This thesis set out to investigate light storage based on dynamic electromagnetically induced transparency (EIT) in a room-temperature atomic ensemble of rubidium as a means to provide a quantum memory for single-photons created by a single rubidium atom coupled to a high-finesse optical resonator. Setting up the light storage medium presented a new addition to the research group's portfolio of experimental techniques and led to investigations of EIT, slow light and stored light in warm rubidium-87 vapour. Lambda level schemes connecting Zeeman or hyperfine substates on the D₁ and D₂ lines were addressed in rubidium vapour cells containing different buffer gases and different isotopic fractions of rubidium-87 and rubidium-85. Single beam spectroscopy with a weak probe was used to characterise the vapour cells. A numerical method to fit the D line spectrum to a theoretical model to include isotopic fractions and collisional broadening of a buffer gas has been implemented. Temperature and isotopic fractions could be reliably extracted from the fit parameters. For an offset-stabilisation of two lasers to address a lambda level scheme connecting the two different hyperfine groundstates in rubidium a phase locked loop including a frequency divider has been designed and implemented. Light storage and retrieval has been demonstrated using a Zeeman scheme on the D1 line. Two microsecond long classical light pulses containing one million photons on average were stored and retrieved with an efficiency of 15% after a delay of one microsecond. Several methods of attenuating the strong co-propagating control laser beam to allow for lowering the signal pulse intensity in future experiments are discussed.

Doctor of Philosophy / Department of Physics / Chii-Dong Lin / Imaging of molecules has always occupied an essential role in physical, chemical and biological sciences. X-ray and electron diffraction methods routinely achieve sub-angstrom spatial resolutions but are limited to probing dynamical timescales longer than a picosecond. With the advent of femtosecond intense lasers, a new imaging paradigm emerges in last decade based on laser-induced electron diffraction (LIED). It has been placed on a firm foundation by the quantitative rescattering theory, which established that large-angle e-ion elastic differential cross sections (DCS) can be retrieved from the LIED spectrum. We further demonstrate that atomic potentials can be accurately retrieved from those extracted DCSs at energies from a few to several tens of electron volts. Extending to molecules, we show mid-infrared (mid-IR) lasers are crucial to generate high-energy electron wavepackets (> 100 eV) to resolve the atomic positions in a molecule. These laser-driven 100 eV electrons can incur core-penetrating collisions where the momentum transfer is comparable to those attained in conventional keV electron diffraction. Thus a simple independent atom model (IAM), which has been widely used in conventional electron diffractions, may apply for LIED. We theoretically examine and validate the applicability of IAM for electron energies above 100 eV using e-molecule large-angle collision data obtained in conventional experiments, demonstrating its resolving powers for bond lengths about 0.05 angstrom. The Validity of IAM is also checked by an experimental LIED investigation of rare gas atoms in the mid-IR regime. We show that the electron’s high energy promotes core-penetrating collisions at large scattering angles, where the e-atom interaction is dominated by the strong short range atomic-like potential. Finally, we analyze the measured LIED spectrum of N[subscript]2 and O[subscript]2 at three mid-IR wavelengths (1.7, 2.0, and 2.3 μm). As expected, the retrieved bond lengths of N[subscript]2 at three wavelengths are about same as the equilibrium N[subscript]2 bond length. For O[subscript]2, the data is also consistent with a bond length contraction of 0.1 angstrom within 4-6 fs after tunnel ionization. This investigation establishes a foundation for this novel imaging method for spatiotemporal imaging of gas-phase molecules at the atomic scale.

