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The manifestation of entanglement within geometric phase is elucidated for spatially-structured bi-photons. Entanglement parameters are shown to influence holonomy in two distinct ways: through statistical superpositions of separable states; and via quantum correlation. These are entwined within geometric phase, motivating the construction of a projective, gauge-invariant measure that allows the manifestation of quantum correlation to be pinpointed and explained. An optical circuit consisting of a pair of misoriented mode converters gives a practical demonstration. This is facilitated by a novel pump engineering method which produces photon pairs with tunable entanglement., Comment: 12 pages, 8 figures

Polarization holonomy is analytically determined for maximally entangled photon pairs that transit a class of closed trajectories in the Kerr metric. This is used to define and investigate an entanglement holonomy not associated with constituent product states., Comment: 8 pages, 9 figures

Polarization holonomy is analytically determined for a class of closed, spherical trajectories of light transiting a black hole in the Kerr metric. The leading order geometric optics approximation admits a closed-form expression of such paths, and sets of source/receiver locations are quantified for a spectrum of black hole angular momenta. A conserved, conformal Yano-Killing scalar is then exploited to determine the evolving polarization. Polarization holonomy, the angle between outgoing and incoming polarizations, is quantified for the spectrum of admissible direct and retrograde trajectories. This offers a means of experimentally measuring Gravitational Faraday Rotation from a single, stationary position., Comment: 11 pages, 7 figures

We propose and experimentally demonstrate a method to directly measure the phase of biphoton states using an entangled mode as a collinear reference. The technique is demonstrated with entangled photonic spatial modes in the Laguerre-Gaussian basis, and it is applicable to any pure quantum system containing an exploitable reference state in its entanglement spectrum. As one particularly useful application, we use the new methodology to directly measure the geometric phase accumulation of entangled photons.

We observe and measure the nonequilibrium dynamics of optical vortices as a function of propagation distance through a nonlinear medium. The precession of a tilted-core vortex is quantified as is vortex-core sharpening, where the infinite width of a linear core subsequently shrinks and approaches the healing length of this nonlinear optical fluid. Experiments are performed with a variable-length nonlinear medium: a nonlinear fluid in a tank with an output window on a translating tube. This provides control over the distance the light propagates in the fluid and allows for the measurement of the dynamics throughout the entire propagation range. Results are compared to the predictions of a computational simulator to find the equivalent dimensionless nonlinear coefficient., Comment: 11 pages, 9 figures

We demonstrate entangled-state swapping, within the Hermite-Gaussian basis of first-order modes, directly from the process of spontaneous parametric down-conversion within a nonlinear crystal. The method works by explicitly tailoring the spatial structure of the pump photon such that it resembles the product of the desired entangled spatial modes exiting the crystal. Importantly, the result is an entangled state of balanced HG modes, which may be beneficial in applications that depend on symmetric accumulations of geometric phase through optics or in applications of quantum sensing and imaging with azimuthal sensitivity. Furthermore, the methods are readily adaptable to other spatial mode bases.

Linear combinations of Bessel beams can be used to effectively trap light within cylindrical domains. Such hard traps can be used to produce states that exhibit stationary arrays of optical vortices from the perspective of a steadily rotating frame. These patterned singularities can be engineered to have singularities of the same or mixed charges and the requisite rotation rates are quantized even though the setting is purely linear. A hydrodynamic interpretation is that the vortices are at rest within a compressible, two-dimensional fluid of light.

We present and implement a method for the experimental measurement of geometric phase of non-geodesic (small) circles on any SU(2) parameter space. This phase is measured by subtracting the dynamic phase contribution from the total phase accumulated. Our design does not require theoretical anticipation of this dynamic phase value and the methods are generally applicable to any system accessible to interferometric and projection measurements. Experimental implementations are presented for two settings: (1) the sphere of modes of orbital angular momentum, and (2) the Poincar\'e sphere of polarizations of Gaussian beams.

