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This is the final report for Classifying the Quantum Phases of Matter, FA8750-12-2-0308. Among other achievements, we made progress toward the following goals: (1) finding a classification of locally definable quantum states (those without symmetries or long - range entanglement), (2) elucidating the properties of three-dimensional quantum codes (in particular those which admit no string - like logical operators. (3) characterizing symmetry-protected fermionic phases, (4) proving the stability of topological phases of matter with respect to generic perturbation.

The final year of research activity witnessed successful completion of the proposed research goals of developing and applying exactly embedded density functional and wavefunction theory methods for the investigation of small-molecular activation catalysis, such as hydrogen and nitrogen reduction. In a significant methodological advance from the past year, we developed an accurate and systematically improvable framework for embedding a correlated wavefunction description of a subsystem in a density functional theory description of the surrounding molecular environment (J. Chem. Phys., 140, 18A507 (2014).). Finally, we applied these newly developed embedding methods to the task of designing new transition-metal catalysts for small-molecule activation. A central challenge in the development of inorganic hydrogen-evolution catalysts is to avoid deleterious coupling of the energetics of metal-site reduction from the kinetics of metal-hydride formation. In work that we are currently preparing for publication, we combined theoretical and experimental methods to investigate a new class of cobalt diimine-dioxime catalysts that shows promise for achieving this aim by introducing an intramolecular proton-shuttle via a pyridyl pendant group., The original document contains color images.

Methods that exploit the intrinsic locality of molecular interactions show significant promise in making tractable the electronic structure calculation of large-scale systems. In particular, embedded density functional theory (e-DFT) offers a formally exact approach to electronic structure calculations in which the interactions between subsystems are evaluated in terms of their electronic density. In the following dissertation, methodological advances of embedded density functional theory are described, numerically tested, and applied to real chemical systems. First, we describe an e-DFT protocol in which the non-additive kinetic energy component of the embedding potential is treated exactly. Then, we present a general implementation of the exact calculation of the non-additive kinetic potential (NAKP) and apply it to molecular systems. We demonstrate that the implementation using the exact NAKP is in excellent agreement with reference Kohn-Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures. Next, we introduce density-embedding techniques to enable the accurate and stable calculation of correlated wavefunction (CW) in complex environments. Embedding potentials calculated using e-DFT introduce the e ect of the environment on a subsystem for CW calculations (WFT-in-DFT). We demonstrate that WFT-in-DFT calculations are in good agreement with CW calculations performed on the full complex.

Our ARO-supported work includes key contributions to the development of rigorous quantum embedding methods for the calculation of ground- and excited-state potential energy surfaces. Quantum embedding has long been recognized as a promising strategy for vastly reducing the cost of rigorous electronic structure theory calculations. However, prior to our work in this area, density functional and wavefunction embedding approaches were only applicable to weakly interacting systems, a severe constraint that excluded essentially all condensed-phase and reactive chemical applications. By developing both inversion-based and projection-based strategies to enable accurate embedding in the context of strongly interacting (i.e., covalently or hydrogen-bonded) systems, we have expanded the applicability of quantum embedding methodologies, an area of intense interest. In addition to developing new algorithms and software, we have demonstrated that our approach enables simulation of large systems with sub-linear scaling of the required computational time; and we have further demonstrated that it dramatically reduces the cost of accurately describing transition-metal complexes and large molecules and clusters. This work opens new doors for the accurate description of decomposition, catalytic, and electronically non-adiabatic processes in complex systems. This research meets the aims of the Army Research Office by significantly advancing the scope and accuracy of first-principles molecular simulations in complex, reactive systems.

We demonstrate sideband-resolved Si3N4 optomechanical crystals supporting 10(exp5) quality factor optical modes at 980 nm, coupled to nearly equal to 4 GHz frequency mechanical modes with quality factors of nearly equal to 3000. Optomechanical electromagnetically induced transparency and absorption are observed at room temperature and in atmosphere with intracavity photon numbers in excess of 10(exp4)., Published in Applied Physics Letters, v104 p041101-1/041101-4, 27 January 2014.

