An understanding of the fundamental mechanism behind the relief of shear stress in single-crystal silicon subject to loading by shock-waves has to this day remained elusive. What is known is that this material undergoes a first-order pressure-induced polymorphic phase transition from its ambient pressure cubic-diamond (cd) crystal structure to its first stable high-pressure phase, known as β-Sn, at a pressure of about 120 kbar under hydrostatic compression. By investigating the evolution of the transition parameters for this phase transition as a function of increasing uniaxial shear stress representative of the effects of shock-compression via ab-initio Density Functional Theory computational techniques, we predict a significant lowering of the stress at which the phase transition occurs. This raises the question as to whether the onset of plastic response at the material's Hugoniot Elastic Limit (HEL) reported in experiments corresponds in fact to the phase transition itself, a very plausible possibility which has never been considered before. Furthermore, we present molecular dynamics simulations using a Tersoff-like potential of shock-compressed single crystals of silicon. We find an elastic response up to a critical stress, above which the shear stress is relieved by an inelastic response associated with a partial transformation to a new high-pressure phase, where both the new phase (Imma) and the original cubic diamond phase are under close to hydrostatic conditions. We note that these simulations are also consistent with shear stress relief provided directly by the shock-induced phase transition itself, without an intermediate state of plastic deformation of the cubic diamond phase.

Quantitative Planar Laser Induced Fluorescence (QPLIF) is developed as a diagnostic technique and then applied to a prototype Jaguar optical internal combustion engine. QPLIF derives quantitative, two-dimensional, spatially-resolved measurements of fuel concentration. This work reports the first demonstration of a fully-fractionated surrogate fuel which exhibits all the characteristics of a typical gasoline. This 'pseudo' fuel, developed in association with Shell UK, is blended to accept a fluorescent tracer which may track one of the light, middle or heavy fractions of the fuel, each of different volatility. The traditional weaknesses of PLIF for quantitative measurements are addressed by use of a fired in-situ calibration method, which maps the quantum efficiency of the tracer and concurrently corrects for window fouling and exhaust gas residuals (EGR). Fuel distributions are presented with an estimated super-pixel accuracy of 10% at different operating conditions, and then compared to the computational fluid dynamics (CFD) predictions of an in-house Jaguar model. Fuel/Air Ratios by Laser Induced thermal Gratings (FARLIG) is developed theoretically, and results of validation experiments conducted in a laboratory setting are reported. FARLIG conceptually enables the measurement of fuel concentration, oxygen concentration and temperature within a spatially-localised probe volume. Uniquely, the technique exploits the dominant influence of molecular oxygen on non-radiative quenching processes in an aromatic tracer molecule. The changing character of a model quenching mechanism potentially allows the oxygen concentration in the measurement volume to be derived. Absolute signal strength is used to determine fuel concentration, while the oscillation period of the signal provides a precise measurement of temperature (~0.3% uncertainty), with accuracy limited by knowledge of the gas composition.

This thesis describes the use of counterpropagating pulse trains to quasi-phase-match high-harmonic generation (HHG). Two novel techniques for generating trains of ultrafast pulses are described and demonstrated. The first method makes use of a birefringent crystal array to split a single pulse into a sequence of pulses. The second method makes use of the time-varying polarisation of a chirped pulse passed through a multiple-order wave plate to generate a train of pulses by the addition of a polariser. It is demonstrated that this second technique can be used to make pulse trains with non-uniform pulse separation by using an acousto-optic programmable dispersive filter to manipulate the higher-order dispersion encountered by the chirped pulse. The crystal array method is used to demonstrate quasi-phase-matching of HHG in a gas-filled capillary, using one and two counterpropagating pulses. Enhancements of up to 60% of the intensity of the 27th harmonic of the 800,nm driving laser light are observed. Information on the spatial and dynamic properties of the HHG process is obtained from measurements of the coherence length in the capillary. Simulations of HHG in a capillary waveguide have been performed. These agree well with the results of the quasi-phase-matching experiments. The effect of mode-beating on the generation process in a capillary and its use as a quasi-phase-matching mechanism are investigated.

