<p> Observing the non-equilibrium dynamics of the invisible ultrafast atomic and sub atomic world requires optical tools with ultrashort bursts of light and wavelengths. Such optical sources can provide us with the ultimate understanding of the quantum universe in the 4D space-time continuum at femto-zeptosecond time and nano-picometer spatial scale. Revealing at the same time, the 'extra dimensions' of the chemical nature of matter with elemental specificity, e.g., oxidation, charge/spin localization to specific elements, etc. To expand the frontiers of knowledge, there is a simple solution: coherent ultrafast X-ray or gamma&ndash;ray laser light. Amongst the numerous X-ray light sources that exist or have been developed to date, there are just two practical complementary alternatives: giant free electron X-ray laser facilities and compact high harmonic generation X-ray lasers. This thesis focuses on the latter. </p><p> High harmonics result from the extreme nonlinear response of matter to strong laser fields. However, due to inability to phase match, the available bright HHG sources were limited to the EUV spectral region ~0.15<i> keV.</i> We report on two routes for efficiently obtaini bright, coherent X-ray light. The first approach, takes advantage of the ultra-high emission per atom and ion species, the large refractive indices, and small phase mismatch, using high intensity UV lasers. Here the specifics of the phase matching and group velocity matching lead to bright soft X-ray emission from ions and atoms, even at ionization levels above 500%. Using UV light at 0.270<i>&micro;m, </i> the harmonics extend above 280<i>eV</i> while the expec phasematching cutoff was believed to be 23<i>eV</i>. Second, using IR lasers, where the process o phase matching favors the coherent buildup of X-rays from many atomic emitters at high gas density over long distances at extremely low ionization levels. The X-rays supercontinua driven by Mid-IR light at &lambda;_L = 3.9<i>&micro;m,</i> extends over ~12 octaves to > 1.6<i>keV,</i> and broadest spectrum generated to date from any small or large source. Calculations indicate that we can extend further the emission to the hard X-ray region and beyond using high laser intensity UV-EUV lasers or low intensities IR-Far IR lasers, without significantly sacrificing the X-ray flux. However, special highly transmissive fibers are required for phase matching in the Mid-IR region, where the propagation distances are longer than the self-guiding lengths. In addition, the flux from the Mid-IR driven HHG is expected to decrease substantially or cease due to a large <i>v</i> vector &times; <i>B</i> vector drift of the returning electrons caused by th magnetic field <i> B</i> vector and because of the large quantum diffusion of the electron wavepacket. We propose and design special photonic bandgap waveguides to resolve all the issues limiting the flux of IR and Mid-IR and UV driven hard X-rays. </p><p> The properties of the X-rays, driven by UV and IR lasers, are completely contrasting: supercontinuum versus isolated sharply peaked harmonics, we predict chirped isolated single pulses on sub or femtosecond scale as opposed to near transform limited train of attosecond pulses, respectively for IR and UV-driven harmonics. While pressure phase matching has been widely used we introduce the concept of pressure-temperature tuned phase matching for the process of HHG generation that additionally increases the flux. </p><p> Moreover, we report on harmonic generation with extremely high flux at near <i>mW</i> and <i>&micro;J</i> level, that allows us to perform experiments, which were previously only possible in large-scale facilities. While a magnetic scattering cross section is orders of magnitude smaller than the charge scattering cross section, we demonstrate resonant magnetic ptychography coherent diffraction imaging at the <i>Fe, M</i>-edge, using narrow bandwidth X-rays light, to lo at buried magnetic domain structure. Using broad 'water window' and keV coherent X-ray supercontinua, we extract atomic structure on picometer spatial resolution and chemical bonds' information, through x-ray absorption spectroscopy measurements at various absorption edges. </p><p> Such unique light tools will make it possible to answer even questions that have not yet been asked or may have never been imagined.</p><p>

<p>Worldwide there are significant efforts to build networks that can distribute photonic entanglement, first with applications in communication, with a long-term vision of constructing fully connected quantum processing networks (QPN). We have constructed a network of atom-light interfaces, providing a scalable QPN platform by creating connected room-temperature qubit memories using dark-state polaritons (DSPs). Furthermore, we combined ideas from two leading elements of quantum information namely collective enhancement effects of atomic ensembles and Cavity-QED to create a unique network element that can add quantum processing abilities to this network. We built a dual connection node consisting of two moderate finesse Fabry-Perot cavities. The cavities are configured to form a cross-cavity layout and coupled to a cold atomic ensemble. The physical regime of interest is the non-limiting case between (i) low N with high cooperativity and (ii) free-space-high-N ensembles. Lastly, we have explored how to use light-matter interfaces to implement an analog simulator of relativistic quantum particles following Dirac and Jackiw-Rebbi model Hamiltonians. Combining this development with the cross-cavity node provides a pathway towards quantum simulation of more complex phenomena involving interacting many quantum relativistic particles.