<p>Radiation damage limits the resolution in imaging experiments. Damage is caused by energy deposited into the sample during exposure. Ultrashort and extremely bright X-ray pulses from free-electron lasers (FELs) offer the possibility to outrun key damage processes, and temporarily improve radiation tolerance. Theoretical models indicate that high detail-resolutions could be realized on non-crystalline samples with very short pulses, before plasma expansion.</p><p>Studies presented here describe the interaction of a very intense and ultrashort X-ray pulse with material, and investigate boundary conditions for flash diffractive imaging both theoretically and experimentally. In the hard X-ray regime, predictions are based on particle simulations with a continuum formulation that accounts for screening from free electrons.</p><p>First experimental results from the first soft X-ray free-electron laser, the FLASH facility in Hamburg, confirm the principle of flash imaging, and provide the first validation of our theoretical models. Specifically, experiments on nano-fabricated test objects show that an interpretable image can be obtained to high resolution before the sample is vaporized. Radiation intensity in these experiments reached 10^14 W/cm^2, and the temperature of the sample rose to 60000 Kelvin after the 25 femtosecond pulse left the sample. Further experiments with time-delay X-ray holography follow the explosion dynamics over some picoseconds after illumination.</p><p>Finally, this thesis presents results from biological flash-imaging studies on living cells. The model is based on plasma calculations and fluid-like motions of the sample, supported by the time-delay measurements. This study provides an estimate for the achievable resolutions as function of wavelength and pulse length. The technique was demonstrated by our team in an experiment where living cells were exposed to a single shot from the FLASH soft X-ray laser.</p>

Radiation damage limits the resolution in imaging experiments. Damage is caused by energy deposited into the sample during exposure. Ultrashort and extremely bright X-ray pulses from free-electron lasers (FELs) offer the possibility to outrun key damage processes, and temporarily improve radiation tolerance. Theoretical models indicate that high detail-resolutions could be realized on non-crystalline samples with very short pulses, before plasma expansion. Studies presented here describe the interaction of a very intense and ultrashort X-ray pulse with material, and investigate boundary conditions for flash diffractive imaging both theoretically and experimentally. In the hard X-ray regime, predictions are based on particle simulations with a continuum formulation that accounts for screening from free electrons. First experimental results from the first soft X-ray free-electron laser, the FLASH facility in Hamburg, confirm the principle of flash imaging, and provide the first validation of our theoretical models. Specifically, experiments on nano-fabricated test objects show that an interpretable image can be obtained to high resolution before the sample is vaporized. Radiation intensity in these experiments reached 10^14 W/cm^2, and the temperature of the sample rose to 60000 Kelvin after the 25 femtosecond pulse left the sample. Further experiments with time-delay X-ray holography follow the explosion dynamics over some picoseconds after illumination. Finally, this thesis presents results from biological flash-imaging studies on living cells. The model is based on plasma calculations and fluid-like motions of the sample, supported by the time-delay measurements. This study provides an estimate for the achievable resolutions as function of wavelength and pulse length. The technique was demonstrated by our team in an experiment where living cells were exposed to a single shot from the FLASH soft X-ray laser.

I present several new methods for the characterisation of ultrashort pulses using interferometry. A generalisation of the concatenation algorithm for spectral shearing interferometry enables interferograms taken at multiple shears to be combined. This improves the precision of the reconstructed phase in the presence of detector noise, and enables the relative phase between disjoint spectral components to be obtained without decreasing the spectral resolution. The algorithm is applied to experimental data from two different implementations of spectral shearing interferometry for ultrashort optical pulses. In one, the shears are acquired sequentially, and in the other they are acquired simultaneously. I develop a form of spatio-temporal ultrashort pulse characterisation which performs both spatial and spectral shearing interferometry simultaneously. It requires a similar geometrical setup to common implementations of spectral phase interferometry for direct electric-field reconstruction, but provides complete amplitude and phase characterisation in time and one spatial dimension. I develop the theory of lateral shearing interferometry for spectrally resolved wavefront sensing of extended ultraviolet and soft x-ray pulses generated using high-harmonic generation. A comprehensive set of wavefront measurements of harmonics 13-25 in Krypton show good agreement with theory, validating the technique. I propose and numerically demonstrate quantum-path interferometry mediated by a weak control field for high harmonic generation. This is a general technique for measuring the amplitude and relative phases of each contributing quantum path. The control field perturbatively modulates the phase of each path. The differing sensitivity of each path to the parameters of the control field allows their contributions to be distinguished from one another.

