Showing papers on "Quadrupole published in 2019"

Helical Topological Edge States in a Quadrupole Phase

Abstract: A topological electric quadrupole is a recently proposed concept that extends the theory of electric polarization of crystals to higher orders. Such a quadrupole phase supports topological states localized on both edges and corners. In this work, we show that in a quadrupole phase of a honeycomb lattice, topological helical edge states and pseudospin-polarized corner states appear by making use of a pseudospin degree of freedom related to point group symmetry. Furthermore, we argue that a general condition for the emergence of helical edge states in a (pseudo)spinful quadrupole phase is the existence of either mirror or time-reversal symmetry. Our results offer a way of generating topological helical edge states without spin-orbital couplings.

Quantized octupole acoustic topological insulator

Abstract: The Berry phase associated with energy bands in crystals can lead to quantized quantities, such as the quantization of electric dipole polarization in an insulator, known as a one-dimensional (1D) topological insulator (TI) phase. Recent theories have generalized such quantization from dipole to higher multipole moments, giving rise to the discovery of multipole TIs, which exhibit a cascade hierarchy of multipole topology at boundaries of boundaries: A quantized octupole moment in the three-dimensional (3D) bulk can induce quantized quadrupole moments on its two-dimensional (2D) surfaces, which then produce quantized dipole moments along 1D hinges. The model of 2D quadrupole TI has been realized in various classical structures, exhibiting zero-dimensional (0D) in-gap corner states. Here we report on the realization of a quantized octupole TI on the platform of a 3D acoustic metamaterial. By direct acoustic measurement, we observe 0D corner states, 1D hinge states, 2D surface states, and 3D bulk states, as a consequence of the topological hierarchy from octupole moment to quadrupole and dipole moment. The critical conditions of forming a nontrivial octupole moment are further demonstrated by comparing with another two samples possessing a trivial octupole moment. Our work thus establishes the multipole topology and its full cascade hierarchy in 3D geometries.

Many-Body Electric Multipole Operators in Extended Systems

Abstract: The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta [Phys. Rev. Lett. 80, 1800 (1998)], who developed a formalism to calculate the electronic polarization as an expectation value of a many-body operator, to include higher multipole moments, e.g., quadrupole and octupole. We define $n\mathrm{th}$-order multipole operators whose expectation values can be used to calculate the $n\mathrm{th}$ multipole moment when all of the lower moments are vanishing (modulo a quantum). We show that changes in our operators are tied to flows of $n\ensuremath{-}1\mathrm{st}$ multipole currents, and encode the adiabatic evolution of the system in the presence of an $n\ensuremath{-}1\mathrm{st}$ gradient of the electric field. Finally, we test our operators on a set of tight-binding models to show that they correctly determine the phase diagrams of topological quadrupole and octupole models, capture an adiabatic quadrupole pump, and distinguish a bulk quadrupole moment from other mechanisms that generate corner charges.

Impact of molecular quadrupole moments on the energy levels at organic heterojunctions

Abstract: The functionality of organic semiconductor devices crucially depends on molecular energies, namely the ionisation energy and the electron affinity. Ionisation energy and electron affinity values of thin films are, however, sensitive to film morphology and composition, making their prediction challenging. In a combined experimental and simulation study on zinc-phthalocyanine and its fluorinated derivatives, we show that changes in ionisation energy as a function of molecular orientation in neat films or mixing ratio in blends are proportional to the molecular quadrupole component along the π-π-stacking direction. We apply these findings to organic solar cells and demonstrate how the electrostatic interactions can be tuned to optimise the energy of the charge-transfer state at the donor−acceptor interface and the dissociation barrier for free charge carrier generation. The confirmation of the correlation between interfacial energies and quadrupole moments for other materials indicates its relevance for small molecules and polymers. The performance of organic semiconductor devices depends heavily on molecular parameters. Here, Schwarze et al. point out that the molecular quadrupole moment largely influences device energy levels and show how quadrupole moments can reduce the energy barrier for charge generation in solar cells.