This document aims to provide information to the United States Air Force about the current status of research in rarefied gas dynamics and related fields, primarily via the 29th International Symposium on Rarefied Gas Dynamics (RGD29) held in Xi'an, China, July 13-18, 2014. The RGD Symposia take place every two years. They are a forum at which scientists and engineers report new developments in the field., Reporting on the International Symposium on Rarefied Gas Dynamics (29th), RGD29, held in Xi an, China, 13-18 July 2014.

Solar cell efficiency is maximized through multijunction architectures that minimize carrier thermalization and increase absorption. Previous proposals suggest that the maximum efficiency for a finite number of subcells is achieved for designs that optimize for light trapping over radiative coupling. We instead show that structures with radiative coupling and back reflectors for light trapping, e.g. spectrum-splitting cells, can achieve higher conversion efficiencies. We model a compatible geometry, the polyhedral specular reflector. We analyze and experimentally verify the effects of spectral window and radiative coupling on voltage and power. Our results indicate that radiative coupling with back reflectors leads to higher efficiencies than previously studied architectures for practical multijunction architectures (i.e., or = 20 subcells)., Published in Energy & Environmental Science, 10.1039/c4ee01060d, 2014.

Using an optical probe along with single photon detection we have performed e ective phonon counting measurements of the acoustic emission and absorption processes in a nanomechanical resonator. Applying these measurements in a Hanbury Brown and Twiss set-up, phonon correlations of the nanomechanical resonator are explored from below to above threshold of a parametric instability leading to self-oscillation of the resonator. Discussion of the results in terms of a \phonon laser, and analysis of the sensitivity of the phonon counting technique are presented

In this final report, we document the achievements made as a result of this Young Investigator Program (YIP) project. We worked on the development of multi scale energy-consistent algorithms to simulate and capture flow phenomena in granular materials. For this, we have made progress in three key areas: i) the development of unprecedented algorithms at the grain scale to simulate flow of complex (real) granular media; ii) the development of multiscale and continuum approaches to simulate the continuum behavior of granular media under large flow; iii) the development of experimental techniques and approaches to model the behavior of granular materials under extreme avalanche flow. In the area of algorithmic development at the grain scale, we have successfully developed a technique, called the granular element method (GEM), and have been able to bypass all the major shortcomings of current discrete element methods (DEM). We have shown that the technique is not only much more efficient algorithmically, but displays a degree of accuracy that is unprecedented for discrete methods. In the area of multiscale and continuum approaches, we have focused our attention on the development of continuum models that are micro-inspired and in this way can bypass much of the phenomenology that plagues current continuum models for granular flow. Finally, in the areas of experimental techniques, we have been able to use clever flow experiments in tandem with our advanced models to decipher the mechanisms controlling the main continuum features observed previously but that have not been able to be captured comprehensively in models. The consequences of these advancements are broad and deep. The GEM method has revolutionized the accuracy of discrete methods: capturing real material behavior for the first time. The multiscale continuum models have been able to explain the source of rate dependence in frictional resistance., The original document contains color images.

The program goal was to develop compact frequency sources capable of maintaining low phase noise under high accelerations or vibrations and over a wide temperature range. The effort strived to better understand, engineer, and demonstrate nonlinear-dynamics-enabled nanoelectromechanical system (NEMS) frequency-source technology., Prepared in cooperation with Michigan State University, East Lansing, MI. Sponsored in part by DARPA/MTO.