The self-annihilation of oppositely charged optical vortices in a quantum fluid is hindered by nonlinearity and promoted by radial confinement, resulting in rich life-cycle dynamics of such pairs. The competing effects generate a biome of peripheral vortices that can directly interact with the original pair to produce a sequence of surrogation events. Numerical simulation is used to elucidate the role of the vortex biome as a function of nonlinearity strength and the initial spacing between the engineered vortices. The results apply directly to other nonlinear quantum fluids as well and may be useful in the control of complex condensates in which vortex dynamics produce topologically protected phases., Comment: 8 pages, 7 figures

We provide the first experimental demonstration of geometric phase generated in association with closed Poincar\'e Sphere trajectories comprised of geodesic arcs that do not start, end, or necessarily even include, the north and south poles that represent pure Laguerre- Gaussian modes. Arbitrarily tilted (elliptical) single vortex states are prepared with a spatial light modulator, and Poincar\'e Sphere circuits are driven by beam transit through a series of {\pi}-converters and Dove prisms.

We propose the braiding of optical vortices in a laser beam with more than 2{\pi} rotation by superposing Bessel modes with a plane wave. We experimentally demonstrate this by using a Bessel-Gaussian beam and a coaxial Gaussian, and we present measurement of three complete braids. The amount of braiding is fundamentally limited only by the numerical aperture of the system and we discuss how braiding can be controlled experimentally for any number of vortices.

We show that a two-dimensional hydrodynamics model provides a physical explanation for the splitting of higher-charge optical vortices under elliptical deformations. The model is applicable to laser light and quantum fluids alike. The study delineates vortex breakups from vortex unions under different forms of asymmetry in the beam, and it is also applied to explain the motion of intact higher-charge vortices.

We present an analytical means of quantifying the fractional accumulation of geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a Sphere of Modes is endowed with a Supplementary Product Space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of geometric phase across a single lens as a function of initial state and lens position within the beam. It can be readily applied to a series of lenses as well., Comment: 10 pages, 13 figures

The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature., Comment: 10 figures; Comments are welcome

The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as the projection of a virtual construct, a circular vortex with a symmetry axis that is tilted with respect to the direction of propagation. The resulting kinetic equation offers insights into how tilt and vortex velocity coevolve in few-body nonequilibrium settings such as vortex pair nucleation and annihilation. The model is developed and applied in association with optical vortices, and optical experiments are used to verify its predictive power. It is valid for quantum fluids and classical hydrodynamics settings as well.

We resolve a fundamental issue associated with the conventional Kohn-Sham formulation of real-time time-dependent density functional theory. We show that unphysical multielectron excitations, generated during time propagation of the Kohn-Sham equations due to fixation of the total number of Kohn-Sham orbitals and their occupations, result in incorrect electron density and, therefore, wrong predictions of physical properties. A new formulation is proposed in that the number of Kohn-Sham orbitals and their occupations are updated on the fly, the unphysical multielectron excitations are removed, and the correct electron density is determined. The correctness of the new formulation is demonstrated by simulations of Rabi oscillation, as analytical results are available for comparison in the case of noninteracting electrons.

An exciton beam splitter is designed and computationally implemented, offering the prospect of excitonic interferometry. Exciton interaction between propagation conduits is modeled using a coupling parameter that varies with position. In practice, this variation can be realized by a change in the distance separating conduits as would occur if they crossed at oblique angles. Two such excitonic beam splitters can be combined to comprise an excitonic analog to a Mach-Zehnder interferometer, allowing the relative phase shift between two signals to be used to tailor the output populations on each channel. In contrast to optical splitters, an excitonic signal can be coherently split among more than two channels. These ideas are computationally demonstrated within an idealized setting in which each site is idealized as a two-level system. Physical implementations include molecular and coupled cavity settings as well as combinations of these. This adds to the developing inventory of excitonic analogs to optical elements., Comment: 5 pages, 7 figures

