporal shapes, allows for the production of photons in an n-time-bin superposition state where each time-bin has an arbitrarily defined amplitude and phase. These photons can be used as photonic qubits, qutrits and qquads, and their properties have been tested using a small linear-optics network.

Over the last few years, the GRAPE algorithm has become of central importance in the development of general purpose control sequences for several branches of Nuclear Magnetic Resonance. In this thesis, the application of the GRAPE algorithm to quantum information processing tasks is considered. First the theory underlying the algorithm is reviewed in detail, then a number of extensions and improvements to the core technique are developed. An implementation of the GRAPE algorithm using GPUs is presented and compared with a standard CPU based implementation. A variety of experimental results are presented covering many different aspects of the practical use of GRAPE. This includes an evaluation of some of the errors that can affect the performance of GRAPE sequences in real experiments, and their relative importance. The strengths and weaknesses of GRAPE compared to the other possible techniques are assessed, and some suggestions made regarding potential developments in this direction. Pseudo-pure states are a crucial component of any NMR based quantum computer, but many current methods for preparing them sacrifice purity in exchange for simplicity in the preparation sequence. This thesis also presents a new method for robustly generating pseudo-pure states with the maximum possible purity.

The major challenges in trapped-ion quantum computation are to scale up few-ion experiments to many qubits and to improve control techniques so that quantum logic gates can be carried out with higher fidelities. This thesis re- ports experimental progress in both of these areas. In the early part of the the- sis we describe the fabrication of a surface-electrode ion trap, the development of the apparatus and techniques required to operate it and the successful trap- ping of ⁴⁰Ca⁺ ions. Notably we developed methods to control the orientation of the principal axes and to minimise ion micromotion. We propose a repumping scheme that simplifies heating rate measurements for ions with low-lying D levels, and use it to characterise the electric field noise in the trap. Surface-electrode traps are important because they offer a route to dense integration of electronic and optical control elements using existing microfabrication technology. We explore this scaling route by testing a series of three traps that were microfabricated at Sandia National Laboratories. Investigations of micromotion and charging of the surface by laser beams were carried out and improvements to future traps are suggested. Using one of these traps we also investigated anomalous electrical noise from the electrode surfaces and discovered that it can be reduced by cleaning with a pulsed laser. A factor of two de- crease was observed; this represents the first in situ removal of this noise source, an important step towards higher gate fidelities. In the second half of the thesis we describe the design and construction of an experiment for the purpose of replacing laser-driven multi-qubit quantum logic gates with microwave-driven ones. We investigate magnetic-field-independent hyperfine qubits in ⁴⁰Ca⁺ as suitable qubits for this scheme. We make a design study of how best to integrate an ion trap with the microwave conductors required to implement the gate and propose a novel integrated resonant structure. The trap was fabricated and ions were successfully loaded. Single-qubit experiments show that the microwave fields above the trap are in excellent agreement with software simulations. There are good prospects for demonstrating a multi-qubit gate in the near future. We conclude by discussing the possibilities for larger-scale quantum computation by combining microfabricated traps and microwave control.

The ability to address and manipulate individual information carriers in a deterministic, coherent, and scalable manner is a central theme in quantum information processing. Neutral atoms trapped by laser light are amongst the most promising candidates for storing and processing information in a quantum computer or simulator, so a scalable and flexible scheme for their control and manipulation is paramount. This thesis demonstrates a fast and versatile method to address and dynamically control the position (the motional degrees of freedom) of neutral atoms trapped in optical tweezers. The tweezers are generated by using the direct image of a Spatial Light Modulator (SLM) which can control and shape a large number of optical dipole-force traps. Trapped atoms adapt to any change in the potential landscape, such that one can re-arrange and randomly access individual sites within atom-trap arrays. A diffraction limited imaging system is used to map the intensity distribution of the SLM onto a cloud of cold atoms captured and cooled using a Magneto Optical Surface Trap (MOST).

Optical frequency standards offer the possibility of a step improvement of up to two orders of magnitude in the accuracy with which the SI second can be realised. ¹⁷¹Yb⁺ possesses two dipole-forbidden optical transitions that are promising candidates for a redefinition of the second. In this thesis, absolute frequency measurements of these two transitions are presented. A number of experimental upgrades have been implemented, which have resulted in a large reduction in both the statistical and systematic uncertainties associated with the measurements and have improved both the reliability and simplicity of the experimental setup. In particular, the replacement of two frequency-doubled Ar⁺-pumped Ti:sapphire lasers with extended cavity diode lasers has eliminated the downtime associated with their maintenance. Additionally, the introduction of polarisation modulation on the cooling light has allowed the residual bias magnetic field required for laser cooling to be reduced by a factor of thirty. The first measurement at the National Physical Laboratory (NPL) of the frequency of the ²S_1/2 (F = 0) → ²D_3/2 (F′ = 2) electric quadrupole (E2) transition at 436 nm is presented. The transition frequency was measured against a hydrogen maser using a femtosecond optical frequency comb, and was determined with a relative standard uncertainty of 1.3 × 10⁻¹⁴. A commercial diode-based laser system was then implemented in order to drive the ²S_1/2 (F = 0) → ²F_7/2 (F′ = 3) electric octupole (E3) transition at 467 nm. The laser frequency was actively stabilised to the ultra-narrow atomic absorption with a resolved linewidth of 11 Hz, allowing the acquisition of ninety hours of frequency data measured relative to the NPL’s primary frequency standard CsF2. Combined with a thorough evaluation of the systematic perturbations, the total fractional uncertainty in the absolute frequency of the transition has been reduced by a factor of twenty to 1 × 10⁻¹⁵. Recent complementary results from Physikalisch-Technische Bundesanstalt (PTB) show that the E3 transition in ¹⁷¹Yb⁺ has the potential to be a highly accurate and reproducible optical frequency standard, and to date these measurements demonstrate the best international agreement between trapped ion optical frequency standards.