When approaching a metal surface, the electronic structure of Rydberg atoms or molecules is perturbed by the surface potential and at close enough distances resonant ionisation of the Rydberg electron into the conduction band of the surface can occur. It is possible to interfere in this process and steer the ionisation distance by making use of the polarisability of the Rydberg orbital in the presence of electric fields. The resulting ions from the surface can extracted via electric fields and subsequently detected via well established ion detection schemes. The question of how this charge-transfer process is affected by different properties of the surface (both electronic and structural) represents the main aspect of the work presented in this thesis. At first, the charge transfer of atomic hydrogen Rydberg atoms with a flat gold metal surface is investigated. While such a surface might appear homogeneous, stray fields are present in its vicinity due to local variations in the surface work function. The surface ionisation process as a function of applied electric field is therefore measured experimentally and the results are compared with classical Monte-Carlo simulations (which include stray field effects). This way the possibility to utilize Rydberg states as a probe of the magnitude of such stray fields is demonstrated. To investigate the effect the surface structure can have on the ionisation process, the interaction of Rydberg atoms with surfaces covered by nanoparticles is investigated. Surface ionisation is measured at a 5 nm nanoparticle monolayer surface and it is shown that population transfer between surface- and vacuum-oriented Rydberg states occurs. In addition, results are presented, which suggest a dependence of the ionisation process on the relative size of Rydberg orbital and nanoparticle. Furthermore, charge transfer between a Rydberg state and discrete electronic states at the surface vacuum interface are investigated by performing experiments with a Cu(100) band-gap semiconductor surface. By analysing surface ionisation as a function of collisional velocity ionisation rates can be determined and are subsequently compared with theoretical predictions. The potential of identifying resonant ionisation is thereby demonstrated. Last, a new method to produce 2s atomic hydrogen via mixing of the 2s and 2p state in an electric field is proposed and first experimental results are presented, thus demonstrating viability of the idea. The experiments presented in this thesis represent the most in depth analysis of the charge-transfer process between atomic hydrogen Rydberg states and a range of different surfaces to date. As such, they demonstrate the potential of utilizing the unique properties of Rydberg states and their applicability as surface probes. In addition, these results pave the way for further experiments involving thin films or the phenomenon of quantum reflectivity.

Device-independent cryptography provides security in various tasks whilst removing an assumption that cryptographers previously thought of as crucial -- complete trust in the machinations of their experimental apparatus. The theory of Bell inequalities as a proof of indeterminism within nature allows for secure device-independent schemes requiring neither trust in the cryptographers' devices nor reliance on the completeness of quantum mechanics. However, the extreme paranoia attributable to the relaxed assumptions within device independence requires an explicit consideration of the previously assumed ability of the experimenters to freely make random choices. This thesis addresses the so-called `free will loophole', presenting Bell tests and associated cryptographic protocols robust against adversarial manipulation of the random number generators with which measurements in a Bell test are selected. We present several quantitative measures for this experimental free will, otherwise known as measurement dependence. We discuss how an eavesdropper maliciously preprogramming the experimenters' untrusted devices can falsely simulate the violation of a Bell inequality. We also bound the amount of Bell violation achievable within a certain degree of measurement dependence. This analysis extends to device-independent randomness expansion, bounding the guessing probability and estimating the amount of privacy amplification required to distil private randomness. The protocol is secure against either arbitrary no-signalling or quantum adversaries. We also consider device-independent key distribution, studying adversarial models that exploit the free will loophole. Finally, we examine a model correlated between the random number generators and Bell devices across multiple runs of a Bell test. This enables an explicit exposition of the optimal cheating strategy and how the correlations manifest themselves within this strategy. We prove that there remain Bell violations for a sufficiently high, yet non-maximal degree of measurement dependence which cannot be simulated by a classical attack, regardless of how many runs of the experiment those choices are correlated over.

