Computable properties of quantum states are given a dual gravitational interpretation via the AdS/CFT correspondence. For holographic states, boundary entanglement entropy is dual to the area of bulk geodesics, known as Ryu-Takayanagi surfaces. Furthermore, the viability of states to admit a holographic dual at all is constrained by their entanglement structure. Entanglement therefore defines a coarse classification of states in the Hilbert space. Similarly, how a state transforms under a group of operators also provides a classification on the Hilbert space. Certain states, e.g. stabilizer states, are invariant under large sets of operations, and consequently can be simulated on a classical computer. Cayley graphs offer a useful representation for a group of operators, where vertices represent group elements and edges represent group generators. In this representation, the orbit of a state under action of the group can also be represented as a ``reachability graph'', defined as a quotient of the group Cayley graph. Reachability graphs can be dressed to encode entanglement information, making them a useful tool for studying entanglement dynamics under quantum operations. Further quotienting a reachability graph by group elements that fix a chosen state property, e.g. entanglement entropy, builds a ``contracted graph''. Contracted graphs provide explicit bounds on state parameter evolution under quantum circuits. In this work, an upper bound on entropy vector evolution under Clifford group action is presented. Another important property of quantum systems is magic, which quantifies the difficulty of classically simulating a quantum state. Magic and entanglement are intimately related, but the two are not equivalent measures of complexity. Nonetheless, entanglement and magic play complementary roles when describing emergent gravitational phenomena in AdS/CFT. This manuscript describes the interplay between entanglement and magic, and offers a holographic interpretation for magic as cosmic brane back-reaction.

The work covered in this dissertation addresses two areas revolving around superconducting nanowire detector development. The first is regarding array architectureused for a large-scale system. The second involves operating under conditions that allow for a linear response in a superconducting nanowire detector. This dissertation provides the relevant theory, design, and measurements to characterize these detectors. The array architecture studied here utilizes a superconducting nanowire single photon detector embedded in an LC resonant structure, allowing multiple pixels to couple to a single transmission line and identify each one by a tuned characteristic frequency. The pixels in the array are DC-biased, allowing them to respond to absorbed single photons and avoiding any dead time associated with RF biasing. Measured results from a 16-pixel array based on chip components are analyzed. The development here directs this architecture towards integrating a proven 16-pixel design onto a single substrate with the capacity to scale to a higher pixel count and integrate into a broad range of applications. This text outlines the theory behind the proposed linear operation regime and details the considerations needed to achieve a response. The basic principle relies on the time-dependent change in kinetic inductance due to an absorbed photon. Under the conditions discussed in the text, this would allow for fast photon number resolution. However, without reaching those conditions, the detector may still operate under a higher incident photon flux. Two device designs are formulated and simulated, weighing the benefits and drawbacks of each approach. One of the device designs uses an impedance-matching taper to minimize reflections between the nanowire and 50 Ohm amplifier. The other design utilizes N parallel nanowires spanning the length of a gap along a 50 Ohm transmission line path. The tapered device is realized to a proof-of-principle stage and measured under conditions that set a limit on the device’s linear response to optical power. The performance of this detector points to areas of improvement that are addressed or circumvented in the parallel bridge design. Potential for future development is discussed for the frequency multiplexed superconducting nanowire single photon detector array and the linear mode detector.

In the developing field of nonlinear plasmonics, it is important to understand the nonlinear responses of the metallic nanostructures. In the present thesis, rigorous electrodynamical simulations based on the fully vectorial three-dimensional nonlinear hydrodynamic Drude model describing metal coupled to Maxwell's equations are performed to investigate linear and nonlinear responses of the plasmonic materials and their coupling with quantum emitters.The first part of this thesis is devoted to analyzing properties of the localized surface plasmon resonances of metallic nanostructures and their nonlinear optical responses. The behavior of the second harmonic is investigated as a function of various physical parameters at different plasmonic interfaces, revealing highly complex dynamics. By collaborating with several research teams, simulations are proven to be in close agreement with experiments, both quantitative and qualitative. The second part of the thesis explores the strong coupling regime and its influence on the second harmonic generation. Considering plasmonic systems of molecules and periodic nanohole arrays on equal footing in the nonlinear regime is done for the first time. The results obtained are supported by a simple analytical model.

Seeking an upper limit of the Neutron Electric Dipole Moment (nEDM) is a test of charge-parity (CP) violation beyond the Standard Model. The present experimentally tested nEDM upper limit is 3x10^(26) e cm. An experiment to be performed at the Oak Ridge National Lab Spallation Neutron Source (SNS) facility seeks to reach the 3x10^(28) e cm limit. The experiment is designed to probe for a dependence of the neutron's Larmor precession frequency on an applied electric eld. The experiment will use polarized helium-3

(3He) as a comagnetometer, polarization analyzer, and detector.

