Experimental measurement of the geometric phase of non-geodesic circles.

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 Poincaré sphere of polarizations of Gaussian beams.

Tilted Poincaré sphere geodesics.

We provide the first, to the best of our knowledge, experimental demonstration of a geometric phase generated in association with closed Poincaré sphere trajectories comprising 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 Poincaré sphere circuits are driven by beam transit through a series of π-converters and Dove prisms.

Hydrodynamics explanation for the splitting of higher-charge optical 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.

Optical vortex braiding with Bessel beams.

We propose the braiding of optical vortices in a laser beam with more than $ 2\pi $2π 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 measurements 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.

Identification and Resolution of Unphysical Multielectron Excitations in the Real-Time Time-Dependent Kohn-Sham Formulation.

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.

Entangled excitons via spontaneous down-conversion.

A class of CN 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 down-conversion 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.

Quantum cutting using organic molecules.

A methodology is presented in which a combination of quantum electrodynamics, time-dependent perturbation theory, and computational electronic structure analysis allow the prospect for organic quantum cutting to be quantitatively examined from first principles. The internal quantum yield of quantum cutting is ultimately expressed in terms of rate equations that account for all relevant processes. These are populated with excited state properties found using time-dependent density functional theory and configuration interaction methods. The rate equations are incorporated into an optimization routine in which the quantum yield is maximized by changing the spacing and orientation of the molecules. Adapting design criteria first developed for energy pooling, a system of squarylium dye III and fluorene was identified as being capable of carrying out meaningful quantum cutting. With relative position and orientation optimized, the internal quantum yield of this test system is predicted to be 1.2. In the absence of non-radiative decay, the internal yield is predicted to be 1.9.

Laser Level Scheme of Self-Interstitials in Epitaxial Ge Dots Encapsulated in Si.

Recently, it was shown that lasing from epitaxial Ge quantum dots (QDs) on Si substrates can be obtained if they are partially amorphized by Ge ion bombardment (GIB). Here, we present a model for the microscopic origin of the radiative transitions leading to enhanced photoluminescence (PL) from such GIB-QDs. We provide an energy level scheme for GIB-QDs in a crystalline Si matrix that is based on atomistic modeling with Monte Carlo (MC) analysis and density functional theory (DFT). The level scheme is consistent with a broad variety of PL experiments performed on as-grown and annealed GIB-QDs. Our results show that an extended point defect consisting of a split-[110] self-interstitial surrounded by a distorted crystal lattice of about 45 atoms leads to electronic states at the Γ-point of the Brillouin zone well below the conduction band minimum of crystalline Ge. Such defects in Ge QDs allow direct transitions of electrons localized at the split-interstitial with holes confined in the Ge QD. We identify the relevant growth and annealing parameters that will let GIB-QDs be employed as an efficient laser active medium.

Bandgap Tuning of Silicon Quantum Dots by Surface Functionalization with Conjugated Organic Groups.

The quantum confinement and enhanced optical properties of silicon quantum dots (SiQDs) make them attractive as an inexpensive and nontoxic material for a variety of applications such as light emitting technologies (lighting, displays, sensors) and photovoltaics. However, experimental demonstration of these properties and practical application into optoelectronic devices have been limited as SiQDs are generally passivated with covalently bound insulating alkyl chains that limit charge transport. In this work, we show that strategically designed triphenylamine-based surface ligands covalently bonded to the SiQD surface using conjugated vinyl connectivity results in a 70 nm red-shifted photoluminescence relative to their decyl-capped control counterparts. This suggests that electron density from the SiQD is delocalized into the surface ligands to effectively create a larger hybrid QD with possible macroscopic charge transport properties.

Energy pooling upconversion in organic molecular systems.

A combination of molecular quantum electrodynamics, perturbation theory, and ab initio calculations was used to create a computational methodology capable of estimating the rate of three-body singlet upconversion in organic molecular assemblies. The approach was applied to quantify the conditions under which such relaxation rates, known as energy pooling, become meaningful for two test systems, stilbene-fluorescein and hexabenzocoronene-oligothiophene. Both exhibit low intramolecular conversion, but intermolecular configurations exist in which pooling efficiency is at least 90% when placed in competition with more conventional relaxation pathways. For stilbene-fluorescein, the results are consistent with data generated in an earlier experimental investigation. Exercising these model systems facilitated the development of a set of design rules for the optimization of energy pooling.

Tailoring the optical gap of silicon quantum dots without changing their size.

The absorption of photons through the direct generation of spatially separated excitons at dot-ligand interfaces is proposed as a promising strategy for tailoring the optical gap of small silicon quantum dots independent of their size. This removes a primary drawback for the use of very small dots in broad range of applications. For instance, the strategy can be applied to solar energy technologies to align the absorption of such dots with the peak of the solar spectrum. The key is to establish both a Type-II energy level alignment and a strong electronic coupling between the dot and ligand. Our first principles analysis indicates that connecting conjugated organic ligands to silicon quantum dots using vinyl connectivity can satisfy both requirements. For a prototype assembly of 2.6 nm dots, we predict that triphenylamine termination will result in a 0.47 eV redshift along with an enhanced near-edge absorption character. Robustness analyses of the influence of oxidation on absorption and of extra alkyl ligands reveal that the control of both factors is important in practical applications.

Charge separation at nanoscale interfaces: energy-level alignment including two-quasiparticle interactions.