Ramsey spectroscopy has become a powerful technique for probing nonequilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to assume the external (motional) degrees of freedom are decoupled from the pseudospin degrees of freedom. Determining the validity of this approximation known as the spin model approximation has not been addressed in detail. Here we shed light in this direction by calculating Ramsey dynamics exactly for two interacting spin-1/2 particles in a harmonic trap. We focus on s-wave-interacting fermions in quasi one- and two-dimensional geometries. We find that in one dimension the spin model assumption works well over a wide range of experimentally relevant conditions, but can fail at time scales longer than those set by the mean interaction energy. Surprisingly, in two dimensions a modified version of the spin model is exact to first order in the interaction strength. This analysis is important for a correct interpretation of Ramsey spectroscopy and has broad applications ranging from precision measurements to quantum information and to fundamental probes of many-body systems., Published in Physical Review Letters, v112 p123001-1/123001-5, 2014.

Established cavity designs for commercial semiconductor lasers are mostly based on Fabry-Perot etalons for edge or surface emission. Similar to the trend of miniaturization of integrated electronics, there is a quest to shrink the size of semiconductor lasers, in order to pack more devices on less material and in the hope of modifying the laser efficiency with control over spontaneous emission in tiny cavities. In this program, we have used microdisk, vertical-cavity and photonic crystal cavities to confine light into smaller and smaller volumes., The original document contains color images.

We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p-wave and s-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA 87Sr and NIST 171Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems., Sponsored in part by Army Research Office and DARPA.

The goals of this effort are to observe the impact of waves on the sea ice cover using remote sensing and to provide analyzed results will be provided to coupled ocean-ice modeling efforts for evaluation and potential incorporation as parameters for model validation and improvement, in support of the Office of Naval Research Arctic and Global Prediction Program.

Fundamental developments in this project include (1) an analytic theory of pooling of infrared quanta on surfaces, with a potential application to laser-selective chemistry, (2) diffusion-electron transfer reaction rate theory for intermittent fluorescence of semiconductor nanoparticles, explaining the power law distribution of bright and dark periods and the exponential tail for bright periods, (3) theory of intermittent fluorescence of dyes on semiconductor nanoparticles and plane surfaces, (4) approximate semiclassical instanton theory for H-tunneling in small and large systems, computationally less demanding than more accurate approaches and whose utility is being explored, and (5) marked improvement of the range of validity of the maximum likelihood method so as to treat power law data, converging when the common method diverges. The theory of infrared quanta pooling (accumulation of quanta in individual adsorbed molecules on surfaces) rapid equilibration of the quanta was assumed among the sites and the results were compared with a kinetic Monte Carlo computational solution of the coupled kinetic differential equations. When the assumption is valid (high light intensities), the theory has applications to infrared laser selective chemistry on surfaces. Research has also been initiated on a fundamental electron transfer theory for perovskite-like and other photovoltaic solar cells.

High throughput (combinatorial) materials science methodology is a relatively new research paradigm that offers the promise of rapid and efficient materials screening, optimization, and discovery. The paradigm started in the pharmaceutical industry but was rapidly adopted to accelerate materials research in a wide variety of areas. High throughput experiments are characterized by synthesis of a library sample that contains the materials variation of interest (typically composition), and rapid and localized measurement schemes that result in massive data sets. Because the data are collected at the same time on the same library sample, they can be highly uniform with respect to fixed processing parameters. This article critically reviews the literature pertaining to applications of combinatorial materials science for electronic, magnetic, optical, and energy-related materials. It is expected that high throughput methodologies will facilitate commercialization of novel materials for these critically important applications. Despite the overwhelming evidence presented in this paper that high throughput studies can effectively inform commercial practice, in our perception, it remains an underutilized research and development tool. Part of this perception may be due to the inaccessibility of proprietary industrial research and development practices, but clearly the initial cost and availability of high throughput laboratory equipment plays a role. Combinatorial materials science has traditionally been focused on materials discovery, screening, and optimization to combat the extremely high cost and long development times for new materials and their introduction into commerce., The original document contains color images. Pub. in Journal of Applied Physics, v113 n23, p231101-1/231101-52, 2013.