Semiclassical wave packet dynamics in nonuniform electric fields

Abstract: We study the semiclassical theory of wave packet dynamics in crystalline solids extended to include the effects of a nonuniform electric field. In particular, we derive a correction to the semiclassical equations of motion (EOMs) for the dynamics of the wave packet center that depends on the gradient of the electric field and on the quantum metric (also called the Fubini-Study, Bures, or Bloch metric) on the Brillouin zone. We show that the physical origin of this term is a contribution to the total energy of the wave packet that depends on its electric quadrupole moment and on the electric-field gradient. We also derive an equation relating the electric quadrupole moment of a sharply peaked wave packet to the quantum metric evaluated at the wave packet center in reciprocal space. Finally, we explore the physical consequences of this correction to the semiclassical EOMs. We show that in a metal with broken time-reversal and inversion symmetry, an electric-field gradient can generate a longitudinal current which is linear in the electric-field gradient, and which depends on the quantum metric at the Fermi surface. We then give two examples of concrete lattice models in which this effect occurs. Our results show that nonuniform electric fields can be used to probe the quantum geometry of the electronic bands in metals and open the door to further studies of the effects of nonuniform electric fields in solids.

Analytical model of resonant electromagnetic dipole-quadrupole coupling in nanoparticle arrays

Abstract: An analytical model for investigations of multipole coupling effects in the finite and infinite nanoparticle arrays supporting electromagnetic resonances is presented and discussed. This model considers the contributions of both electric and magnetic modes excited in the nanoparticles, including electric and magnetic dipoles and electric and magnetic quadrupoles. The magnetic quadrupole propagator (Green's tensor) that describes the electromagnetic field generated by a point magnetic quadrupole source in all wave zones is derived. As an example, we apply the developed model to study infinite two-dimensional rectangular periodic arrays of spherical silicon nanoparticles supporting the dipole and quadrupole resonant responses. The correctness and accuracy of the analytical model are confirmed by the agreement of its results with the results of full-wave numerical simulations. Using the developed model, we show the electromagnetic coupling between electric dipole and magnetic quadrupole moments as well as between magnetic dipole and electric quadrupole moments even for the case of an infinite rectangular periodic array of spherical nanoparticles. The strong suppression of the dipole or quadrupole moment due to the coupling effects is demonstrated and discussed for spherical nanoparticle arrays. The analytical expressions for the reflection and transmission coefficients written with the effective dipole and quadrupole polarizabilities are derived for normal light incidences and zero-order diffraction. The derived expressions are applied to explain the lattice anapole (invisibility) states when the incident light is transmitted unperturbed through the silicon nanoparticle array. The important role of dipole and quadrupole excitations in scattering compensation resulting in the lattice anapole effect is explicitly demonstrated. The presented approach can be used for designing metasurfaces and further utilizing them in developing ultrathin functional optical elements.

Difficulties in operator-based formulation of the bulk quadrupole moment

Abstract: Electric multipole moments are the most fundamental properties of insulating materials. However, the general formulation of bulk multipoles has been a long-standing problem. The solution for the electric dipole moment was provided decades ago by King-Smith, Vanderbilt, and Resta. Recently, there have been attempts at generalizing Resta's formula to higher-order multipoles. We point out several issues in the recent proposals.

Enhanced absorption in all-dielectric metasurfaces due to magnetic dipole excitation.

Abstract: All-dielectric nanophotonics lies at a forefront of nanoscience and technology as it allows to control light at the nanoscale using its electric and magnetic components. Bulk silicon does not experience any magnetic response, nevertheless, we demonstrate that the metasurface made of silicon parallelepipeds allows to excite the magnetic dipole moment leading to the broadening and enhancement of the absorption. Our investigations are underpinned by the numerical predictions and the experimental verifications. Also surprisingly we found that the resonant electric quadrupole moment leads to the enhancement of reflection. Our results can be applied for a development of absorption based devices from miniature dielectric absorbers, filters to solar cells and energy harvesting devices.