The universal and fundamental criteria for charge separation at interfaces involving nanoscale materials are investigated. In addition to the single-quasiparticle excitation, all the two-quasiparticle effects including exciton binding, Coulomb stabilization, and exciton transfer are considered, which play critical roles on nanoscale interfaces for optoelectronic applications. We propose a scheme allowing adding these two-quasiparticle interactions on top of the single-quasiparticle energy level alignment for determining and illuminating charge separation at nanoscale interfaces. Employing the many-body perturbation theory based on Green's functions, we quantitatively demonstrate that neglecting or simplifying these crucial two-quasiparticle interactions using less accurate methods is likely to predict qualitatively incorrect charge separation behaviors at nanoscale interfaces where quantum confinement dominates.

First principles analysis of the initial oxidation of Si(001) and Si(111) surfaces terminated with H and CH3.

Transition state analyses have been carried out within a density functional theory setting to explain and quantify the distinctly different ways in which hydrogen and methyl terminations serve to protect silicon surfaces from the earliest onset of oxidation. We find that oxidation occurs via direct dissociative adsorption, without any energy barrier, on Si(111) and reconstructed Si(001) that have been hydrogen terminated; oxidation initiates with a barrier of only 0.05 eV on unreconstructed Si(001). The commonly measured protection afforded by hydrogen is shown to derive from a coverage-dependent dissociation rate combined with barriers to the hopping of adsorbed oxygen atoms. Methyl termination, in contrast, offers an additional level of protection because oxygen must first undergo interactions with these ligands in a three-step process with significant energy barriers: adsorption of O(2) into a C-H bond to form a C-O-O-H intermediate; decomposition of C-O-O-H into C-O-H and C=O intermediates; and, finally, hopping of oxygen atoms from ligands to the substrate.

Confinement of vibrational modes within crystalline lattices using thin amorphous layers.

It is possible to confine vibrational modes to a crystal by encapsulating it within thin disordered layers with the same average properties as the crystal. This is not due to an impedance mismatch between materials but, rather, to higher order moments in the distribution of density and stiffness in the disordered phase-i.e. it is a result of material substructure. The concept is elucidated in an idealized one-dimensional setting and then demonstrated for a realistic nanocrystalline geometry. This offers the prospect of specifically engineering higher order property distributions as an alternate means of managing phonons.

Experimental demonstration of photon upconversion via cooperative energy pooling.

Photon upconversion is a fundamental interaction of light and matter that has applications in fields ranging from bioimaging to microfabrication. However, all photon upconversion methods demonstrated thus far involve challenging aspects, including requirements of high excitation intensities, degradation in ambient air, requirements of exotic materials or phases, or involvement of inherent energy loss processes. Here we experimentally demonstrate a mechanism of photon upconversion in a thin film, binary mixture of organic chromophores that provides a pathway to overcoming the aforementioned disadvantages. This singlet-based process, called Cooperative Energy Pooling (CEP), utilizes a sensitizer-acceptor design in which multiple photoexcited sensitizers resonantly and simultaneously transfer their energies to a higher-energy state on a single acceptor. Data from this proof-of-concept implementation is fit by a proposed model of the CEP process. Design guidelines are presented to facilitate further research and development of more optimized CEP systems.

Grain-boundary free energy in an assembly of elastic disks.

Grain-boundary free energy is estimated as a function of misoriention for symmetric tilt boundaries in an assembly of nearly hard disks. Fluctuating cell theory is used to accomplish this since the most common techniques for calculating interfacial free energy cannot be applied to such assemblies. The results are analogous to those obtained using a Leonard-Jones potential, but in this case the interfacial energy is dominated by an entropic contribution. Disk assemblies colorized with free and specific volume elucidate differences between these two characteristics of boundary structure. Profiles are also provided of the Helmholtz and Gibbs free energies as a function of distance from the grain boundaries. Low angle grain boundaries are shown to follow the classical relationship between dislocation orientation/spacing and misorientation angle.

Parametric links among Monte Carlo, phase-field, and sharp-interface models of interfacial motion.

Parametric links are made among three mesoscale simulation paradigms: phase-field, sharp-interface, and Monte Carlo. A two-dimensional, square lattice, 1/2 Ising model is considered for the Monte Carlo method, where an exact solution for the interfacial free energy is known. The Monte Carlo mobility is calibrated as a function of temperature using Glauber kinetics. A standard asymptotic analysis relates the phase-field and sharp-interface parameters, and this allows the phase-field and Monte Carlo parameters to be linked. The result is derived without bulk effects but is then applied to a set of simulations with the bulk driving force included. An error analysis identifies the domain over which the parametric relationships are accurate.

Efficient exciton transport between strongly quantum-confined silicon quantum dots.

Many-body Green function analysis and first-order perturbation theory 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 for the same center-to-center separation. This surprising result offers the prospect of designing assemblies of quantum dots through which excitons can travel for long distances, a game-changing paradigm shift for next-generation solar energy harvesting. We also find that surface reconstruction significantly influences the absorption cross section and leads to a large reduction in both transport rate and efficiency. Further, exciton transport efficiency is higher for hydrogen-passivated dots as compared with those terminated with more electronegative ligands, a result not predicted by Förster theory.

Optimal size regime for oxidation-resistant silicon quantum dots.

First-principles computations have been carried out to predict that appropriately terminated silicon quantum dots with diameters in the range of 1.2-2 nm will offer a superb resistance to oxidation. This is because surface treatments can produce dangling bond defect densities sufficiently low that dots of this size are unlikely to have any defect at all. On the other hand, these dots are large enough that the severe angles between facets do not expose bonds that are vulnerable to subsequent oxygen attack. The absence of both surface defects and geometry-related vulnerabilities allows even very short passivating ligands to generate an effective barrier, an important consideration for charge and exciton transport within quantum dot assemblies. Our computations, which employ many-body perturbation theory using Green functions, also indicate that dots within this size regime have optical and electronic properties that are robust to small amounts of inadvertent oxidation, and that any such oxygen incorporation is essentially frozen in place.