A chain of cofacial molecules with CN or CNh symmetry supports excitonic states with a screw-like structure. These can be quantified with the combination of an axial wavenumber and an azimuthal winding number. Combinations of these states can be used to construct excitonic wave packets that spiral down the chain with well-determined linear and angular momenta. These twisted exciton wave packets can be created and annihilated using laser pulses, and their angular momentum can be optically modified during transit. This allows for the creation of opto-excitonic circuits in which information, encoded in the angular momentum of light, is converted into excitonic wave packets that can be manipulated, transported, and then re-emitted. A tight-binding paradigm is used to demonstrate the key ideas. The approach is then extended to quantify the evolution of twisted exciton wave packets in a many-body, multi-level time-domain density functional theory setting. In both settings, numerical methods are developed that allow the site-to-site transfer of angular momentum to be quantified., Comment: 10 pages, 11 figures

A class of centrosymmetric molecules support excitons with a well-defined quasi-angular momentum. Cofacial arrangements of these molecules can be engineered so that quantum cutting produces a pair of excitons with angular momenta that are maximally entangled. The Bell state constituents can subsequently travel in opposite directions down molecular chains as ballistic wave packets. This is a direct excitonic analog to the entangled polarization states produced by the spontaneous parametric downconversion of light. As in optical settings, the ability to produce Bell states should enable foundational experiments and technologies based on non-local excitonic quantum correlation. The idea is elucidated with a combination of quantum electrodynamics theory and numerical simulation., Comment: 5 pages, 5 figures

The radiative lifetime of molecules or atoms can be increased by placing them within a tuned conductive cavity that inhibits spontaneous emission. This was examined as a possible means of enhancing three-body, singlet-based upconversion, known as energy pooling. Achieving efficient upconversion of light has potential applications in the fields of photovoltaics, biofuels, and medicine. The affect of the photonically constrained environment on pooling efficiency was quantified using a kinetic model populated with data from molecular quantum electrodynamics, perturbation theory, and ab initio calculations. This model was applied to a system with fluorescein donors and a hexabenzocoronene acceptor. Placing the molecules within a conducting cavity was found to increase the efficiency of energy pooling by increasing both the donor lifetime and the acceptor emission rate--i.e. a combination of inhibited spontaneous emission and the Purcell effect. A model system with a free-space pooling efficiency of 23% was found to have an efficiency of 47% in a rectangular cavity., Comment: 10 pages, 8 figures, Journal of Physical Chemistry C April 2017

Molecules with C_N or C_Nh symmetry can absorb quanta of optical angular momentum to generate twisted excitons with well-defined quasi-angular momenta of their own. Angular momentum is conserved in such interactions at the level of a paraxial approximation for the light beam. A sequence of absorption events can thus be used to create a range of excitonic angular momenta. Subsequent decay can produce radiation with a single angular momentum equal to that accumulated. Such molecules can thus be viewed as mediators for changing the angular momentum of light. This sidesteps the need to exploit nonlinear light-matter interactions based on higher-order susceptibilities. A tight-binding paradigm is used to verify angular momentum conservation and demonstrate how it can be exploited to change the angular momentum of light. The approach is then extended to a time-dependent density functional theory setting where the key results are shown to hold in a many-body, multi-level setting., Comment: 29 pages, 13 figures

Laguerre-Gaussian (LG) beams reflected from a multi-layered dielectric experience a shift in their centroid that is different than that from a single interface. This has been previously investigated for linearly polarized beams and, to a much lesser extent, beams with spin angular momentum. Here a combination of perturbation and computational analyses is used to provide a unified quantification of these shifts in layered dielectrics with two parallel interfaces. The approach is then extended to consider the qualitatively new behavior that results when the light is endowed with an intrinsic orbital angular momentum--i.e. vortex beams. Destructive interference causes singular lateral shifts in the centroid of the reflected vortex beam for which spin alone produces only a mild modulation. In the case of total internal reflection, both spin and intrinsic orbital angular momentum contribute to an enhancement of these lateral shifts as the interlayer thickness is decreased. This is just the opposite of the trend associated with longitudinal shifts. Two geometries are considered: air/glass/air and glass/air/glass multi-layers. A commonly available glass is used to show that vortex beams can result in centroid shifts on the order of microns for beams with a significant reflection coefficient., Comment: 10 pages, 11 figures

