The establishment of robust laser-cooling techniques for the formation of ultracold atoms has provided a test-bed for low-temperature science, with scattering events changing character from incoherent thermal interactions to coherent quantum mechanical events. A natural extension is the pursuit of ultracold molecules in prescribed low-energy internal states. Atomic cooling techniques, however, do not generalize to the molecular regime due to the complex energy-level structure afforded by its extra degrees of motion. An indirect approach to ultracold molecule formation - photoassociation using ultrafast laser pulses - is the focus of this thesis. A broadband field associates atom pairs into a localized molecular wavepacket that evolves within the attractive excited-state potential. A suitably timed dump pulse may thus be applied to stabilize population into deeply bound ground vibrational states. This strategy may be generalized to any species whose spectroscopy matches the pulse spectrum, and offers a coherent population transfer scheme that does not require precise knowledge of the system. This thesis presents experiments using high-energy photoassociation pulses applied to ultracold rubidium atoms. The pulses quench the background ground-state molecular population but form bound dimers within the excited state. A pump-probe experiment was designed to chart the excited-state dynamics; however, the oscillations predicted by theoretical calculations were not evident in the molecular signal. The nature of the dynamics is expected to be strongly dependent on the initial state of the atom pairs addressed by the ultrafast pulse: a bound molecular population provides an additional candidate to free atoms. A spectroscopic measurement characterizes these bound molecules and identifies their formation mechanism. A subsequent experiment provides evidence that the predominant contributor to the pump-probe signal is the unbound initial population. The consequences with regard to both the observation of excited-state dynamics and the subsequent application of a dump pulse are discussed.

Atoms in optical lattices are promising candidates to implement quantum information processing. Their behaviour is well understood on a microscopic level, they exhibit excellent coherence properties, and they can be easily manipulated using external fields. In very deep optical lattices, each atom is restricted to a single lattice site and can be used as a qubit. If the lattice is shallow enough such that the atoms can move, their properties can be used to simulate certain condensed matter phenomena such as superconductivity. In this thesis, we show how technical problems of optical lattices such as restricted decoherence times, or fundamental shortcomings such as the lack of phonons or strong spin interactions, can be overcome by using current or near-future experimental techniques. We introduce a scheme that makes it possible to simulate model Hamiltonians known from high-temperature superconductivity. For this purpose, previous simulation schemes to realise the spin interaction terms are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. This scheme makes a large range of parameters accessible, which is difficult to cover with a condensed matter setup. We also investigate the properties of optical lattices submerged into a Bose-Einstein condensate (BEC). A weak-coupling expansion in the BEC-impurity interaction strength is used to derive a model that describes the lattice atoms in terms of polarons, i.e.~atoms dressed by Bogoliubov phonons. This is analogous to the description of electrons in solids, and we observe similar effects such as a crossover from coherent to incoherent transport for increasing temperatures. Moreover, the condensate mediates an attractive off-site interaction, which leads to macroscopic clusters at experimentally realistic parameters. Since the atoms in the lattice can also be used as a quantum register with the BEC mediating a two-qubit gate, we derive a quantum master equation to examine the coherence properties of the atomic qubits. We show that the system exhibits sub- and superdecoherence and that a fast implementation of the two-qubit gate competes with dephasing. Finally, we show how to realise the encoding of qubits in a decoherence-free subspace (DFS) using optical lattices. We develop methods for implementing robust gate operations on qubits encoded in a DFS exploiting collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of the gate operations and show that a robust implementation of quantum repeaters can be achieved using our setup. We compare the robust repeater scheme to one that makes use of conventional qubits only, and show the conditions under which one outperforms the other.

Single photons - discrete wavepackets of light - are one of the most fundamental entities in physics. In recent years, the ability to consistently create and manipulate both single photons and pairs of photons has facilitated everything from tests of quantum theory to the implementation of quantum-enhanced precision measurements. These activities all fall within the scope of the rapidly-growing field of quantum information - the exploitation of the properties of quantum states (and specifically their capability to exist in superpositions) to accomplish tasks that would not be possible with classical objects. One stated goal of research in quantum information is to build a device consisting of a network of quantum logic gates that can evaluate quantum algorithms. The photonic implementation of individual logic gates has already been demonstrated. However, partly due to standard methods of preparing single photons, current schemes have severe limitations in terms of scaling up from a single logic gate to multiple concatenated operations. Until now it has not been proven that single photons can be generated in pure and indistinguishable quantum states, something upon which the successful operation of optical quantum logic gates relies. This thesis presents an experimental demonstration of simultaneous generation of almost identical single photons in highly pure states from two independent sources based on parametric downconversion. This is a process of photon pair generation during the passage of a light beam through a nonlinear crystal; one photon from the resulting pair is detected to herald the other. The work herein describes, refines, and implements a technique that minimises the strong quantum correlations usually present within each pair by spectral engineering of the source. This allows the heralded single photons to be in pure states, a property that is confirmed by observing a high-visibility two-photon interference effect without spectral filtering.