In this thesis we have focused on two topics: Discrete Quantum Walks and Quantum Image Processing. Our work is a contribution within the field of quantum computation from the perspective of a computer scientist. With the purpose of finding new techniques to develop quantum algorithms, there has been an increasing interest in studying Quantum Walks, the quantum counterparts of classical random walks. Our work in quantum walks begins with a critical and comprehensive assessment of those elements of classical random walks and discrete quantum walks on undirected graphs relevant to algorithm development. We propose a model of discrete quantum walks on an infinite line using pairs of quantum coins under different degrees of entanglement, as well as quantum walkers in different initial state configurations, including superpositions of corresponding basis states. We have found that the probability distributions of such quantum walks have particular forms which are different from the probability distributions of classical random walks. Also, our numerical results show that the symmetry properties of quantum walks with entangled coins have a non-trivial relationship with corresponding initial states and evolution operators. In addition, we have studied the properties of the entanglement generated between walkers, in a family of discrete Hadamard quantum walks on an infinite line with one coin and two walkers. We have found that there is indeed a relation between the amount of entanglement available in each step of the quantum walk and the symmetry of the initial coin state. However, as we show with our numerical simulations, such a relation is not straightforward and, in fact, it can be counterintuitive. Quantum Image Processing is a blend of two fields: quantum computation and image processing. Our aim has been to promote cross-fertilisation and to explore how ideas from quantum computation could be used to develop image processing algorithms. Firstly, we propose methods for storing and retrieving images using non-entangled and entangled qubits. Secondly, we study a case in which 4 different values are randomly stored in a single qubit, and show that quantum mechanical properties can, in certain cases, allow better reproduction of original stored values compared with classical methods. Finally, we briefly note that entanglement may be used as a computational resource to perform hardware-based pattern recognition of geometrical shapes that would otherwise require classical hardware and software.

Detailed understanding of the equation of state of light elements such as the hydrogen isotopes in the warm dense matter (WDM) regime is essential for the modeling of the inner structure of many astrophysical objects, in particular Jovian planets as well as inertial confinement fusion (ICF) research. In these systems quantum degeneracy and strong inter-particle forces play an important role making its theoretical description extremely challenging. The Omega laser was used to drive a planar shock wave in cryogenically cooled deuterium creating WDM conditions. We used a set of independent diagnostics to measure the thermodynamic conditions of WDM including velocity interferometry (VISAR), streaked optical pyrometry (SOP) and x-ray Thomson scattering (XRTS). With a narrow-band x-ray backlighter probe at backscattering geometry the spectrally resolved XRTS accessed the boundary of collective and non-collective regimes making our measurement sensitive to both electron temperature and density. This work presents a full set of measurements of the thermodynamic properties for different laser intensity drives creating warm dense deuterium at various degrees of degeneracy and coupling. The measured electron densities and temperatures ranged between 0.2 and 2.15x10²³ cm^−3 and 0.6 − 20 eV respectively. The scattering measurement confirmed the findings from the VISAR and SOP data and together densityfunctional molecular dynamics (DFT-MD) simulations provides a novel self-consistent approach for an accurate characterization of the microscopic structure of WDM. Complementary to the laser compression work, findings from project employing static compression hydrogen with the use of diamond anvil cells is also be presented. The first direct measurement of the local field correction to the Coulomb interactions in degenerate plasma was obtained from inelastic scattering (20 keV probe) at the Diamond Light Source synchrotron facility.