When a semiconductor absorbs light, the resulting electron-hole superposition amounts to a uncontrolled quantum ripple that eventually degenerates into diffusion. If the conformation of these excitonic superpositions could be engineered, though, they would constitute a new means of transporting information and energy. We show that properly designed laser pulses can be used to create such excitonic wave packets. They can be formed with a prescribed speed, direction and spectral make-up that allows them to be selectively passed, rejected or even dissociated using superlattices. Their coherence also provides a handle for manipulation using active, external controls. Energy and information can be conveniently processed and subsequently removed at a distant site by reversing the original procedure to produce a stimulated emission. The ability to create, manage and remove structured excitons comprises the foundation for opto-excitonic circuits with application to a wide range of quantum information, energy and light-flow technologies. The paradigm is demonstrated using both Tight-Binding and Time-Domain Density Functional Theory simulations., Comment: 16 figures

It is possible to confine vibrational modes to silicon nanocrystals by encapsulating them within hydrogenated amorphous silicon. This is not because of the small impedance mismatch between materials but, rather, is due to higher order moments in the distribution of density and stiffness in the amorphous phase--i.e. it is a result of material substructure. The concept is elucidated using an idealized one-dimensional setting and then demonstrated for a realistic nanocrystalline geometry. Beyond the immediate focus on amorphous encapsulation, this offers the prospect of specifically engineering higher order property distributions as an alternate means of managing phonons. The approach could be applied, for instance, to design deterministically ordered materials which exploit this means of control., Comment: 6 pages, 6 figures

Resonant energy transfer, energy transfer upconversion, and energy pooling are considered within optical cavities to elucidate the relationship between exciton dynamics and donor/acceptor separation distance. This is accomplished using perturbation theory to derive analytic expressions for the electric dipole coupling tensors of perfect planar and rectangular channel reflectors---directly related to a number of important energy transfer processes. In the near field, the separation dependence along the cavity axis is not influenced by the cavity and is essentially the same as for three-dimensional, free space. This is in sharp contrast to the reduced sensitivity to separation found in idealized low-dimensional settings. The cavity dynamics only correspond to their reduced dimensional counterparts in the far field where such excitonic processes are not typically of interest. There is an intermediate regime, though, where sufficiently small cavities cause a substantial decrease in separation sensitivity that results in one component of the dipole-dipole coupling tensor being much larger than those of free space., Comment: 7 figures

It is shown that quantum interference can be employed to create an exciton transistor. An applied potential gates the quasi-particle motion and also discriminates between quasi-particles of differing binding energy. When implemented within nanoscale assemblies, such control elements could mediate the flow of energy and information. Quantum interference can also be used to dissociate excitons as an alternative to using heterojunctions. A finite molecular setting is employed to exhibit the underlying discrete, two-particle, mesoscopic analog to Fano anti-resonance. Selected entanglement measures are shown to distinguish regimes of behavior which cannot be resolved from population dynamics alone., Comment: 5 pages, 5 figures

A first principles, excited state analysis is carried out to identify ways of producing silicon quantum dots with low excitonic reorganization energy. These focus on the general strategy of either reducing or constraining exciton-phonon coupling, and four approaches are explored. The results can be implemented in quantum dot solids to mitigate polaronic effects and increase the lifetime of coherent excitonic superpositions. It is demonstrated that such designs can also be used to alter the shape of the spectral density for reorganization so as to reduce the rates of both decoherence and dissipation. The results suggest that it may be possible to design quantum dot solids that support partially coherent exciton transport.