This thesis presents results from two strands of work towards realizing a free-electron laser (FEL) driven by electron bunches generated by a laser-wakefield accelerator (LWFA). The first strand focuses on selecting operating parameters for such a light source, on the basis of currently achievable bunch parameters as well as near-term projections. The viability of LWFA-driven incoherent undulator sources producing nanojoule-level pulses of femtosecond duration at wavelengths of 5 nm and 0.5 nm is demonstrated. A study on the prospective operation of an FEL at 32 nm is carried out, on the basis of scaling laws and full 3-D time-dependent simulations. A working point is selected, based on realistic bunch parameters. At that working point saturation is expected to occur within a length of 1.6 m with peak power at the 0.1 GW-level. This level, as well as the stability of the amplification process, can be improved significantly by seeding the FEL with an external radiation source. In the context of FEL seeding, we study the ability of conventional simulation codes to correctly handle seeds from high-harmonic generation (HHG) sources, which have a broad bandwidth and temporal structure on the attosecond scale. Namely, they violate the slowly-varying envelope approximation (SVEA) that underpins the governing equations in conventional codes. For this purpose we develop a 1-D simulation code that works outside the SVEA. We carry out a set of benchmarks that lead us to conclude that conventional codes are adequately capable of simulating seeding with broadband radiation, which is in line with an analytical treatment of the interaction. The second strand of work is experimental, and focuses on on the use of coherent transition radiation (CTR) as an electron bunch diagnostic. The thesis presents results from two experimental campaigns at the MPI für Quantenoptik in Garching, Germany. We present the first set of single-shot measurements of CTR over a continuous wavelength range from 420 nm to 7 μm. Data over such a broad spectral range allows for the first reconstruction of the longitudinal profiles of electron bunches from a laser-wakefield accelerator, indicating full-width at half-maximum bunch lengths around 1.4 μm (4.7 fs), corresponding to peak currents of several kiloampères. The bunch profiles are reconstructed through the application of phase reconstruction algorithms that were initially developed for studying x-ray diffraction data, and are adapted here for the first time to the analysis of CTR data. The measurements allow for an analysis of acceleration dynamics, and suggest that upon depletion of the driving laser the accelerated bunch can itself drive a wake in which electrons are injected. High levels of coherence at optical wavelengths indicate the presence of an interaction between the bunch and the driving laser pulse.

Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to perform. In the first part of this thesis we quantify the effective entanglement when operations are additionally restricted to account for both fundamental restrictions on operations, such as those arising from superselection rules, as well as experimental errors arising from the imperfections in the apparatus. For an important class of errors we find a linear relationship between the usual and effective higher dimensional generalization of concurrence, a measure of entanglement. Following the treatment of effective entanglement, we focus on a related concept of nonlocality in the presence of superselection rules (SSR). Here we propose a scheme that may be used to activate nongenuinely multipartite nonlocality, in that a single copy of a state is not multipartite nonlocal, while two or more copies exhibit nongenuinely multipartite nonlocality. The states used exhibit the more powerful genuinely multipartite nonlocality when SSR are not enforced, but not when they are, raising the question of what is needed for genuinely multipartite nonlocality. We show that whenever the number of particles is insufficient, the degrading of genuinely multipartite to nongenuinely multipartite nonlocality is necessary. While in the first few chapters we focus our attention on understanding the resources present in quantum states, in the final part we turn the picture around and instead treat operations themselves as a resource. We provide our observers with free access to classical operations - ie. those that cannot detect or generate quantum coherence. We show that the operation of interest can then be used to either generate or detect quantum coherence if and only if it violates a particular commutation relation. Using the relative entropy, the commutation relation provides us with a measure of nonclassicality of operations. We show that the measure is a sum of two contributions, the generating power and the distinguishing power, each of which is separately an essential ingredient in quantum communication and information processing. The measure also sheds light on the operational meaning of quantum discord - we show it can be interpreted as the difference in superdense coding capacity between a quantum state and a classical state.