In spite of being the subject of intense research, several key but complex questions on the nonequilibrium physics of correlated quantum systems remain controversial. For example, the nature of particle and energy transport in different interacting regimes, the relevance of integrability and the impact of environmental coupling are still under active debate. These problems can now be approached numerically, due to the development of powerful algorithms which allow the efficient simulation of the dynamics of correlated systems. In the present thesis we study numerically and analytically the transport properties of low-dimensional quantum systems. In particular, we consider the steady-state spin and energy conduction through XXZ boundary-driven spin-1/2 chains. In the first part, we analyse the transport through chains with only coherent processes in the bulk. For spin transport induced by a magnetisation imbalance between the boundaries, previously identified ballistic, diffusive and negative differential conductivity regimes are reproduced. We provide a comprehensive explanation of the latter. The energy conduction induced by this driving scheme features the same properties as spin transport. For thermally-driven chains, we discuss the nature of energy transport and the emergence of local thermal states when the integrability of the Hamiltonian is broken. In the second part of the thesis we analyse the effect of bulk incoherent effects on the transport properties previously discussed. First we find that for weak particle-particle interactions, pure dephasing degrades spin and energy conduction. In contrast, for strong interactions dephasing induces a significant transport enhancement. We identify the underlying mechanism and discuss its generality. Finally, motivated by the lattice structure of several organic conductors, we study the interplay between coherent and incoherent processes in systems of weakly-coupled chains. We find an enhancement effect due to incoherent interchain hopping, stronger than that by dephasing, which increases with the chain length and relates to superdiffusive transport.

A novel dispersion-managed breathing-mode semiconductor mode-locked ring laser is developed. The "breathing-mode" designation derives from the fact that intracavity pulses are alternately stretched and compressed as they circulate around the ring resonator. The pulses are stretched before entering the semiconductor gain medium to minimize the detrimental strong integrating self-phase modulation and to enable efficient pulse amplification. Subsequently compressed pulses facilitate bleaching the semiconductor saturable absorber. The intracavity pulse compression ratio is higher than 50. Down chirping when compared to up chirping allows broader mode-locked spectra and shorter pulse generation owing to temporal and spectral semiconductor gain dynamics. Pulses as short as 185 fs, with a peak power of ~230 w, and a focused intensity of ~4.6 gw/cm2 are generated by linear down chirp compensation and characterized by shg-frog method. To our knowledge, this is the highest peak power and the shortest pulse generation from an electrically pumped all-semiconductor system. The very good agreement between the simulated and the measured results verifies our understanding and ability to control the physical mechanisms involved in the pulse shaping within the ring cavity. Application trends such as continuum generation via a photonic crystal fiber, two-photon fluorescence imaging, and ultrafast pulse source for pump-probe experiments are demonstrated.

Photonics has consistently played an important role in the investigation of quantum-enhanced technologies and the corresponding study of fundamental quantum phenomena. The majority of these experiments have relied on the free space propagation of light between bulk optical components. This relatively simple and flexible approach often provides the fastest route to small proof-of-principle demonstrations. Unfortunately, such experiments occupy significant space, are not inherently phase stable, and can exhibit significant scattering loss which severely limits their use. Integrated photonics offers a scalable route to building larger quantum states of light by surmounting these barriers. In the first half of this thesis, we describe the operation of on-chip heralded sources of single photons. Loss plays a critical role in determining whether many quantum technologies have any hope of outperforming their classical analogues. Minimizing loss leads us to choose Spontaneous Four-Wave Mixing (SFWM) in a silica waveguide for our source design; silica exhibits extremely low scattering loss and emission can be efficiently coupled to the silica chips and fibers that are widely used in quantum optics experiments. We show there is a straightforward route to maximizing heralded photon purity by minimizing the spectral correlations between emitted photon pairs. Fabrication of identical sources on a large scale is demonstrated by a series of high-visibility interference experiments. This architecture offers a promising route to the construction of nonclassical states of higher photon number by operating many on-chip SFWM sources in parallel. In the second half, we detail one of the first proof-of-principle demonstrations of a new intermediate model of quantum computation called boson sampling. While likely less powerful than a universal quantum computer, boson sampling machines appear significantly easier to build and may allow the first convincing demonstration of a quantum-enhanced computation in the not-distant future. Boson sampling requires a large interferometric network which are challenging to build with bulk optics, we therefore perform our experiment on-chip. We model the effect of loss on our postselected experiment and implement a circuit characterization technique that accounts for this loss. Experimental imperfections, including higher-order emission from our photon pair sources and photon distinguishability, are modeled and found to explain the sampling error observed in our experiment.