Magnetic quadrupole assemblies with arbitrary shapes and magnetizations

Abstract: Magnetic dipole-dipole interactions govern the behavior of magnetic matter across scales from micrometer colloidal particles to centimeter magnetic soft robots. This pairwise long-range interaction creates rich emergent phenomena under both static and dynamic magnetic fields. However, magnetic dipole particles, from either ferromagnetic or paramagnetic materials, tend to form chain-like structures as low-energy configurations due to dipole symmetry. The repulsion force between two magnetic dipoles raises challenges for creating stable magnetic assemblies with complex two-dimensional (2D) shapes. In this work, we propose a magnetic quadrupole module that is able to form stable and frustration-free magnetic assemblies with arbitrary 2D shapes. The quadrupole structure changes the magnetic particle-particle interaction in terms of both symmetry and strength. Each module has a tunable dipole moment that allows the magnetization of overall assemblies to be programmed at the single module level. We provide a simple combinatorial design method to reach both arbitrary shapes and arbitrary magnetizations concurrently. Last, by combining modules with soft segments, we demonstrate programmable actuation of magnetic metamaterials that could be used in applications for soft robots and electromagnetic metasurfaces.

Excitation of E1-forbidden atomic transitions with electric, magnetic, or mixed multipolarity in light fields carrying orbital and spin angular momentum [Invited]

Abstract: Photons carrying a well-defined orbital angular momentum have been proven to modify spectroscopic selection rules in atomic matter. Excitation profiles of electric quadrupole transitions have been measured with single trapped Ca40+ ions for varying polarizations. We further develop the photo-absorption formalism to study the case of arbitrary alignment of the beam’s optical axis with respect to the ion’s quantization axis and mixed multipolarity. Thus, predictions for M1-dominated Ar4013+, E3-driven Yb171+ and Yb172+, and B-like Ne205+ are presented. The latter case displays novel effects, coming from the presence of a strong photon–magnetic dipole coupling.

Quadrupole Topological Photonic Crystals

Abstract: Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwell's equations for a photonic crystal (PhC) and identify quadrupole topological photonic crystals formed through a band inversion process. Unlike prior studies relying on threaded flux, our quadrupole moment is quantized purely by crystalline symmetries, which we confirm using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands, and the expectation value of the quadrupole operator. Furthermore, through the bulk-edge correspondence of Wannier bands, we reveal the boundary manifestations of nontrivial quadrupole phases as quantized polarizations at edges and bound states at corners. Finally, we relate the nontrivial corner states to the emergent phenomena of quantized fractional corner charges and a filling anomaly as first predicted in electronic systems. Our work paves the way to further explore higher-order topological phases in nanophotonic systems and our method of inducing quadrupole phase transitions is also applicable to other wave systems, such as electrons, phonons and polaritons.

Visualizations of Electric and Magnetic Interactions in Electronic Circular Dichroism and Raman Optical Activity.

Abstract: The chiral source and its mechanism in the molecular system are of great significance in many fields. In this work, we proposed visualized methods to investigate the physical mechanism of a chiral molecule, where the electric and magnetic interactions are visualized with the transitional electric dipole moment, the transitional magnetic dipole moment, and the transitional electric quadrupole moment, and their tensor product. This will also serve as an effective means of visualizing the interaction of light with matter. The relationship between the molecular Raman optical activity (ROA) response and molecular structure was analyzed in an intuitive way. The relationship between chromophore chirality and molecular vibration mode are revealed via interaction between the transition electric dipole moment and the transition magnetic dipole moment. The molecular chirality is derived from the anisotropy of the molecular transition electric dipole moment and the transition magnetic dipole moment. The anisotropic dipole moment localized molecular chromophore is the source of the vibration mode in which the ROA responds to the reverse.