First-order perturbation theory and many-body Green function analysis are used to quantify the influence of size, surface reconstruction and surface treatment on exciton transport between small silicon quantum dots. Competing radiative processes are also considered in order to determine how exciton transport efficiency is influenced. The analysis shows that quantum confinement causes small (~1 nm) Si quantum dots to exhibit exciton transport efficiencies far exceeding that of their larger counterparts. We also find that surface reconstruction significantly influences the absorption cross section and leads to a large reduction in both transport rate and efficiency. Exciton transport efficiency is higher for hydrogen passivated dots as compared with those terminated with more electronegative ligands. This is because such ligands delocalize electron wave functions towards the surface and result in a lower dipole moment. Such behavior is not predicted by F\"orster theory, built on a dipole-dipole approximation, because higher order multi-poles play a significant role in the exciton dynamics.

A parallelized hybrid Monte Carlo (HMC) methodology is devised to quantify the microstructural evolution of polycrystalline material under elastic loading. The approach combines a time explicit material point method (MPM) for the mechanical stresses with a calibrated Monte Carlo (cMC) model for grain boundary kinetics. The computed elastic stress generates an additional driving force for grain boundary migration. The paradigm is developed, tested, and subsequently used to quantify the effect of elastic stress on the evolution of texture in nickel polycrystals. As expected, elastic loading favors grains which appear softer with respect to the loading direction. The rate of texture evolution is also quantified, and an internal variable rate equation is constructed which predicts the time evolution of the distribution of orientations., Comment: 20 pages, 8 figures

Toroidal carbon nanotubes can serve as hosts for encapsulated loops of atomic metal wires. Such composite structures have been analyzed using density functional theory for a semiconducting C$_{120}$ torus encapsulating chains of Fe, Au and Cu atoms. The sheathed metal necklaces form a zigzag structure and drops the HOMO/LUMO bandgap to less than 0.1 eV. The iron composite is ferromagnetic with a magnetic moment essentially the same as that of bcc iron. The azimuthal symmetry of these toroidal composites suggests that they may offer novel elecromagnetic properties not associated with straight, metal-encapsulated carbon nanotubes., Comment: 6 pages, 9 figures

An extended one-dimensional defect that has the potential to act as a conducting wire has been embedded in another perfect graphene sheet., Comment: 2 pages, 1 figure

The multiplication rates of hot carriers in CdSe quantum dots are quantified using an atomistic pseudopotential approach and first order perturbation theory. Both excited holes and electrons are considered, and electron-hole Coulomb interactions are accounted for. We find that holes have much higher multiplication rates than electrons with the same excess energy due to the larger density of final states (positive trions). When electron-hole pairs are generated by photon absorption, however, the net carrier multiplication rate is dominated by photogenerated electrons, because they have on average much higher excess energy. We also find, contrary to earlier studies, that the effective Coulomb coupling governing carrier multiplication is energy dependent. We show that smaller dots result in a decrease in the carrier multiplication rate for a given absolute photon energy. However, if the photon energy is scaled by the volume dependent optical gap, then smaller dots exhibit an enhancement in carrier multiplication for a given relative energy., Comment: 19 pages, 6 figures

A hybrid Monte Carlo (HMC) approach is employed to quantify the influence of inelastic deformation on the microstructural evolution of polycrystalline materials. This approach couples a time explicit material point method (MPM) for deformation with a calibrated Monte Carlo model for grain boundary motion. A rate-independent crystal plasticity model is implemented to account for localized plastic deformations in polycrystals. The dislocation energy difference between grains provides an additional driving force for texture evolution. This plastic driving force is then brought into a MC paradigm via parametric links between MC and sharp-interface (SI) kinetic models. The MC algorithm is implemented in a parallelized setting using a checkerboard updating scheme. As expected, plastic loading favors texture evolution for grains which have a bigger Schmid factor with respect to the loading direction, and these are the grains most easily removed by grain boundary motion. A macroscopic equation is developed to predict such texture evolution., Comment: 21 Pages

