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Molecules are traditionally treated quantum mechanically using the Born-Oppenheimer formalism. In this formalism, different electronic states of the molecule are treated independently. However, most photo-initiated phenomena occurring in nature are driven by the couplings between different electronic states in both isolated molecules and molecular aggregates, and therefore occur beyond the Born-Oppenheimer formalism. These couplings are relevant in reactions relating to the perception of vision in the human eye, the oxidative damage and repair of DNA, the harvesting of light in photosynthesis, and the transfer of charge across large chains of molecules. While these reaction dynamics have traditionally been studied with visible and ultraviolet spectroscopy, attosecond XUV pulses formed through the process of high harmonic generation form a perfect tool for probing coupled electronic dynamics in molecules. In this thesis, I will present our work in using ultrafast, XUV spectroscopy to study these dynamics in molecules of increasing complexity. We begin by probing the relaxation dynamics of superexcited states in diatomic O₂. These states can relax via two types of electronic couplings, either through autoionization or neutral dissociation. We find that our pump-probe scheme can disentangle the two relaxation mechanisms and independently measure their contributing lifetimes. Next, we present our work in observing a coherent electron hole wavepacket initiated by the ionization of polyatomic CO₂ near a conical intersection. The electron-nuclear couplings near the conical intersection drive the electron hole between different orbital configurations. We find that we can not only measure the lifetime of quantum coherence in the electron hole wavepacket, but also control its evolution with a strong, infrared probing field. Finally, we propose an experiment to observe the migration of an electron hole across iodobenzene on the few-femtosecond timescale. We present experimenta

This dissertation presents research on scanning probe microscopy and spectroscopy of graphene and carbon nanotubes. In total three experiments will be discussed. The first experiment uses a scanning tunneling microscope (STM) to study the topographic and spectroscopic properties of graphene on hexagonal boron nitride (hBN). Graphene was first isolated and identified on SiO₂ substrates, which was later found to be the source of graphene quality degradation, e.g. large surface roughness, increased resistivity and random doping etc. Researchers have been trying to replace SiO₂ with other materials and hBN is by far the most successful one. Our STM study shows an order of magnitude reduction in surface roughness and electrostatic potential variation compared with graphene on SiO₂.The second experiment shows a novel quantum interference effect of electron waves in graphene, loosely referred to as "Friedel oscillations." These arise when incident electron waves interfere with waves scattered from defects in the sample. This interference pattern shows up as a spatial variation in the local density of states, which can be probed by the STM. We measured such Friedel oscillations in graphene near step edges of hBN. Due to its peculiar band structure, the oscillations in graphene have a faster decay rate and their wavelength is an order of magnitude longer than similar oscillations previously observed on noble metal surfaces. By measuring the dependence of the Friedel oscillations on electron energy, we map out the band structure of graphene. The last experiment studies a different system: carbon nanotube quantum dots. By combining scanning probe microscopy and transport measurements, we obtain spatial information about quantum dots formed in a carbon nanotube field effect transistor. We also demonstrate the ability to tune the coupling strength between two quantum dots in series.

A coherent optical THz (1.5 THz, 200 µm) source was developed based on pulsed, near IR, fiber lasers, and frequency mixing in nonlinear crystals. The generated THz frequency is determined by the difference frequency of two high peak power pulsed fiber lasers at 1550 nm and 1538 nm. When incident to the crystal, the near IR lasers induce a polarization at their beat frequency which generates the THz radiation. The pulsed fiber lasers are single transverse mode, have high pulse energy and peak powers of 0.38 mJ and 128 kW respectively. They are transform limited at a few ns in duration with very good beam quality of M² ≈ 1.2. The pulse seed was created by modulating a constant laser beam with an electro-optic modulator. An arbitrary waveform generator was used to pre-shape these pulses to compensate for pulse distortion caused by pump gain depletion in the subsequent fiber amplifiers. Pre-amplifiers were constructed using commercial erbium doped silica fiber. Special, highly doped, large core, phosphate fiber was developed in-house to further amplify the pulses, while avoiding nonlinear scattering processes such as stimulated Brillouin scattering and stimulated Raman scattering. THz generation was achieved in both ZnGeP₂ and GaP which were chosen based on their low pump and THz absorption, as well as high nonlinear coefficient. Angle tuning was used to phase match all three optical frequencies in ZnGeP₂ thanks to its birefringence. Layers of GaP ~500 µm thick were pressed together alternately rotated 180° around the normal to quasi-phase match the pump and THz frequencies. To increase the efficiency of the THz generation an external optical cavity was used to enhance and recycle the IR pump pulses. The nonlinear crystal was placed inside the cavity and 151 times enhancement of THz power was observed.

We calculate the strange quark content of the nucleon, − <0|ss|0> using a novel method with the MILC lattice QCD gauge ensembles. The strangeness of the nucleon is related to the interaction cross section between dark matter and ordinary nuclear matter (e.g. in detectors) in many models. Previous results for this quantity suffered from uncontrolled systematic errors and/or large statistical uncertainties. The first result using our methods was the first modern calculation of the strangeness of the nucleon[76] with good control of systematic errors and reasonably small statistical errors, greatly reducing the uncertainty in dark matter detection cross sections. A refinement of this method allows for further reduction of statistical error. On the MILC Asqtad data, we obtain = 0.637(55)(stat)(74)(sys). The results obtained from this method are consistent with those obtained from other commonly-used methods applied to the MILC data. We also calculate the disconnected part of the pion-nucleon sigma term and the intrinsic charm of the nucleon using this method. The intrinsic charm has large statistical errors but is consistent with a perturbative calculation.