Shape staggering of midshell mercury isotopes from in-source laser spectroscopy compared with density-functional-theory and Monte Carlo shell-model calculations

Abstract: Neutron-deficient 177−185Hg isotopes were studied using in-source laser resonance-ionization spectroscopy at the CERN-ISOLDE radioactive ion-beam facility in an experiment combining different detection methods tailored to the studied isotopes. These include either α-decay tagging or multireflection time-of-flight gating for isotope identification. The endpoint of the odd-even nuclear shape staggering in mercury was observed directly by measuring for the first time the isotope shifts and hyperfine structures of 177−180Hg. Changes in the mean-square charge radii for all mentioned isotopes, magnetic dipole, and electric quadrupole moments of the odd-A isotopes and arguments in favor of I=7/2 spin assignment for 177,179Hg were deduced. Experimental results are compared with density functional theory (DFT) and Monte Carlo shell model (MCSM) calculations. DFT calculations using Skyrme parametrizations predict a jump in the charge radius around the neutron N=104 midshell, with an odd-even staggering pattern related to the coexistence of nearly degenerate oblate and prolate minima. This near-degeneracy is highly sensitive to many aspects of the effective interaction, a fact that renders perfect agreement with experiments out of reach for current functionals. Despite this inherent difficulty, the SLy5s1 and a modified UNEDF1SO parametrization predict a qualitatively correct staggering that is off by two neutron numbers. MCSM calculations of states with the experimental spins and parities show good agreement for both electromagnetic moments and the observed charge radii. A clear mechanism for the origin of shape staggering within this context is identified: a substantial change in occupancy of the proton πh9/2 and neutron νi13/2 orbitals.

Footprint of two-form field: Statistical anisotropy in primordial gravitational waves

Abstract: We study the observational signatures of two-form field in the inflationary cosmology. In our setup a two-form field is kinetically coupled to a spectator scalar field and generates sizable gravitational waves and smaller curvature perturbation. We find that the sourced gravitational waves have a distinct signature: they are always statistically anisotropic and their spherical moments are non-zero for hexadecapole and tetrahexacontapole, while the quadrupole moment vanishes. Since their amplitude can reach $\mathcal{O}(10^{-3})$ in the tensor-to-scalar ratio, we expect this novel prediction will be tested in the next generation of the CMB experiments.

Mass, charge, and radius of droplets in a linear quadrupole electrodynamic balance

Abstract: Single particle levitation is a key tool in the analysis of the physicochemical properties of aerosol particles. Central to these techniques is the ability to determine the size of the confined par...

The full infrared spectrum of molecular hydrogen

Abstract: Context . The high spectral resolution R ∼ 45 000 provided by IGRINS (Immersion Grating INfrared Spectrometer) at MacDonald Observatory and R ∼ 100 000 achieved by CRIRES (CRyogenic high-resolution InfraRed Echelle Spectrograph) at VLT (Very Large Telescope) challenges the present knowledge of infrared spectra.Aims . We aim to predict the full infrared spectrum of molecular hydrogen at a comparable accuracy.Methods . We take advantage of the recent theoretical ab initio studies on molecular hydrogen to compute both the electric quadrupole and magnetic dipole transitions taking place within the ground electronic molecular state of hydrogen.Results . We computed the full infrared spectrum of molecular hydrogen at an unprecedented accuracy and derive for the first time the emission probabilities including both electric quadrupole (ΔJ = 0, ±2) and magnetic dipole transitions (ΔJ = 0) as well as the total radiative lifetime of each rovibrational state. Inclusion of magnetic dipole transitions increases the emission probabilities by factors of a few for highly excited rotational levels, which occur in the 3–20 μ range.

Theoretical determination of energies, wavelengths, and transition probabilities for EUV and SXR spectral lines in Rb XXXIV, Sr XXXV, Zr XXXVII, and Nb XXXVIII