This thesis describes methods for using spectral interferometry for the complete space-time characterisation of few-cycle near-infrared femtosecond pulses and extreme ultraviolet (XUV) attosecond pulses produced via high harmonic generation (HHG). Few-cycle pulses tend to exhibit one or more of the following: (1) an octave-spanning bandwidth, (2) a highly modulated spectrum and (3) space-time coupling. These characteristics, coupled with the desire to measure them in a single-shot (to characterise shot-to-shot fluctuations) and in real-time (for online optimisation and control) causes problems for conventional characterisation techniques. The first half of this thesis describes a method, based on a spatially encoded arrangement for spectral phase interferometry for direct electric-field reconstruction (SEA-SPIDER). SEA-SPIDER is demonstrated for sub-10fs pulses with a central wavelength near 800nm, a bandwidth over 350nm, and a pulse energy of several nano-Joules. In addition, the pulses exhibit a modulated spectrum and space-time coupling. The spatially-dependent temporal intensity of the pulse is reconstructed and compared to other techniques: interferometric frequency-resolved optical gating (IFROG) and spectral phase interferometry for direct electric field reconstruction (SPIDER). SEA-SPIDER will prove useful in both femtoscience, which requires accurate knowledge of the space-time character of few-cycle pulses, and in HHG, which requires the precise knowledge of the driving pulse for seeding into simulations and controlling the generation process itself. Pulses arising from HHG are known to exhibit significant space-time coupling. The second half of this thesis describes how spectral interferometry may be performed to obtain the complete space-time nature of these fields via the use of lateral shearing interferometry. Finally, it is shown, via numerical simulations, how to extend the SPIDER technique for temporal characterisation of XUV pulses from HHG by driving the process with two spectrally-sheared driving pulses. Different experimental configurations and their applicability to different laser systems are discussed. This method recovers the space-time nature of the harmonics in a single shot, thus reducing the stability constraint currently required for photoelectron based techniques and may serve as a complimentary method for studying interactions of XUV attosecond pulses with matter.

This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped ⁴³Ca⁺ ions for quantum information processing. I present a rate equations model of ⁴³Ca⁺, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100 μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a ⁴⁰Ca⁺ and a ⁴³Ca⁺ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of pi-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n+1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magnetic-field-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.

In this thesis we investigate strongly-correlated states of ultracold bosonic atoms in rotating ring lattices and arrays of double-well potentials. In the first part of the thesis, we study the tunneling dynamics of ultracold bosons in double-well potentials. In the non-interacting limit single-particle transitions dominate, while in the interaction-dominated regime correlated tunneling of all particles prevails. At intermediate times of the many-particle flopping process correlated states occur, but the timescales of these processes increase dramatically with the number of particles. Using an array of double-well potentials, a large number of such few-particle superposition states can be produced in parallel. In the second part of the thesis, we study the effects of rotation on ultracold bosons confined to one-dimensional ring lattices. We find that at commensurate filling there exists a critical rotation frequency, at which the ground state of the weakly-interacting gas is fragmented into a macroscopic superposition of different quasi-momentum states. We demonstrate that the generation of such superposition states using slightly non-uniform ring lattices has several practical advantages. Moreover, we show that different quasi-momentum states can be distinguished in time-of-flight absorption imaging and propose to probe correlations via the many-body oscillations induced by a sudden change in the rotation frequency. Finally, we compare these macroscopic superposition states to those occurring in superconducting quantum interference devices. In the third part of the thesis, we demonstrate the creation of entangled states with ultracold bosonic atoms by dynamical manipulation of the shape of the lattice potential. To this end, we consider an optical superlattice that allows both the splitting of each site into a double-well potential and the variation of the height of the potential barrier between the sites. We show how to use this array of double-well potentials to perform entangling operations between neighboring qubits encoded on the Zeeman levels of the atoms. As one possible application, we present a method of realizing a resource state for measurement-based quantum computation via Bell-pair measurements. In the final part of the thesis, we study ultracold bosons on a two-dimensional square lattice in the presence of an effective magnetic field and point out a couple of features this system has in common with ultracold bosons in one-dimensional rotating ring lattices.