This project focused on transmission and storage of information in networks, and considered robustness to adversarial errors, packet losses, link failure, mobility and topology dynamics. It established fundamental limits on performance (capacity, reliability and delay), as well as practical coding schemes and optimization techniques. Among our results, we developed network error correction theory for networks with non-uniform link capacities, non-multicast and a priori unknown number of errors. We applied this theory to design coding schemes for robust key distribution and streaming. We designed codes for error estimation, universal multicast codes robust to changes in network size and number of receivers, and error detection codes for distributed storage. We proposed efficient methods for obtaining network capacity bounds, characterized the impact of the failure of a single link on capacity of some families of networks, and showed equivalence between the Shannon capacity for saturated sources and the stable capacity of networks with probabilistic message arrivals. We characterized optimal resource allocation for maximizing the probability of data recovery under probabilistic access or failure of storage nodes, and optimizing transmission delay in disruption tolerant networks., The original document contains color images.

This report documents the progress of the MURI on 'Materials on the brink: Unprecedented transforming materials' for the period of 2012-2013., The original document contains color images.

Although autism spectrum disorder (ASD) is defined by core behavioral impairments, gastrointestinal (GI) symptoms are commonly reported. Subsets of ASD individuals display dysbiosis of the gut microbiome, and some exhibit increased intestinal permeability. We demonstrate GI barrier defects in a mouse model of an important ASD risk factor, maternal immune activation (MIA). Remarkably, oral treatment of MIA offspring with the human commensal Bacteroides fragilis corrects gut permeability and ameliorates defects in communicative, stereotypic, anxiety-like and sensorimotor behaviors. MIA offspring also display an altered serum metabolomic profile, and B. fragilis normalizes levels of several of the serum metabolites. These findings suggest a gut-microbiome-brain connection in autism, and identify a potential probiotic therapy for ASD. We have now developed assays for some of these serum metabolites and are beginning to assay them in ASD serum samples, The original document contains color images.

Recent empirical research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the l1 minimization method for identifying a sparse vector from random linear samples. Indeed, this approach succeeds with high probability when the number of samples exceeds a threshold that depends on the sparsity level; otherwise it fails with high probability. This paper provides the first rigorous analysis that explains why phase transitions are ubiquitous in random convex optimization problems. It also describes tools for making reliable predictions about the quantitative aspects of the transition, including the location and the width of the transition region. These techniques apply to regularized linear inverse problems with random measurements, to demixing problems under a random incoherence model and also to cone programs with random affine constraints. These applications depend on foundational research in conic geometry. This paper introduces a new summary parameter, called the statistical dimension, that canonically extends the dimension of a linear subspace to the class of convex cones. The main technical result demonstrates that the sequence of conic intrinsic volumes of a convex cone concentrates sharply near the statistical dimension. This fact leads to an approximate version of the conic kinematic formula that gives bounds on the probability that a randomly oriented cone shares a ray with a fixed cone., Sponsored in part by AFOSR Contract no. FA9550-09-1-0643.

Wavepackets are large-scale turbulent structures that are correlated and advected over distances that are large compared to the integral scales of turbulence, and have been shown to be responsible for the peak noise radiated at aft angles to the jet axis. The present paper discusses linear models of these wavepackets for supersonic turbulent jets based on Parabolized Stability Equations (PSE). In the past, results of this approach were shown to be in excellent agreement with coherent structures extracted from experimental near-field pressure and velocity data in subsonic jets. Here, we make use of a Large Eddy Simulation (LES) database for an isothermal and a moderately heated Mach 1.5 turbulent jets. Careful comparisons of the PSE models with near-field pressure fields from LES, filtered by means of Proper Orthogonal Decomposition (POD), demonstrate acceptable fidelity of the model. Finally, the acoustic far-field associated with the PSE wavepackets is computed using a Kirchhoff surface method, capturing reasonably well the far-field pressure at angles close to the peak., Presented at the AIAA/CEAS Aeroacoustics Conference (19th) held in Berlin, Germany on 27-29 May 2013. Sponsored in part by ONR.