This thesis describes experimental work towards developing a trapped ion quantum information processor. An existing ion trap apparatus was capable of trapping and laser-cooling single ions or small ion strings of 40 Ca+, and had been used for studies of quantum jumps and natural lifetime measurements in Ca. This thesis describes improvements in this apparatus, which have allowed the stability and the flexibility of experimental control of the ions to be greatly increased. This enabled experiments to read out the spin state of a single trapped ion, and to load ions with isotope selectivity through photoionization. The optical systems were improved by installation of new lasers, optical reference cavities, and a system of acousto-optic modulators for laser intensity switching and frequency control. The photon counting for fluorescence detection was improved, and a new photon time-of-arrival correlation circuit developed. This has permitted rapid and more sensitive detection of micromotion, and hence cancellation of stray fields in the trap. A study of resonant circuits in the low RF, high voltage (10 MHz, 1 kV) regime was carried out with a view to developing a new RF supply for the Paul trap with reduced noise and increased power. A new supply based on a helical resonator was built and used to trap ions. This technique has reduced noise and will permit higher secular frequencies to be attained in the future. A magnetic field B in the ion trap is used to define a quantization axis, and in one series of experiments was required to be of order 100 G to provide a substantial Zeeman splitting. A set of magnetic field coils to control the size and direction of B is described. The design of these posed some problems owing to an unforseen issue with the vacuum chamber. In short, it is magnetizable and acts to first approximation like a magnetic shield. The field coils had to be sufficiently substantial to produce the desired field at the ion even in the presence of this shielding effect, and dark resonance (and other) spectra with Zeeman splitting were obtained to calibrate the field using the ion as a probe. Finally, the thesis describes the successful loading of the ion trap by laser photoionization from a weak atomic beam. This involved two new lasers at 423 nm and 389 nm. Saturated absorption spectroscopy of neutral calcium is first described, then transverse excitation of an atomic beam in our vacuum chamber is used to identify all the main isotopes of calcium and confirm their abundances in our source (a heated sample of natural calcium). Finally, photoionization is used to load the trap. This has three advantages over electron-impact ionization. By avoiding an electron gun, we avoid charging of insulating patches and subsequent electric field drift as they discharge; the flux in the atomic beam and hence calcium (and other) deposits on the electrodes can be greatly reduced; and most importantly, the photoionization is isotope selective. Evidence is presented which suggests that even with an non-enriched source, the rare isotope 43 Ca can be loaded with reasonable efficiency. This isotope is advantageous for quantum information experiments for several reasons, but chiefly because its ground state hyperfine structure can act as a stable qubit.

The recent development of free-electron lasers operating at XUV and X-ray wavelengths are proving vital for the exploration of matter in extreme conditions. The ultra-short pulse length and high peak brightness these light sources provide, combined with a tunable X-ray wavelength range, makes them ideally suited both for creating high energy density samples and for their subsequent study. In this thesis I describe the work done on the XUV free-electron laser FLASH in Hamburg, aimed at creating homogeneous samples of warm dense matter through the process of volumetric XUV photo-absorption, and the theoretical work undertaken to understand the process of high-intensity laser-matter interactions. As a first step, we have successfully demonstrated intensities above 10¹⁷ Wcm-2 at a wavelength of 13.5 nm, by focusing the FEL beam to micron and sub-micron spot sizes by means of a multilayer-coated off-axis parabolic mirror. Using these record high intensities, we have demonstrated for the first time saturable absorption in the XUV. The effect was observed in aluminium and magnesium samples and is due to the bleaching of a core-state absorption channel by the intense radiation field. This result has major implications for the creation of homogeneous high energy density systems, as a saturable absorption channel allows for a more homogeneous heating mechanism than previously thought possible. Further, we have conducted soft X-ray emission spectroscopy measurements which have delivered a wealth of information on the highly photo-excited system under irradiation, immediately after the excitation pulse, yet before the system evolves into the warm dense matter state. Such strongly photo-excited samples have also been studied theoretically, by means of density functional theory coupled to molecular dynamics calculations, yielding detailed electronic structure information. The use of emission spectroscopy as a probe for solid-density and finite-temperature systems is discussed in light of these results. Theoretical efforts have further been made in the study of the free-free absorption of aluminium as the system evolves from the solid state to warm dense matter. We predict an absorption peak in temperature as the system heats and forms a dense plasma. The physical significance of this effect is discussed in terms of intense light-matter interactions on both femtosecond and picosecond time-scales.