Abstract: Energy levels, radiative processes and lifetimes are studied among the 98 lowest levels of the 1s22snl and 1s22pnl (n = 2–4, l = 0–3) configurations of Rb XXXIV, Sr XXXV, Zr XXXVII, and Nb XXXVIII. The GRASP2K (General-purpose Relativistic Atomic Structure Package) is adopted, in which the orbital set is systematically expanded within the orbital space up to n = 9, and the Breit interaction and leading quantum electrodynamical corrections are considered. Results are provided for four types of transitions:electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole. Similar data for the 166 lowest states belonging to the n ≤ 5 configurations are also determined using the second-order relativistic many-body perturbation theory to assess the accuracy of the calculations, taking Sr XXXV as an example. Good agreement is found between results of this work and available values from the Atomic Spectra Database of the National Institute of Standards and Technology and other theoretical reports. The accuracy for energies and radiative rates is estimated to be about 0.02% and 5%, respectively. These accurate theoretical data can aid line identifications in extreme ultraviolet (EUV) and soft X-ray (SXR) spectra. The present work should be useful for diagnostics of hot plasmas in fusion applications.

Spin-induced deformations and tests of binary black hole nature using third-generation detectors

Abstract: In a recent letter [N. V. Krishnendu et al., Phys. Rev. Lett. 119, 091101 (2017)] we explored the possibility of probing the binary black hole nature of coalescing compact binaries, by measuring their spin-induced multipole moments, observed in advanced LIGO detectors. Coefficients characterizing the spin-induced multipole moments of Kerr black holes are predicted by the ``no-hair'' conjecture and appear in the gravitational waveforms through quadratic and higher order spin interactions and hence can be directly measured from gravitational wave observations. By employing a nonprecessing post-Newtonian (PN) waveform model, we assess the capabilities of the third-generation gravitational wave interferometers such as Cosmic Explorer and Einstein Telescope in carrying out such measurements and use them to test the binary black hole nature of observed binaries. In this paper, we extend the investigations of [N. V. Krishnendu et al., Phys. Rev. Lett. 119, 091101 (2017)], limited to measuring the binary's spin-induced quadrupole moment using their observation in second generation detectors, by proposing to measure (a) spin-induced quadrupole effects using third generation detectors, (b) simultaneous measurements of spin-induced quadrupole and octupole effects, again in the context of the third-generation detectors. We study the accuracy of these measurements as a function of total mass, mass ratio, spin magnitudes, and spin alignments. Further, we consider two different binary black hole populations, as proxies of the population that will be observed by the third generation detectors, and obtain the resulting distribution of the spin-induced quadrupole coefficient. This helps us assess how common are those cases where this test would provide very stringent constraints on the black hole nature. These error bars provide us upper limits on the values of the coefficients that characterize the spin-induced multipoles. We find that, using third-generation detectors the symmetric combination of coefficients associated with the spin-induced quadrupole moment of each binary component may be constrained to a value $\ensuremath{\le}1.1$ while a similar combination of coefficients for spin-induced octupole moment may be constrained to $\ensuremath{\le}2$, where both combinations take the value of 1 for a binary black hole system. These estimates suggest that third-generation detectors can accurately constrain the first four multipole moments of the compact objects (mass, spin, quadrupole, and octupole) facilitating a thorough probe of their black hole nature.

Type-II quadrupole topological insulators

Abstract: Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery of the so-called quadupole topological insulator. It has been established by a classical electromagnetic theory that in a two-dimensional material the quantized properties for the quadupole topological insulator should satisfy a basic relation. Here we discover a new type of quadrupole topological insulator (dubbed type-II) that violates this relation due to the breakdown of the correspondence that a Wannier band and an edge energy spectrum close their gaps simultaneously. We find that, similar to the previously discovered (referred to as type-I) quadrupole topological insulator, the type-II hosts topologically protected corner states carrying fractional corner charges. However, the edge polarizations only occur at a pair of boundaries in the type-II insulating phase, leading to the violation of the classical constraint. We demonstrate that such new topological phenomena can appear from quench dynamics in non-equilibrium systems, which can be experimentally observed in ultracold atomic gases. We also propose an experimental scheme with electric circuits to realize such a new topological phase of matter. The existence of the new topological insulating phase means that new multipole topological insulators with distinct properties can exist in broader contexts beyond classical constraints.

