Abstract: We have studied the dependence of the binding energy of a cubane dimer on the mutual orientation of and the distance between the composing monomers employing the second-order Møller-Plesset perturbation scheme (MP2) with the cc-pVDZ molecular basis set. We have found that the MP2 contribution from the molecular correlations is responsible for the bound state of the cubane dimer, whereas the Hartree-Fock contribution remains anti-bonding at all intermolecular distances. Starting with two molecules in the standard orientation and centers of mass at (0,0,0) and (0,0,d), respectively, the maximal binding energy is found at d = 5.125 Å and one of the monomers rotated by 45° about the z-axis. This configuration implies that the hydrogen atoms belonging to different monomers tend to repel each other. The results are in agreement with experimental data on the optimal packing of cubane molecules in the solid state.

Abstract: Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow variations in the single-particle density of states driven by the size quantization. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size coherent effects, overlooked previously. The many-body physics is revealed here in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. The single-particle energy spectrum for the transverse dimensions is tightly bound, whereas for the longitudinal direction it resembles a quasi-free dispersion. This results in the formation of a series of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subband, and the aggregate condensate contains both BCS and BEC-like components.

Abstract: A uniform ground-state three-dimensional Fermi gas with short-range repulsive pairwise interaction is under consideration. Its kinetic and interaction energies are calculated up to the second order of the expansion in the gas parameter. Similar to recent results for an interacting Bose gas, the quantities in question are found to depend on the pairwise interaction through two characteristic lengths: the former, a, is the s-wave scattering length, and the latter, b, is related to a by b=a-m(partial derivativea/partial derivativem), where m stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest “from scratch.” The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.

Abstract: The recent demonstration of electron vortex beams has opened up the new possibility of studying orbital angular momentum (OAM) in the interaction between electron beams and matter. To this aim, methods to analyze the OAM of an electron beam are fundamentally important and a necessary next step. We demonstrate the measurement of electron beam OAM through a variety of techniques. The use of forked holographic masks, diffraction from geometric apertures, and diffraction from a knife edge and the application of an astigmatic lens are all experimentally demonstrated. The viability and limitations of each are discussed with supporting numerical simulations.

Abstract: By considering a cylindrically symmetric generalization of a plane wave, the first-order Born approximation of screened Coulomb scattering unfolds two new dimensions in the scattering problem: transverse momentum and orbital angular momentum of the incoming beam. In this paper, the elastic Coulomb scattering amplitude is calculated analytically for incoming Bessel beams. This reveals novel features occurring for wide-angle scattering and quantitative insights for small-angle vortex scattering. The result successfully generalizes the well-known Rutherford formula, incorporating transverse and orbital angular momentum into the formalism.

Abstract: We investigate topological aspects of subnanometer electron vortex beams upon elastic propagation through atomic scattering potentials. Two main aspects can be distinguished: (i) significantly reduced delocalization compared to a similar nonvortex beam if the beam centers on an atomic column and (ii) site symmetry dependent splitting of higher-order vortex beams. Furthermore, the results provide insight into the complex vortex line fabric within the elastically scattered wave containing characteristic vortex loops predominantly attached to atomic columns and characteristic twists of vortex lines around atomic columns. DOI: 10.1103/PhysRevA.87.033834

Abstract: The orbital angular momentum (OAM) of light and matter waves is a parameter that has been getting increasingly more attention over the past couple of years. Beams with a well-defined OAM, the so-called vortex beams, are applied already in, e.g., telecommunication, astrophysics, nanomanipulation, and chiral measurements in optics and electron microscopy. Also, the OAM of a wave induced by the interaction with a sample has attracted a lot of interest. In all these experiments it is crucial to measure the exact (local) OAM content of the wave, whether it is an incoming vortex beam or an exit wave after interacting with a sample. In this work we investigate the use of spiral phase plates (SPPs) as an alternative to the programmable phase plates used in optics to measure OAM. We derive analytically how these can be used to study the local OAM components of any wave function. By means of numerical simulations we illustrate how the OAM of a pure vortex beam can be measured. We also look at a sum of misaligned vortex beams and show how, by using SPPs, the position and the OAM of each individual beam can be detected. Finally, we look at the OAM induced by a magnetic dipole on a free-electron wave and show how the SPP can be used to localize the magnetic poles and measure their “magnetic charge.” Although our findings can be applied to study the OAM of any wave function, our findings are of particular interest for electron microscopy where versatile programmable phase plates do not yet exist.

Abstract: The Higgs amplitude mode of the order parameter of an ultracold confined Fermi gas in the BCS regime after a quench of the coupling constant is analyzed theoretically. A characteristic feature is a damped oscillation which at a certain transition time changes into a rather irregular dynamics. We compare the numerical solution of the full set of nonlinear equations of motion for the normal and anomalous Bogoliubov quasiparticle excitations with a linearized approximation. In doing so the transition time as well as the difference between resonant systems, i.e., systems where the Fermi energy is close to a sub-band minimum, and off-resonant systems can be well understood and traced back to the system and geometry parameters.

Abstract: Friedel's law states that the modulus of the Fourier transform of real functions is centrosymmetric, while the phase is antisymmetric. As a consequence of this, elastic scattering of plane-wave photons or electrons within the first-order Born-approximation, as well as Fraunhofer diffraction on any aperture, is bound to result in centrosymmetric diffraction patterns. Friedel's law, however, does not apply for vortex beams, and centrosymmetry in general is not present in their diffraction patterns. In this work we extend Friedel's law for vortex beams by showing that the diffraction patterns of vortex beams with opposite topological charge, scattered on the same two-dimensional potential, always are centrosymmetric to one another, regardless of the symmetry of the scattering object. We verify our statement by means of numerical simulations and experimental data. Our research provides deeper understanding in vortex-beam diffraction and can be used to design new experiments to measure the topological charge of vortex beams with diffraction gratings or to study general vortex-beam diffraction.

Abstract: We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system.

Abstract: We report on the pressure-driven superconductor-insulator transition in heavily boron-doped nanodiamond films. By systematically increasing the pressure, we suppress the Josephson coupling between the superconducting nanodiamond grains. The diminished intergrain coupling gives rise to an overall insulating state in the films, which is interpreted in the framework of a parallel-series circuit model to be the result of bosonic insulators with preserved localized intragrain superconducting order parameters. Our investigation opens up perspectives for the application of high pressure in research on quantum confinement and coherence. Our data unveil the percolative nature of the electrical transport in nanodiamond films, and highlight the essential role of grain boundaries in determining the electronic properties of this material.

Abstract: Nano-sized nitrogen-doped carbon spheres are synthesized from two cheap, readily available and sustainable precursors: tannic acid and urea. In combination with a polymer structuring agent, nitrogen content, sphere size and the surface (up to 400 m(2)g(-1)) can be conveniently tuned by the precursor ratio, temperature and structuring agent content. Because the chosen precursors allow simple oven synthesis and avoid harsh conditions, this carbon nanosphere platform offers a more sustainable alternative to classical soots, for example, as printing pigments or conduction soots. The carbon spheres are demonstrated to be a promising as conductive carbon additive in anode materials for lithium ion batteries.