This thesis describes the development of several spectroscopic methods based on impulsive vibrational spectroscopy as well as of the technique itself. The first chapter describes the ultrafast time domain Raman spectrometer including the development of two noncollinear optical parametric amplifiers for sub-10 fs pulse generation with 343 or 515 nm pumping. In the first spectroscopic study we demonstrate, for the first time, that impulsive vibrational spectroscopy can be used for recording transient Raman spectra of molecules in excited electronic states. We obtain spectra of beta-carotene with comparable, or better, quality than established frequency domain based nonlinear Raman techniques. The following two chapters address the questions on the fate of vibrational coherences when generated on a reactive potential energy surface. We photoexcite bacteriorhodopsin and observe anharmonic coupling mediated vibrational coherence transfer to initially silent vibrational modes. Additionally, we are able to correlate the vibrational coherence activation with the efficiency of the isomerisation reaction in bR. Upon generation of vibrational coherence in the second excited electronic state of beta-carotene, by excitation from the ground electronic state, we are able to follow the wavepacket motion out of the Franck-Condon region. We observe vibrationally coherent internal conversion, through a conical intersection, into the first excited electronic state and are hence able to demonstrate that electronic surface crossings can occur in a vibrationally coherent fashion. Additionally, we find strong evidence for vibronic coupling mediated back and forth crossing between the two electronic states. As a combination of this work we develop a IVS based technique that allows for the direct recording of background and baseline free Raman spectra in the time domain. Several proof of principle experiments highlight the capabilities of this technique for time resolved Raman spectroscopy. In the final chapter we present work on weak-field coherent control. Here, we address the question of whether a photochemical reaction can be controlled by the phase term of an electric excitation field, in the one photon excitation limit. We study the systems rhodamine 101, bacteriorhodopsin, rhodopsin and isorhodopsin and, contrary to previous reports, find no evidence for one photon control.

In 2010 high harmonic generation (HHG) in solids was first observed where high order harmonics of a strong laser field's frequency were observed. HHG in solids is now a rapidly developing field that allows for exciting applications like fully solid state attosecond XUV sources and new ultrafast resolution imaging techniques for quantum dynamics in solids. HHG in solids has been explained by two mechanisms: an interband mechanism, due to polarization associated with separate energy bands, and an intraband mechanism that results from nonlinearities and population changes associated with each individual band. While interband HHG has been seen in wide bandwidth semiconductors, intraband HHG has been observed in narrow bandwidth dielectrics. There has not yet been an explanation of the alternation of mechanisms with material differences. The main goal of this thesis is to attempt to provide a better understanding of the most important mechanisms and where they prevail. Although numerical modelling of HHG requires consideration of multiple energy bands, a two-band model consisting only of a valence band and a single conduction band can explain the most important mechanisms. This model requires a given material's band gap between its valence and conduction bands as well as dipole matrix elements between the bands. In this thesis we follow the Kronig-Penney model to develop a 1D delta-function potential model of solids to obtain these properties required of the two-band model. We implement this in a Wannier quasi-classical (WQC) model of interband HHG in semiconductors that explains the dominant dynamics leading to such through quasi-classical real space electron-hole pair trajectories. Although HHG in solids can be explained to be the result of a resonant process in which an electron-hole pair is generated in the first step, there are also virtual transition processes that lack consideration. These processes do not conserve energy and correspond to transitions to conduction bands resulting from field induced distortions of the ground state. We use methodology introduced by Keldysh for optical field ionization of atoms and solids along with the 1D delta-function potential model to quantify how both resonant and virtual transitions lead to HHG in solids for wide and low bandwidth solids.

Die Messung ultrakurzer Laserpulse ist ein Eckpfeiler der ultraschnellen Laserphysik, da die Gültigkeit eines Experiments von der Glaubwürdigkeit seiner Messtechnik abhängt. Etablierte Puls-Charakterisierungstechniken beruhen jedoch häufig auf einer Mittelung über viele Pulse. Daher können sie falsche Informationen liefern, wenn die zeitliche Form von Puls zu Puls variiert. Diese Dissertation bietet Strategien zum sicheren Erfassen und Messen einer Degradierung der Puls-Kohärenz mit Hilfe von frequenzaufgelöstem optischem Gating (FROG), spektraler Phaseninterferometrie für die direkte Rekonstruktion elektrischer Felder (SPIDER) und Dispersionsscan (D-scan). Zu diesem Zweck werden Verbesserungen der Charakterisierungstechniken entwickelt. Die in dieser Arbeit entwickelten neuen Werkzeuge eröffnen nun einen Weg zur Untersuchung der Degradierung der Inter-Puls-Kohärenz, was eine zuverlässige Ultrakurzpulsmetrologie ermöglicht und das zuvor nicht nachweisbare Problem der Pulsfolgeninstabilität löst. / The measurement of ultrashort laser pulses is a cornerstone of ultrafast laser physics, as the validity of any experiment depends on the credibility of its measurement technique. However, established pulse characterization techniques often rely on averaging over many pulses. Therefore, they can return incorrect information if the temporal shape varies from pulse to pulse. This thesis provides strategies to safely detect and measure interpulse coherence degradation, using frequency-resolved optical gating (FROG), spectral phase interferometry for direct electric-field reconstruction (SPIDER), and dispersion scan (d-scan). To this end, improvements of the characterization techniques themselves are devised. The set of new tools developed in this thesis now opens up an avenue for the investigation of interpulse coherence degradation, leading to a more reliable ultrashort pulse metrology and solving the previously undetectable problem of pulse train instability.