Advances in several areas of scientific research is currently hampered by the slow progress in developing a non-viral, high precision technique capable of safely and efficiently injecting targeted single cells with impermeable molecules. To date, one of the most promising techniques employs the laser to temporarily create a pore in the cell membrane to allow the entry of exogenous molecules. This technique has potentially wide applications. In this thesis, I utilised the precision of laser transfection, also known as optoporation, to deliver two histone demethylase inhibitors (8-hydroxyquinoline and FMF1293) of the JmjC-domain protein JMJD3 into vital cells. The enzyme, JMJD3, demethylates histone H3 lysine K27, the methylation state of which has been shown in previous studies to regulate genes in such a way as to play a key role in the formation of tumours and even maintenance of stem cell pluripotency. The research here shows proof of principle that optoporation can be employed to quickly screen and test the efficacy of novel drugs by delivering them into cells at significantly low concentrations while still maintaining inhibition activity. I also used optoporation to deliver relatively large proteins such as bovine serum albumin (BSA), phalloidin and novel synthetic antibodies into living cells without fixatives. This offers the possibility of using reporter systems to monitor living cells over time. Finally, an attempt was made to generate iPS colonies by optoporating plasmid DNA into somatic cells, however, I find that this technique was unable to efficiently transfect and reprogram primary cells. Two automated image-based systems that can be integrated into existing microscopes are presented here. First, an image processing algorithm that can quickly identify stem cell colonies non-invasively was implemented. When tested, the algorithm’s resulting specificity was excellent (95 – 98.5%). Second, because optoporation is a manual and time consuming procedure, an algorithm to automate optoporation by using image processing to locate the position of cells was developed. To my knowledge, this is the first publication of a system which automates optoporation of human fibroblasts in this way.

The main topic of this thesis is the development of novel diagnostics for the characterisation of infrared femtosecond and extreme-ultraviolet (XUV) attosecond pulses. High-resolution interferometric methods are applied to high harmonic radiation, both to measure the properties of the XUV light and to relate this information to the physics of the fundamental generation process. To do so, a complete high harmonic beamline has been built and optimised to enable the observation of strong signatures of the macroscopic response of the medium. The distinct spatial characteristics of long and short trajectories are studied, as well as the interference between them. An interferometric measurement allows the extraction of the atomic dipole phase, which gives direct access to the sub-cycle electron dynamics. A major focus of this thesis is on the development of a novel method which simultaneously characterises two independent electric fields as a function of any degree of freedom in which it is possible to shear one of the beams. Since each field alternately takes the role of the reference to retrieve the other field, this technique is referred to as mutual interferometric characterisation of electric-fields (MICE). One of the key features of MICE is that no sheared but otherwise identical replica of the test pulse needs to be generated, which is a typical requirement of self-referencing techniques. Furthermore, no a priori information is needed for the reconstruction. The strength and the wide applicability of MICE are demonstrated using two fundamentally different examples. First, the temporal pulse profiles of two infrared femtosecond pulses are simultaneously reconstructed in a single laser shot. In the second demonstration, the MICE approach is used to simultaneously reconstruct the wavefronts of two high harmonic beams. Having this new technique at hand, the phase properties of the different quantum trajectories are compared. All pulse characterisation techniques implicitly assume full coherence of the beam. This, however, is often not the case in practice, in particular when dealing with complex XUV light sources. Here the standard characterisation techniques fail to provide an accurate description of the electric field. Instead, the electric field must be seen as a statistical mixture of different contributions to the overall field. Here an interferometric experiment is first proposed and then performed involving multiple lateral shears to measure the two-point correlation function of high harmonic radiation. This directly provides information about the existence and the magnitude of partial coherence of high harmonics.