Modern aircraft increasingly rely on electric power for subsystems that have traditionally run on mechanical power. The complexity and safety-criticality of aircraft electric power systems have therefore increased, rendering the design of these systems more challenging. This work is motivated by the potential that correct-by-construction reactive controller synthesis tools may have in increasing the effectiveness of the electric power system design cycle. In particular, we have built an experimental hardware platform that captures some key elements of aircraft electric power systems within a simplified setting. We intend to use this platform for validating the applicability of theoretical advances in correct-by-construction control synthesis and for studying implementation-related challenges. We demonstrate a simple design work ow from formal specifications to auto-generated code that can run on software models and be used in hardware implementation. We show some preliminary results with different control architectures on the developed hardware testbed., Prepared in collaboration with the University of Pennsylvania and KTH Royal Institute of Technology.

We present a new method for stability and modal analysis of shear flows and their acoustic radiation. The Euler equations are modified and solved as a spatial initial value problem in which initial perturbations are specified at the ow inlet and propagated downstream by integration of the equations. The modified equations, which we call one-way Euler equations, differ from the usual Euler equations in that they do not support upstream acoustic waves. It is necessary to remove these modes from the Euler operator because, if retained, they cause instability in the spatial marching procedure. These modes are removed using a two-step process. First, the upstream modes are partially decoupled from the down- stream modes using a linear similarity transformation. Second, the error in the first step is eliminated using a convergent recursive filtering technique. A previous spatial marching method called the parabolized stability equations uses numerical damping to stabilize the march, but this has the unintended consequence of heavily damping the downstream acoustic waves. Therefore, the one-way Euler equation could be used to obtain improved accuracy over the parabolized stability equations as a low-order model for noise simulation of mixing layers and jets., Presented at the 19th AIAA/CEAS Aeroacoustics Conference held in Berlin, Germany on 27-29 May 2013. Sponsored in part by NAVAIR.

The development of a room temperature (50C) fuel cell that could use a generally available fuel such as JP8 would be most valuable. However there are no known catalysts that can selectively activate the CC bonds of such fuels at such temperature. The goal of this project was to investigate the whether it is plausible to develop such a catalysts. To do this we used validated first-principles (quantum mechanics) based simulations to investigate the barriers for alkyl carbon-carbon cleavage for two prototypical systems: A metal alloy catalyst & An organometallic cluster catalyst. That might serve as an anode for electrochemical power generation. For the metal alloy catalyst we used a Top-down approach where we determined the bond energies to the alloy catalyst to various fuel fragments necessary to achieve room temperature decomposition of butane and oxidation to CO2. For organometallic cluster catalyst we used a bottom-up strategy, determining specific metals, ligand compositions, solvents and operating conditions to evaluate which conditions could lead to reasonable rates at room temperature. For the bottom up approach we the density functional theory (DFT) form of quantum mechanics to investigated homogeneous catalysts. We decided that Rh is the best metal for a low temperature oxidation of C-H and C-C bonds. We then considered a number of possible mechanisms and reaction pathways for butane oxidation. The lowest barriers we determined for these mechanisms are 30 kcal/mol, which is probably too high for reasonable rates at room temperature (probably requiring 200C). We then began a study of Rh/O2 complexes, such as spin singlet RhCl3(O2)2- and the spin doublet RhIII superoxide complex RhCl3(H2O)(O2)1-,which we consider would be accessible under reaction conditions. We conclude that these might serve as 3- or 4-electron oxidants. Further research is needed to draw a firm conclusion about prospect of these and other possible metal complexes to provide s, The original document contains color images.