Here it is demonstrated that nanofabricated structures can be used as electron optical elements in new types of electron interferometers. This enables novel investigations with electrons analogous to experiments in light and atom optics. Far field diffraction from a single nanograting is used to examine the force on a charge moving in close proximity to a surface. Near field diffraction from the nanograting is investigated in a Talbot interferometer. It is found that electron waves form replicas of the grating in free space, and these replicas can be de-magnified using illumination by a converging beam. An electron Lau interferometer has the same grating configuration as the Talbot interferometer, but uses spatially incoherent beams that give rise to drastically different interference behavior. A single optical theory is developed to efficiently model a variety of grating interferometers under a diverse set of illumination conditions, and it is used to understand the experiments described here. Applications for these new interferometers are discussed, as well as possible directions for future research.

Cooperative effects in many-particle systems can be exploited to achieve measurement outcomes not possible with independent probe particles. We explore two measurement applications based on the cooperative phenomenon of superradiance or on correlated quantum states closely related to superradiance. In the first application we study the off-resonant superradiant Raman scattering of light from an ultracold Bose atomic vapor. We investigate the temperature dependence of superradiance for a trapped vapor and show that in the regime where superradiance occurs on a timescale comparable to a trap frequency, scattering takes place preferentially from atoms in the lowest trap levels due to Doppler dephasing. As a consequence, below the critical temperature for Bose condensation, absorption images of transmitted light serve as a direct probe of the condensed state. Subsequently, we consider a pure condensate and study the time-dependent spatial features of transmitted light, obtaining good qualitative agreement with recent imaging experiments. Inclusion of quantum fluctuations in the initial stages of the superradiant emission accounts well for shot-to-shot fluctuations. Secondly, we have used simulated annealing, a global optimization strategy, to systematically search for correlated quantum interferometer input states that approach the Heisenberg limited uncertainty in estimates of the interferometer phase shift. That limit improves over the standard quantum limit to the phase sensitivity of interferometric measurements by a factor of 1√N, where N is the number of interfering particles. We compare the performance of these states to that of other non-classical states already known to yield Heisenberg limited uncertainty.

Suspensions of the aerobic bacteria {\it Bacilus subtilis} develop patterns and flows from the interplay of motility, chemotaxis and buoyancy.In sessile drops, such bioconvectively driven flows carry plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom.These dynamics are explained quantitatively by a mathematical model consisting of oxygen diffusion and consumption, chemotaxis, and viscous fluid dynamics.Concentrated regions in both geometries comprise nearly close-packed populations, forming the collective ``Zooming BioNematic'' (ZBN) phase.This state exhibits large-scale orientational coherence, analogous to the molecular alignment of nematic liquid crystals, coupled with remarkable spatial and temporal correlations of velocity and vorticity, as measured by both novel and standard applications of particle imaging velocimetry.To probe mechanisms leading to this phase, response of individual cells to steric stress was explored, finding that they can reverse swimming direction at spatial constrictions without turning the cell body.The consequences of this propensity to flip the flagella are quantified, showing that "forwards" and "backwards" motion are dynamically and morphologically indistinguishable.Finally, experiments and mathematical modeling show that complex flows driven by previously unknown bipolar flagellar arrangements are induced when {\it B. subtilis} are confined in a thin layer of fluid, between asymmetric boundaries.The resulting driven flow circulates around the cell body ranging over several cell diameters, in contrast to the more localized flows surrounding free swimmers.This discovery extends our knowledge of the dynamic geometry of bacteria and their flagella, and reveals new mechanisms for motility-associated molecular transport and inter-cellular communication.

Our Galactic center hosts the closest known supermassive black hole candidate. With a mass of approximately 3.7 million solar masses, this compact object, known as Sgr A*, has a considerable influence on the central parsecs of the Galaxy. However, many observed features of the Galactic center result from the presence of and interactions among other stellar and gaseous components, including clusters of massive, wind-producing stars, ionized gas streamers, dense molecular clouds, and supernova remnants. We present a series of simulations and studies of the interactions among these components. In each case, we attempt to explain a particular feature or present a new interpretation of recent observations of the Galactic center. Our simulations of interactions among stellar winds in the central parsec of the Galaxy and in the Arches and Quintuplet clusters are able to explain the diffuse X-ray emission observed there by the Chandra X-ray Observatory. Similarly, our simulations of the explosive formation of the synchrotron shell source Sgr A East place tight constraints on the age and progenitor of such an explosion and might explain the observed X-ray fluorescence of molecular clouds at larger distances from the Galactic center. Finally, our studies of accretion disks around Sgr A* provide a first three-dimensional look at the structure of the accretion flow onto this supermassive black hole and pave the way for full simulations of accretion from length scales of parsecs down to Schwarzschild radii.