Due to the recent success, in terms of accuracy and precision, of a number of strontium optical lattice optical frequency standards, and the classification of the 5s² ¹S₀ to 5s5p ³P₀ transition in neutral strontium as a secondary definition of the SI unit of the second, many new strontium lattice clocks are under development. The strontium optical lattice clock (Sr OLC) at the National Physical Laboratory (NPL) is one such project. This thesis describes the design and build of the NPL Sr OLC, discussing the considerations behind the design. Details of the first cooling stage are given, which includes the characterisation of a novel permanent-magnet Zeeman slower by measurements of the longitudinal velocity distributions and loading of the MOT at 461 nm. Development of a narrow linewidth laser system at 689 nm is described, which is used for initial spectroscopy of the second-stage cooling transition. In particular, this work describes progress towards two independent ultra-narrow linewidth clock lasers. The new generation of strontium lattice clock experiments have focused on characterising the systematic frequency shifts and reducing their associated fractional frequency uncertainties, as well as reducing the fractional frequency instability of the measurement. One focus of the Sr OLC at NPL is to help characterise the frequency shift of the clock transition due to black-body radiation (BBR), which is currently the largest contributor to the uncertainty budget of the measured clock frequency. Our approach, discussed here, is to make a direct, differential measurement of the shift with the atoms housed alternately in environments of differing temperatures. Better characterisation and control of the BBR frequency shift of the strontium clock transition is crucial for the future of the Sr OLC as a leading frequency standard.

The warm dense matter regime (WDM), defined by temperatures of a few electron volts and densities comparable with solids, is a complex state of matter where multi-body particle correlations and quantum effects play an important role in determining the overall structure and equation of state. The study of WDM states represents the laboratory analogue of the astrophysical environments found in the cores of planets and in the crusts of old stars, but also has practical applications for controlled thermonuclear fusion. Time resolved X-ray diffraction is used to study the temporal evolution of a sample from solid state towards WDM, either after irradiation with an intense proton/electron beam, in carbon samples, or direct laser illumination, in thin gold nanofoils. The electron-ion equilibration time is extracted through the use of the two-temperature model and in highly excited carbon shown to be longer than previously thought, this is attributed to strong ion-ion coupling screening the interaction (coupled mode theory). Calculation of the dynamic ion-ion structure factor is performed using orbital-free density functional theory (OF-DFT) and shown to compare well with Kohn-Sham DFT in both the static and dynamic cases. Experimental verification of these results is vital and measurement of the microscopic dynamics of warm dense aluminium have been successfully demonstrated through inelastic X-ray scattering. Using the self-seeded beam at the linear coherent light source (LCLS) scattering at a small momentum exchange allowed the first direct measurement of ion acoustic waves in WDM. This data provides the basis for a direct experimental test of many dense plasma theories through direct comparison with the ion-ion dynamic structure factor.

Laser-plasma accelerators are of great interest because of their ability to sustain extremely large acceleration gradients, enabling compact accelerating structures. Laser-plasma acceleration is realized by using a high-intensity short pulse laser to drive a large plasma wave or wakefield in an underdense plasma. This thesis considers the effect of axial plasma density upramps on laser wakefield acceleration. Theoretical groundwork shows that tapered plasma channels can be used to mitigate one of the main limitations of laser plasma acceleration, that is, dephasing of an electron beam with respect to the plasma wave. It is shown that it is possible to maintain an electron bunch at constant phase in the longitudinal electric fields of the laser wake field. This leads to an increased energy gain of an electron trapped in the wakefield. The required shape of the density slope is difficult to implement in experiments. Therefore, a linear density ramp is also considered which is predicted to also increase the energy gain beyond that possible in a uniform density plasma. Towards an experimental implementation it was studied how a suitable gas density profile can be established in a capillary. This was done employing simulations using the computational fluid dynamics tool kit OpenFoam and comparing these to measurements of the axial density profile based on Raman scattering. It was demonstrated that a linear density ramp could be established by applying different pressures on the capillary gas inlets. The dependence of the density profile on the capillary parameters, such as, capillary diameter and length and inlet diameter were also studied. The results of the simulations and the measurement showed excellent agreement and demonstrate that approximately linear density ramps can be generated by flowing gas along a capillary of constant cross-section Laser wakefield acceleration in plasmas with longitudinally varying density was investigated in an experiment at the Astra Laser at Rutherford Laboratories. The experiment utilised ionisation injection in order to operate in the mildly non-linear regime of laser-wakefield acceleration. The measured electron energies agree well with the theoretical predictions. It was demonstrated that an increase in the energy gain can be obtained by driving the accelerator in a ramped plasma, the electron spectrum is more narrow and the injected charge increases significantly. Measurements of the X-ray spectrum emitted by the betatron motion of the accelerated electron bunch allowed the transverse radius of the bunch to be deduced. These measurements showed that retrieved electron bunch radius is inversely proportional to the longitudinal density gradient, that is a plasma density upramp (downramp) has a decreased (increased) electron bunch radius.