Strong photon coupling to the quadrupole moment of an electron in solid state

Abstract: The implementation of circuit quantum electrodynamics allows coupling distant qubits by microwave photons hosted in on-chip superconducting resonators. Typically, the qubit-photon interaction is realized by coupling the photons to the electric dipole moment of the qubit. A recent proposal suggests storing the quantum information in the electric quadrupole moment of an electron in a triple quantum dot. The qubit is expected to have improved coherence since it is insensitive to dipolar noise produced by distant voltage fluctuators. Here we experimentally realize a quadrupole qubit in a linear array of three quantum dots in a GaAs/AlGaAs heterostructure. A high impedance microwave resonator coupled to the middle dot interacts with the qubit quadrupole moment. We demonstrate strong quadrupole qubit--photon coupling and observe improved coherence properties when operating the qubit in the parameter space where the dipole coupling vanishes.

“Stiff” deformed nuclei, configuration dependent pairing and the $\beta$β and $\gamma$γ degrees of freedom

Abstract: We review the current experimental data on collective structures within the pairing gap of even-even deformed nuclei, with emphasis on nuclei near mass number $A \sim 150$. The essential physics that determines the characteristics of the first excited 0+ (02+) state in these nuclei has been in dispute for several decades. Interpretation of these states in terms of surface $\beta$ quadrupole vibrations has often been challenged. We examine the role that configuration dependent pairing can play in these levels particularly at the onset of deformation as major shells fill. In all deformed nuclei rotational bands are found experimentally, starting at a state with spin 2+ with excitation energies near the middle of the pairing gap. These rotational bands, with quantum number $K^{\pi} = 2^{+}$, are usually referred to as $\gamma$ bands and have been identified with quadrupole surface vibrations in the plane perpendicular to the major axis of deformation. However $K^{\pi} = 2^{+}$ bands can also arise due to the breaking of axial symmetry of the quadrupole shape. We discuss data that can help with these different interpretations.

Enhancement of and interference among higher order multipole transitions in molecules near a plasmonic nanoantenna

Abstract: Spontaneous emission of quantum emitters can be modified by their optical environment, such as a resonant nanoantenna. This impact is usually evaluated under assumption that each molecular transition is dominated only by one multipolar channel, commonly the electric dipole. In this article, we go beyond the electric dipole approximation and take light-matter coupling through higher-order multipoles into account. We investigate a strong enhancement of the magnetic dipole and electric quadrupole emission channels of a molecule adjacent to a plasmonic nanoantenna. Additionally, we introduce a framework to study interference effects between various transition channels in molecules by rigorous quantum-chemical calculations of their multipolar moments and a consecutive investigation of the transition rate upon coupling to a nanoantenna. We predict interference effects between these transition channels, which allow in principle for a full suppression of radiation by exploiting destructive interference, waiving limitations imposed on the emitter’s coherence time by spontaneous emission. Here, the authors study the interference effects between different multipole transition channels by coupling a molecule to a plasmonic nanoantenna. Controlling different emission pathways of quantum emitters allows selective enhancement or suppression of the transition rate through devoted illumination schemes.

Electric Quadrupole Moment and the Tensor Magnetic Polarizability of Twisted Electrons and a Potential for their Measurements

Abstract: For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that a twisted spin-1/2 particle possesses a tensor magnetic polarizability and a measurable (spectroscopic) electric quadrupole moment. We have calculated the former parameter and have evaluated the latter one for a twisted electron. The tensor magnetic polarizability of the twisted electron can be measured in a magnetic storage ring because a beam with an initial orbital tensor polarization acquires a horizontal orbital vector polarization. The electric quadrupole moment is rather large and strongly influences the dynamics of the intrinsic orbital angular momentum (OAM). Three different methods of its measurements, freezing the intrinsic orbital angular momentum and two resonance methods, are proposed. The existence of the quadrupole moment of twisted electrons can lead to practical applications.

The full infrared spectrum of molecular hydrogen.