This thesis presents an experimental and theoretical study of the collision dynamics of OH(A²Σ⁺) with Kr and Xe. These two systems both exhibit a significant degree of electronically non-adiabatic behaviour, and a particular emphasis of the work presented here is to characterise the competition and interplay between electronic quenching on the one hand, and electronically adiabatic collisional processes on the other. Quenching takes place close to the bottom of the deepest potential well for both systems. In collisions that remain in the excited electronic state, this same region of the potential is also largely responsible for rotational energy transfer (RET) and the collisional depolarisation of angular momentum. Therefore, the direct competition between these processes suppresses the cross-sections for RET and collisional depolarisation from their expected value in the absence of quenching. To investigate this, experiments were carried out to measure cross-sections for the collisional transfer of electronic, vibrational and rotational energy in OH(A, v=0,1) + Kr and OH(A, v=0) + Xe. In addition, measurements were made of the j-j' correlation -- that is, the relationship between the angular momentum of the OH radical before and after a collision -- in collisions with Kr and Xe, using the experimental technique of Zeeman quantum beat spectroscopy. Collisions with both Kr and Xe tend to effectively depolarise the angular momentum of the OH radical, due to the very anisotropic character of the potential on which the process occurs. Electronic quenching, which plays an essential role in both systems, is more prevalent with xenon as the crossing to the ground state potential is located in a more accessible location. These experimental results were compared with single surface quasi-classical trajectory (QCT) calculations, where the overestimate of rotational energy transfer or collisional depolarisation helps to elucidate the degree to which the presence of quenching suppresses these processes. Surface hopping QCT was then used to account for non-adiabatic transitions in the theory, which led to an improvement in agreement with experiment. However, standard surface hopping QCT theory failed to account for the full extent of quenching in these two systems. A major focus of this work is therefore on the development of an extension to standard surface hopping QCT theory to incorporate rovibronic couplings. In non-linear configurations, the excited state of the OH + Kr, Xe systems has A' symmetry, while the ground state is split into symmetric (A') and antisymmetric (A'') components. For these symmetry reasons, coupling is restricted to the two states of the same symmetry, however a rotation of the correct (A'') symmetry can induce transitions to the A'' state too. Inclusion of all three electronic states, and the relevant couplings between them, is found to be crucial for a proper description of experimental reality.

Many problems in applied mathematics and physics are formulated most naturally in terms of matrices, and can be solved by computing functions of these matrices. For example, in quantum mechanics, the coherent dynamics of physical systems is described by the matrix exponential of their Hamiltonian. In state of the art experiments, one can now observe such unitary evolution of many-body systems, which is of fundamental interest in the study of many-body quantum phenomena. On the other hand the theoretical simulation of such non-equilibrium many-body dynamics is very challenging. In this thesis, we develop a symbolic approach to matrix functions and quantum dynamics based on a novel algebraic structure we identify for sets of walks on graphs. We begin by establishing the graph theoretic equivalent to the fundamental theorem of arithmetic: all the walks on any finite digraph uniquely factorise into products of prime elements. These are the simple paths and simple cycles, walks forbidden from visiting any vertex more than once. We give an algorithm that efficiently factorises individual walks and obtain a recursive formula to factorise sets of walks. This yields a universal continued fraction representation for the formal series of all walks on digraphs. It only involves simple paths and simple cycles and is thus called a path-sum. In the second part, we recast matrix functions into path-sums. We present explicit results for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We introduce generalised matrix powers which extend desirable properties of the Drazin inverse to all powers of a matrix. In the third part, we derive an intermediary form of path-sum, called walk-sum, relying solely on physical considerations. Walk-sum describes the dynamics of a quantum system as resulting from the coherent superposition of its histories, a discrete analogue to the Feynman path-integrals. Using walk-sum we simulate the dynamics of quantum random walks and of Rydberg-excited Mott insulators. Using path-sum, we demonstrate many-body Anderson localisation in an interacting disordered spin system. We give two observable signatures of this phenomenon: localisation of the system magnetisation and of the linear magnetic response function. Lastly we return to the study of sets of walks. We show that one can construct as many representations of series of walks as there are ways to define a walk product such that the factorisation of a walk always exist and is unique. Illustrating this result we briefly present three further methods to evaluate functions of matrices. Regardless of the method used, we show that graphs are uniquely characterised, up to an isomorphism, by the prime walks they sustain.