Systematic influences on the nEDM measurement investigated in this thesis include (a) room temperature measurements on polarized 3He in a measurement cell made from the same materials as the nEDM experiment, (b) research and development of the Superconducting QUantum Interference Devices (SQUID) which will be used in the nEDM experiment, (c) design contributions for an experiment with nearly all the same conditions as will be present in the nEDM experiment, and (d) scintillation studies in superfluid helium II generated from alpha particles which are fundamentally similar to the nEDM scintillation process. The result of this work are steps toward achievement of a new upper limit for the nEDM experiment at the SNS facility.

A domain decomposition method for analyzing very large FDTD domains, hundreds of thousands of wavelengths long, is demonstrated by application to the problem of radar scattering in the maritime environment. Success depends on the elimination of artificial scattering from the “sky” boundary and is ensured by an ultra-high-performance absorbing termination which eliminates this reflection at angles of incidence as shallow as 0.03 degrees off grazing. The two-dimensional (2D) problem is used to detail the features of the method. The results are cross-validated by comparison to a parabolic equation (PE) method and surface integral equation method on a 1.7km sea surface problem, and to a PE method on propagation through an inhomogeneous atmosphere in a 4km-long space, both at X-band. Additional comparisons are made against boundary integral equation and PE methods from the literature in a 3.6km space containing an inhomogeneous atmosphere above a flat sea at S-band. The applicability of the method to the three-dimensional (3D) problem is shown via comparison of a 2D solution to the 3D solution of a corridor of sea. As a technical proof of the scalability of the problem with computational power, a 5m-wide, 2m-tall, 1050m-long 3D corridor containing 321.8 billion FDTD cells has been simulated at X-band. A plane wave spectrum analysis of the (X-band) scattered fields produced by a 5m-wide, 225m-long realistic 3D sea surface, and the 2D analog surface obtained by extruding a 2D sea along the width of the corridor, reveals the existence of out-of-plane 3D phenomena missed by the traditional 2D analysis. The realistic sea introduces random strong flashes and nulls in addition to a significant amount of cross-polarized field. Spatial integration using a dispersion-corrected Green function is used to reconstruct the scattered fields outside of the computational FDTD space which would impinge on a 3D target at the end of the corridor. The proposed final approach is a hybrid method where 2D FDTD carries the signal for the first tens of kilometers and the last kilometer is analyzed in 3D.

While the use of super-cooled gasses as a tool for the study of macroscopic quantum effects has only become experimentally viable in recent years, theories involing such gasses have existed almost as long as quantum theory itself. Albert Einstein first proposed the concept of what is known today as a Bose-Einstein condensate; the driving principle behind his theory was a deliberate exploitation of the symmetric property of multiparticle bosonic wavefunctions. Specifically, since the Bose-Einstein statistics of bosons dic- tate that any arbitrary number of particles can occupy the same state, it is possible in an extremely low energy environment for particles on the order of Avagadro's number to all condense into the ground state. This state of matter is now called a Bose-Einstein condensate (hereafter referred to as a BEC). This state of matter is interesting because having such a large number of particles in the same state allows for the observation of macroscopic quantum effects.

CTB-MPR is a fusion protein between the B subunit of cholera toxin (CTB) and the membrane-proximal region of gp41 (MPR), the transmembrane envelope protein of Human immunodeficiency virus 1 (HIV-1), and has previously been shown to induce the production of anti-HIV-1 antibodies with antiviral functions. To further improve the design of this candidate vaccine, X-ray crystallography experiments were performed to obtain structural information about this fusion protein. Several variants of CTB-MPR were designed, constructed and recombinantly expressed in Escherichia coli. The first variant contained a flexible GPGP linker between CTB and MPR, and yielded crystals that diffracted to a resolution of 2.3 Å, but only the CTB region was detected in the electron-density map. A second variant, in which the CTB was directly attached to MPR, was shown to destabilize pentamer formation. A third construct containing a polyalanine linker between CTB and MPR proved to stabilize the pentameric form of the protein during purification. The purification procedure was shown to produce a homogeneously pure and monodisperse sample for crystallization. Initial crystallization experiments led to pseudo-crystals which were ordered in only two dimensions and were disordered in the third dimension. Nanocrystals obtained using the same precipitant showed promising X-ray diffraction to 5 Å resolution in femtosecond nanocrystallography experiments at the Linac Coherent Light Source at the SLAC National Accelerator Laboratory. The results demonstrate the utility of femtosecond X-ray crystallography to enable structural analysis based on nano/microcrystals of a protein for which no macroscopic crystals ordered in three dimensions have been observed before.