This is a summary of significant accomplishments in investigations on the dispersion, mixing, and combustion in uniform- and variable-density air-breathing high-speed propulsion flows related to scramjet propulsion. In experimental work, progress made in the development of testsection modifications allowed inclined-jet injection in supersonic flow to be studied with and without chemical reactions and heat release. Work on hydrocarbon flames was completed and published, and preliminary investigations on high-pressure effects were conducted. Large-eddy simulations (LES) were performed on chemically reacting flows in complex geometries, achieving both grid convergence and agreement with experiment. The same computational framework was successfully applied to simulations of inclined-jet injection into a supersonic Mach 3.6 stream. A model for an ethylene-fueled scramjet was developed to facilitate parametric studies of ignition delays in flight-relevant environments. Accomplishments in diagnostic developments enabled many of the experiments and included high framing-rate schlieren digitalimaging technologies, two-dimensional temperature-field measurement technologies, advances in data processing and visualization, and advances in multi-component computer control of experiments.

We describe one-dimensional (1D) photonic crystals that support a guided mode suitable for atom trapping within a unit cell, as well as a second probe mode with strong atom photon interactions. A new hybrid trap is analyzed that combines optical and Casimir Polder forces to form stable traps for neutral atoms in dielectric nanostructures. By suitable design of the band structure, the atomic spontaneous emission rate into the probe mode can exceed the rate into all other modes by more than tenfold. The unprecedented single-atom reflectivity r0 / 0.9 for the guided probe field should enable diverse investigations of photon-mediated interactions for 1D atom chains and cavity quantum electrodynamics., Published in the New Journal of Physics, v15 article ID 083026, 9 Aug 2013. Prepared in collaboration with the Institute for Quantum Information and Matter and the Thomas J Watson, Sr, Laboratory of Applied Physics, California Institute of Technology, Pasadena, and the ICFO Institut de Ciencies Fotoniques, Barcelona, Spain. Sponsored in part by DoD and NSF PHY0652914.

The gas-phase chemistry of the hypergolic system CH3NHNH2 monomethylhydrazine (MMH), with oxidizers NO2/N2O4 at room temperature and 1 atm N2 was investigated experimentally using a gold-coated chamber reactor, coupled with a Fourier transform infrared (FTIR) spectrometer. The IR-active species identified in the early reactions include HONO, monomethylhydrazinium nitrite (MMH . HONO), methyl diazene (CH3N=NH), methyl nitrate (CH3ONO2), methyl nitrite (CH3ONO), nitromethane (CH3NO2), methyl azide (CH3N3), H2O, N2O and NO. In order to elucidate the mechanisms by which these observed products are formed, we carried out quantum mechanics calculations [CCSD(T)/M06-2X] for the possible reaction pathways. Based on these studies, we propose that the oxidation of MMH in an atmosphere of NO2 occurs via two mechanisms: (1) sequential H-abstraction and HONO formation, and (2) reaction of MMH with asymmetric ONONO2, leading to formation of methyl nitrate. These mechanisms successfully explain all intermediates observed experimentally. We conclude that the formation of asymmetric ONONO2 is assisted by an aerosol formed by HONO and MMH that provides a large surface area for ONONO2 to condense, leading to the generation of methyl nitrate. Thus we propose that the overall pre-ignition process involves both gas-phase and aerosol-phase reactions., Published in Combustion and Flame, v160 p970-981, 15 Feb 2013. Preapred in collaboration with the Materials and Process Simulation Center (MSC), California Institute of Technology, Pasadena and the Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park. Sponsored in part by ARL.

We present the measurement of squeezed light generation using an engineered optomechanical system fabricated from a silicon microchip and composed of a micromechanical resonator coupled to a nanophotonic cavity. Laser light is used to measure the fluctuations in the position of the mechanical resonator at a measurement rate comparable to the free dynamics of the mechanical resonator, and greater than its thermal decoherence rate. By approaching the strong continuous measurement regime we observe, through homodyne detection, non-trivial modifications of the reflected light's vacuum fluctuation spectrum. In spite of the mechanical resonator's highly excited thermal state (10,000 phonons), we observe squeezing at the level of 4.5 plus or minus 0.5% below that of shot-noise over a few MHz bandwidth around the mechanical resonance frequency of 28 MHz. This squeezing is interpreted as an unambiguous quantum signature of radiation pressure shot-noise., Sponsored in part by DARPA.