This thesis describes experimental demonstrations of high-fidelity readout of trapped ion quantum bits ("qubits") for quantum information processing. We present direct single-shot measurement of an "optical" qubit stored in a single calcium-40 ion by the process of resonance fluorescence with a fidelity of 99.991(1)% (surpassing the level necessary for fault-tolerant quantum computation). A time-resolved maximum likelihood method is used to discriminate efficiently between the two qubit states based on photon-counting information, even in the presence of qubit decay from one state to the other. It also screens out errors due to cosmic ray events in the detector, a phenomenon investigated in this work. An adaptive method allows the 99.99% level to be reached in 145us average detection time. The readout fidelity is asymmetric: 99.9998% is possible for the "bright" qubit state, while retaining 99.98% for the "dark" state. This asymmetry could be exploited in quantum error correction (by encoding the "no-error" syndrome of the ancilla qubits in the "bright" state), as could the likelihood values computed (which quantify confidence in the measurement outcome). We then extend the work to parallel readout of a four-ion string using a CCD camera and achieve the same 99.99% net fidelity, limited by qubit decay in the 400us exposure time. The behaviour of the camera is characterised by fitting experimental data with a model. The additional readout error due to cross-talk between ion images on the CCD is measured in an experiment designed to remove the effect of qubit decay; a spatial maximum likelihood technique is used to reduce this error to only 0.2(1)x10^{-4} per qubit, despite the presence of ~4% optical cross-talk between neighbouring qubits. Studies of the cross-talk indicate that the readout method would scale with negligible loss of fidelity to parallel readout of ~10,000 qubits with a readout time of ~3us per qubit. Monte-Carlo simulations of the readout process are presented for comparison with experimental data; these are also used to explore the parameter space associated with fluorescence detection and to optimise experimental and analysis parameters. Applications of the analysis methods to readout of other atomic and solid-state qubits are discussed.

This thesis presents results from three strands of experimental work aimed towards establishing more reproducible, higher energy, and more accurately measured electron beams generated by a laser-driven plasma accelerator. The first experiment calibrated two types of detector frequently used to measure the bunch charge in laser wakefield accelerator experiments, namely scintillating screens and image plates. The experiments undertaken at the DAFNE beam test facility in Frascati, Italy, confirmed that the fluorescence signal from Kodak Lanex Regular screens varies linearly with the charge density for a nanosecond elec- tron bunch for charge densities in the range between ρ = 2 × 10⁻⁷ ^C/_m² to ρ = 10−5 ^C/_m². A sensitivity measurement of FUJIFILM BAS-IP MS image plates resulted in a sensitivity of SMS = (0.0487 ± 0.0028 ) PSL, which is 2.4 times higher than had been assumed prior to this work. The second strand aimed at improving the operation of the capillary discharge waveguide by re-designing the discharge circuit and the waveguide housing. The experiment showed that combining a glow discharge circuit with the pulsed discharge circuit of the capillary discharge waveguide reduced electrical noise, the timing jitter between the trigger pulse and the discharge, and the voltage required to initially break down the capillary gas for pressures below 10 mbar and above 150 mbar. The size of the housing of the capillary discharge waveguide was reduced in all three dimensions by an average of 60 %, enabling the device to be used in future staging experiments, and an open design of the housing eliminated the possibility of unwanted discharges. The new capillary design performed without flaw in the Astra-Gemini experiment and no disadvantages compared with the old housing were found. The third strand of work describes an experiment undertaken with the Astra-Gemini laser at the Central Laser Facility of the Rutherford Appleton Laboratory, United Kingdom. The improved capillary discharge waveguide was used to generate GeV-scale electron beams with good reproducibility. Beams of electrons with energies above 900 MeV, and with root- mean-square divergence of 3.5 mrad, were observed for a plasma density of 2.2 × 10¹⁸ cm⁻³ and a peak input laser power of 55 TW. The variation of the maximum electron energy with the plasma density was measured and found to agree well with simple models. The energy spectra of the generated electron beams exhibited good shot-to-shot reproducibility, with the observed variations attributable to the measured shot-to-shot jitter of the laser parameters. Two methods for correcting the effect of beam pointing variations on the measured energy spectrum were tested and it was found that using a thin Lanex screen in front of the electron spectrometer was easy to implement and did not degrade the recorded energy spectrum. The first observation of temporal compression of a laser pulse within a plasma channel with simultaneous electron acceleration to energies higher than 500 MeV is also presented. This measurement suggests that the pulse compresses linearly from the back as predicted by theory.

Molecular dynamics (MD) simulations are used to compute the equilibrium dynamics of a single component fluid with Yukawa interaction potential v(r) = (Ze)^2 exp(−r/λs )/4π eps_0 r. This system, which is known as the Yukawa one-component plasma (YOCP), represents a simplified description of a non-ideal plasma consisting of ions, charge Ze, and electrons. For finite screening lengths λs, the MD results are used to investigate the domain of validity of the hydrodynamic description, i.e., the description given by the Navier-Stokes equations. The way in which this domain depends on the thermodynamic conditions of the YOCP, as well as the strength and range of the interactions, is determined. Remarkably, it is found that the domain of validity is completely determined by the range of the interactions (i.e., λs); this alone determines the maximum wave number k_max at which the hydrodynamic description is applicable. The dynamics of the YOCP at wavevectors beyond k_max are then investigated; these are shown to be in striking agreement with a simple and well known generalisation of the Navier-Stokes equations. In the extreme case of the Coulomb interaction potential (λs = ∞), the very existence of a hydrodynamic description is a known but unsolved problem [Baus & Hansen, 1980]. For this important special case, known as the one-component plasma (OCP), it is shown that the ordinary hydrodynamic description is never valid. Since the OCP is the prototypical system representing a non-ideal plasma, a number of different approaches for modelling its dynamics have been formulated previously. By computing the relevant quantities with MD, the applicability of a number of models proposed in the literature is examined for the first time.