We compare three schemes for time-resolved X-ray diffraction from protein nanocrystals using an X-ray free-electron laser. We find expressions for the errors in structure factor measurement using the Monte Carlo pump-probe method of data analysis with a liquid jet, the fixed sample pump-probe (goniometer) method (both diffract-and-destroy, and below the safe damage dose), and a proposed two-color method. Here, an optical pump pulse arrives between X-ray pulses of slightly different energies which hit the same nanocrystal, using a weak first X-ray pulse which does not damage the sample. (Radiation damage is outrun in the other cases.) This two-color method, in which separated Bragg spots are impressed on the same detector readout, eliminates stochastic fluctuations in crystal size, shape, and orientation and is found to require two orders of magnitude fewer diffraction patterns than the currently used Monte Carlo liquid jet method, for 1% accuracy. Expressions are given for errors in structure factor measurement for the four approaches, and detailed simulations provided for cathepsin B and IC3 crystals. While the error is independent of the number of shots for the dose-limited goniometer method, it falls off inversely as the square root of the number of shots for the two-color and Monte Carlo methods, with a much smaller pre-factor for the two-color mode, when the first shot is below the damage threshold.

Phase problem has been long-standing in x-ray diffractive imaging. It is originated from the fact that only the amplitude of the scattered wave can be recorded by the detector, losing the phase information. The measurement of amplitude alone is insufficient to solve the structure. Therefore, phase retrieval is essential to structure determination with X-ray diffractive imaging. So far, many experimental as well as algorithmic approaches have been developed to address the phase problem. The experimental phasing methods, such as MAD, SAD etc, exploit the phase relation in vector space. They usually demand a lot of efforts to prepare the samples and require much more data. On the other hand, iterative phasing algorithms make use of the prior knowledge and various constraints in real and reciprocal space. In this thesis, new approaches to the problem of direct digital phasing of X-ray diffraction patterns from two-dimensional organic crystals were presented. The phase problem for Bragg diffraction from two-dimensional (2D) crystalline monolayer in transmission may be solved by imposing a compact support that sets the density to zero outside the monolayer. By iterating between the measured stucture factor magnitudes along reciprocal space rods (starting with random phases) and a density of the correct sign, the complex scattered amplitudes may be found (J. Struct Biol 144, 209 (2003)). However this one-dimensional support function fails to link the rod phases correctly unless a low-resolution real-space map is also available. Minimum prior information required for successful three-dimensional (3D) structure retrieval from a 2D crystal XFEL diffraction dataset were investigated, when using the HIO algorithm. This method provides an alternative way to phase 2D crystal dataset, with less dependence on the high quality model used in the molecular replacement method.

The superior brightness and ultra short pulse duration of X-ray free electron laser

(XFEL) allows it to outrun radiation damage in coherent diffractive imaging since elastic scattering terminates before photoelectron cascades commences. This “diffract-before-destroy” feature of XFEL opened up new opportunities for biological macromolecule imaging and structure studies by breaking the limit to spatial resolution imposed by the maximum dose that is allowed before radiation damage. However, data collection in serial femto-second crystallography (SFX) using XFEL is affected by a bunch of stochastic factors, which pose great challenges to the data analysis in SFX. These stochastic factors include crystal size, shape, random orientation, X-ray photon flux, position and energy spectrum. Monte-Carlo integration proves effective and successful in extracting the structure factors by merging all diffraction patterns given that the data set is sufficiently large to average out all stochastic factors. However, this approach typically requires hundreds of thousands of patterns collected from experiments. This dissertation explores both experimental and algorithmic methods to eliminate or reduce the effect of stochastic factors in data acquisition and analysis. Coherent convergent X-ray beam diffraction (CCB) is discussed for possibilities of obtaining single-shot angular-integrated rocking curves. It is also shown the interference between Bragg disks helps ab-initio phasing. Two-color diffraction scheme is proposed for time-resolved studies and general data collection strategies are discussed based on error metrics. A new auto-indexing algorithm for sparse patterns is developed and demonstrated for both simulated and experimental data. Statistics show that indexing rate is increased by 3 times for I3C data set collected from beam time LJ69 at Linac coherent light source (LCLS). Finally, dynamical inversion from electron diffraction is explored as an alternative approach for structure determination.