Abstract: The high spectral resolution R about 45,000 provided by IGRINS (Immersion Grating INfrared Spectrometer) at MacDonald Observatory and R 100,000 achieved by CRIRES (CRyogenic high-resolution InfraRed Echelle Spectrograph) at VLT (Very Large Telescope) challenges the present knowledge of infrared spectra. aims We aim to predict the full infrared spectrum of molecular hydrogen at a comparable accuracy. methods We take advantage of the recent theoretical ab initio studies on molecular hydrogen to compute both the electric quadrupole and magnetic dipole transitions taking place within the ground electronic molecular state of hydrogen. results We computed the full infrared spectrum of molecular hydrogen at an unprecedented accuracy and derive for the first time the emission probabilities including both electric quadrupole ($\Delta J = 0, \pm$2) and magnetic dipole transitions ($\Delta J = 0$) as well as the total radiative lifetime of each rovibrational state. Inclusion of magnetic dipole transitions increases the emission probabilities by factors of a few for highly excited rotational levels, which occur in the 3-20 $\mu$ range}

Quasinormal Modes of a Black Hole with Quadrupole Moment

Abstract: We analytically determine the quasinormal mode (QNM) frequencies of a black hole with quadrupole moment in the eikonal limit using the light-ring method. The generalized black holes that are discussed in this work possess arbitrary quadrupole and higher mass moments in addition to mass and angular momentum. Static collapsed configurations with mass and quadrupole moment are treated in detail and the QNM frequencies associated with two such configurations are evaluated to linear order in the quadrupole moment. Furthermore, we touch upon the treatment of rotating systems. In particular, the generalized black hole that we consider for our extensive QNM calculations is a completely collapsed configuration whose exterior gravitational field can be described by the Hartle-Thorne spacetime [Astrophys. J. 153, 807-834 (1968)]. This collapsed system as well as its QNMs is characterized by mass $M$, quadrupole moment $Q$ and angular momentum $J$, where the latter two parameters are treated to first and second orders of approximation, respectively. When the quadrupole moment is set equal to the relativistic quadrupole moment of the corresponding Kerr black hole, ${J}^{2}/(M{c}^{2})$, the Hartle-Thorne QNMs reduce to those of the Kerr black hole to second order in angular momentum $J$. Using ringdown frequencies, one cannot observationally distinguish a generalized Hartle-Thorne black hole with arbitrary quadrupole moment from a Kerr black hole provided the dimensionless parameter given by $|QM{c}^{2}\ensuremath{-}{J}^{2}|{c}^{2}/({G}^{2}{M}^{4})$ is sufficiently small compared to unity.

Intrinsic multipole moments of non-Gaussian wave packets

Abstract: The charged wave packets with non-Gaussian spatial profiles are shown to possess intrinsic multipole moments. The magnetic dipole moment and the electric quadrupole moment are found for a wide class of the packets, including the vortex electrons with orbital angular momentum $\ell$, the Airy beams, the so-called Schr\"odinger's cat states, and their generalizations. For the packets with no phase vortices, the electric quadrupole moment is shown to grow quadratically with the packet's width, $|Q_{\alpha\beta}| \sim e\cdot \sigma_{\perp}^2$, while it is also $|\ell|$ times enhanced for the vortex beams. For available beams of electron microscopes, these multipole moments are relatively easily adjusted and can be quite large, which affects the packets' electromagnetic fields and also allows one to develop new diagnostic tools for materials science, atomic and molecular physics, nuclear physics, and so forth.

Near-Field Directionality Beyond the Dipole Approximation: Electric Quadrupole and Higher-Order Multipole Angular Spectra

Abstract: A paramount example among spin-related optical phenomena is the quantum spin Hall effect of light, by which the direction of propagating guided modes can be controlled by the spin of the source. For unidirectional excitation of guided waves, the focus has been only on dipolar sources, leaving aside higher-order multipoles. Exploiting the angular-spectrum representation, the authors present a general analytical treatment of near-field directionality beyond the dipole approximation. This enables a considerable advance toward full control of spin-dependent directionality at the nanoscale, and should be useful for engineering light-matter coupling in nanophotonics and quantum optics.