This thesis describes the development of a relatively novel technique for the gen- eration and subsequent trapping of cold species. Molecules in a pulsed supersonic expansion are photolysed, such that the centre-of-mass velocity vector of one of the fragments is equal in magnitude but opposed in orientation to the lab-frame velocity of the precursor molecule. This technique, known as ‘Photostop’, leaves a fraction of the fragments with a narrow velocity distribution, centered around zero velocity in the lab-frame. They can be shown to have zero velocity by changing the time between photodissociation and ionisation; fragments with a high kinetic energy will leave the ionisation volume prior to interrogation. The underlying velocity distribu- tion is uncovered by using the velocity-map imaging technique, and the temperature of the fragments can be determined. The method was originally optimised for the molecular case. Cold NO has been produced from the dissociation of NO₂ molecules, and a single rotational state has been shown to remain in the ionisation volume 10 μs after dissociation, implying a sample temperature of 1.17 K. Using the optimised experimental conditions de- rived from the velocity cancellation of NO, the atomic case is demonstrated for the dissociation of Br₂ to give zero-velocity Br fragments. The Br atoms are seen for delay times in excess of 100 μs, showing the greater applicability of the method to the atomic case. The temperature of the residual atoms is shown to be in the milliKelvin regime, as determined through detailed Monte Carlo simulation of the motion of the stopped atoms. The possibility of trapping the ultracold Br atoms in a magnetic field is explored, and a quadrupolar trap created between two per- manent bar magnets is demonstrated to confine the atoms spatially, within the ion extraction optics, for delays in excess of 1 ms. The Photostop technique is intended to be a stepping stone on the way to widening the number of chemical species available for study in the ultracold regime. The possibility of improvements to the experiment is considered, in order to increase the efficiency of the experiment such that the number density becomes high enough to be viable as a source of atoms for use in cold chemical reactive studies. The possibility of extending the method so as to be used as a tunable velocity source of atoms is also discussed.

This thesis reports work extending the scope of a recently developed gas sensing technique, multi-mode absorption spectroscopy (MUMAS). The ability of MUMAS to simultaneously detect multiple species from a mixture is demonstrated for the first time. The technique is subsequently extended to mid-infrared wavelengths, realising large gains in sensitivity. A solid-state, multi-mode laser has been developed to provide a high-performance comb source for use with MUMAS. This in-house constructed, diode-pumped, Er/Yb:glass laser operates on 10 longitudinal modes, separated by 18 GHz and centred close to 1565 nm. The extensive development and prototyping work leading to this final laser design is described. Multi-species detection with MUMAS is reported for the first time, thus demonstrating the ability of this technique to perform multi-gas sensing using a single laser and simple detection scheme. The previously described Er/Yb multi-mode laser was used to record MUMAS signals from a sample containing CO, C₂H₂, and N₂O. The components of the mixture were detected simultaneously by identifying multiple transitions in each of the species. Temperature- and pressure-dependent modelled spectral fits to the data were used to determine the partial pressures of each species in the mixture with an uncertainty better than +/-2%. Multi-mode radiation has been successfully generated at 3.3 μm using quasi phase matched difference frequency generation (QPM-DFG). A mid-infrared laser comb was produced by optically mixing the near-infrared, multi-mode comb produced by the previously developed Er/Yb:glass laser with the single-mode output of a Nd:YAG laser operating at 1064 nm. This multi-frequency laser source was characterised to verify performance, and subsequently used to perform proof-of-principle MUMAS measurements on the strong transitions found in this spectral region. Spectra were recorded of NH₃ and CH₄ both individually and as components of a mixture. A minimum detection level for this system was determined to be 4.3 μbar m^-1 for CH₄, a sensitivity increase of 300 over similar measurements performed in the near-IR.