Four fundamental dimer manipulations can be used to produce a variety of localized and extended defect structures in graphene. Two-dimensional templates result in graphene allotropes, here viewed as extended defects, which can exhibit either metallic or semiconducting electrical character. \emph{Embedded allotropic ribbons}--i.e. thin swaths of the new allotropes--can also be created within graphene. We examine these ribbons and find that they maintain the electrical character of their parent allotrope even when only a few atoms in width. Such extended defects may facilitate the construction of monolithic electronic circuitry., Comment: 24 pages, 21 figures

We show that patterned defects can be used to disrupt the sub-lattice symmetry of graphene so as to open up a band gap. This way of modifying graphene's electronic structure does not rely on external agencies, the addition of new elements or special boundaries. The method is used to predict a planar, low energy, graphene allotrope with a band gap of 1.2 eV. This defect engineering also allows semiconducting ribbons of carbon to be fabricated within graphene. Linear arrangements of defects lead to naturally embedded ribbons of the semiconducting material in graphene, offering the prospect of two-dimensional circuit logic composed entirely of carbon., Comment: 4 pages, 5 figures

Computational experiments are used to show that grain boundary mobility is independent of driving force in a two-dimensional, square-lattice Ising model with Metropolis kinetics. This is established over the entire Monte Carlo temperature range. A calibration methodology is then introduced which endows the Monte Carlo algorithm with time and length scales and allows the Monte Carlo parameters to be expressed directly in terms of experimentally measurable parameters. A comparison of results obtained for a variety of driving forces and temperature conditions indicates that such Calibrated Monte Carlo models are able to capture the grain boundary kinetics predicted by sharp-interface theory., Comment: 9 pages, 13 figures

We analyze a new fundamental building block for monolithic nanoengineering on graphene: the Inverse-Stone-Thrower-Wales (ISTW) defect. The ISTW is formed from a pair of joined pentagonal carbon rings placed between a pair of heptagonal rings; the well-known Stone-Thrower-Wales (STW) defect is the same arrangement, but with the heptagonal rather than pentagonal rings joined. When removed and passivated with hydrogen, the structure constitutes a new molecule, diazulene, which may be viewed as the result of an ad-dimer defect on anthracene. Embedding diazulene in the honeycomb lattice, we study the effect of ad-dimers on planar graphene. Because the ISTW defect has yet to be experimentally identified, we examine several synthesis routes and find one for which the barrier is only slightly higher than that associated with adatom hopping on graphene. ISTW and STW defects may be viewed as fundamental building blocks for monolithic structures on graphene. We show how to construct extended defect domains on the surface of graphene in the form of blisters, bubbles, and ridges on a length scale as small as 2 angstroms by 7 angstroms. Our primary tool in these studies is density functional theory., Comment: 10 pages, 13 figures

Monolithic structures can be built into graphene by the addition and subsequent re-arrangement of carbon atoms. To this end, ad-dimers of carbon are a particularly attractive building block because a number of emerging technologies offer the promise of precisely placing them on carbon surfaces. In concert with the more common Stone-Wales defect, repeating patterns can be introduced to create as yet unrealized materials. The idea of building such allotropes out of defects is new, and we demonstrate the technique by constructing two-dimensional carbon allotropes known as haeckelite. We then extend the idea to create a new class of membranic carbon allotropes that we call \emph{dimerite}, composed exclusively of ad-dimer defects., Comment: 5 pages, 5 figures

We present a new way of nano-engineering graphene using defect domains. These regions have ring structures that depart from the usual honeycomb lattice, though each carbon atom still has three nearest neighbors. A set of stable domain structures is identified using density functional theory (DFT), including blisters, ridges, ribbons, and metacrystals. All such structures are made solely out of carbon; the smallest encompasses just 16 atoms. Blisters, ridges and metacrystals rise up out of the sheet, while ribbons remain flat. In the vicinity of vacancies, the reaction barriers to formation are sufficiently low that such defects could be synthesized through the thermally activated restructuring of coalesced adatoms., Comment: 4 pages, 5 figures