Multipole Moments Research Articles

Near-field enhancement of light by higher-order multipole excitations in a metal nanodisc trimer

Near-field enhancement of light by dipole excitations in plasmonic nanoparticles plays an important role in many applications of optical nanotechnology, including solar cells, plasmonic sensors, and nonlinear optical devices. Recently, we have shown that a seemingly weak octupole resonance in a pair of metal nanospheres can provide a higher near-field enhancement than the dipole resonance. Being motivated by this discovery, we now design a plasmonic nanodisc trimer that supports hybridized higher-order excitations and simultaneously suppresses the dipole excitation. We show that, under these conditions, the near-field enhancement can reach a high level, exceeding the value achievable with a corresponding dimer structure. The interference of the electric currents belonging to different multipole moments is found to play an important role in the enhancement. We believe that arrays of similar metal nanostructures can be designed to enhance optical fields via higher-order resonances for many applications, e.g., in nonlinear optics and optical sensing based on surface-enhanced fluorescence or Raman scattering.

Selective and Tunable Absorption of Twisted Light in Achiral and Chiral Plasmonic Metasurfaces.

The symmetry of achiral metasurfaces suggests selective absorption is nonexistent when irradiated either by circularly polarized Gaussian or twisted light beams carrying orbital angular momentum (OAM). In chiral metasurfaces, the lack of symmetry leads to differential absorption when probed with chiral light either in the form of circular polarization (circular dichroism) or helical phase fronts (helical dichroism). Here, we demonstrate differential absorption of asymmetric twisted light beams, known as helical dichroism, which exist in an array and a single achiral structure and can be controlled. When extended to chiral structures, these asymmetrical chiral light modes enable to enhance and tune chiroptical sensitivity. Our technique offers more control parameters than just changing the OAM value, as presented in previous studies. Selective response to asymmetric helical light beams is qualitatively explained in terms of induced multipole moments. The presence of dichroism in achiral nanostructures offers a significant fabrication advantage over complex chiral structures and enables the development of next-generation plasmonic-based chiroptical spectroscopy and molecular sensing.

Many-Body Non-Hermitian Skin Effect for Multipoles.

In this Letter, we investigate the fate of the non-Hermitian skin effect in one-dimensional systems that conserve the dipole moment and higher moments of an associated global U(1) charge. Motivated by field theoretical arguments and lattice model calculations, we demonstrate that the key feature of the non-Hermitian skin effect for m-pole conserving systems is the generation of an (m+1)th multipole moment. For example, in contrast to the conventional skin effect where charges are anomalously localized at one boundary, the dipole-conserving skin effect results in charges localized at both boundaries, in a configuration that generates an extremal quadrupole moment. In addition, we explore the dynamical consequences of the m-pole skin effect, focusing on charge and entanglement propagation. Both numerically and analytically, we provide evidence that long-time steady states have Fock-space localization and an area-law scaling of entanglement entropy, which serve as quantum indicators of the skin effect.

Excitation and manipulation of toroidal dipole response in an antenna

The toroidal dipole is always overlooked due to its relatively weak interaction with the electromagnetic fields, but it actually exhibits tremendous potential for the design of advanced photonic devices. Here, we demonstrate the existence of toroidal dipole in plasma antenna system, which is rarely observed in the antenna design. It consists of a half-wavelength antenna and eight plasma rings to excite the toroidal dipole to enhance the electromagnetic radiation of the whole antenna system, whose mechanism is different from conventional antenna, which is a multiband antenna. We further confirm that the hybrid mode, which combines the toroidal dipole and multipole moments, can be dynamically adjusted to control both return loss and the opening of operating windows. This allows for flexible tuning of the multiband antenna simply by manipulating the response of the toroidal dipole. Furthermore, the toroidal dipole antenna is stable in dusty plasma, making it suitable for solving the problem of ‘blackout’ phenomena in aerospace communications, which exhibits the additional benefits of reduced cost and easier to manufacture.

Higher memory effects and the post-Newtonian calculation of their gravitational-wave signals

Abstract A new hierarchy of lasting gravitational-wave effects (the higher memory effects) was recently identified in asymptotically flat spacetimes, with the better-known displacement, spin, and center-of-mass memory effects included as the lowest two orders in the set of these effects. These gravitational-wave observables are determined by a set of temporal moments of the news tensor, which describes gravitational radiation from an isolated source. The moments of the news can be expressed in terms of changes in charge-like expressions and integrals over retarded time of flux-like terms, some of which vanish in the absence of radiation. In this paper, we compute expressions for the flux-like contributions to the moments of the news in terms of a set of multipoles that characterize the gravitational-wave strain. We also identify a part of the strain that gives rise to these moments of the news. In the context of post-Newtonian theory, we show that the strain related to the moments of the news is responsible for the many nonlinear, instantaneous terms and "memory" terms that appear in the post-Newtonian expressions for the radiative multipole moments of the strain. We also apply our results to compute the leading post-Newtonian expressions for the moments of the news and the corresponding strains that are generated during the inspiral of compact binary sources. These results provide a new viewpoint on the waveforms computed from the multipolar post-Minkowski formalism, and they could be used to assess the detection prospects of this new class of higher memory effects.

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Toward Gaussian Process Regression Modeling of a Urea Force Field.

FFLUX is a next-generation, machine-learnt force field built on three cornerstones: quantum chemical topology, Gaussian process regression, and (high-rank) multipolar electrostatics. It is capable of performing molecular dynamics with near-quantum accuracy at a lower computational cost than standard ab initio molecular dynamics. Previous work with FFLUX was concerned with water and formamide. In this study, we go one step further and challenge FFLUX to model urea, a larger and more flexible system. In result, we have trained urea models at the B3LYP/aug-cc-pVTZ level of theory, with a mean absolute error of 0.4 kJ mol-1 and a maximum prediction error below 7.0 kJ mol-1. To test their performance in molecular dynamics simulations, two sets of FFLUX geometry optimizations were carried out: 5 dimers corresponding to energy minima and 75 random dimers. The 5 dimers were recovered with a root-mean-square deviation below 0.1 Å with respect to their ab initio references. Out of the 75 random dimers, 68% converged to the qualitatively same dimer as those obtained at the ab initio level. Furthermore, we have ranked the 5 FFLUX-optimized dimers in the order of their relative FFLUX single-point energies and compared them with the ab initio method. The energy ranking fully agreed but for one crossover between two successive minima. Finally, we have demonstrated the importance of geometry-dependent (i.e., flexible) multipole moments, showing that the lack of multipole moment flexibility can lead to average errors in the total intermolecular electrostatic energy of more than 2 orders of magnitude.

Completely Multipolar Model as a General Framework for Many-Body Interactions as Illustrated for Water.

We introduce a general framework for many-body force fields, the Completely Multipolar Model (CMM), that utilizes multipolar electrical moments modulated by exponential decay of electron density as a common functional form for all terms of an energy decomposition analysis of intermolecular interactions. With this common functional form, the CMM model establishes well-formulated damped tensors that reach the correct asymptotes at both long- and short-range while formally ensuring no short-range catastrophes. CMM describes the separable EDA terms of dispersion, exchange polarization, and Pauli repulsion with short-ranged anisotropy, polarization as intramolecular charge fluctuations and induced dipoles, while charge transfer describes explicit movement of charge between molecules, and naturally describes many-body charge transfer by coupling into the polarization equations. We also utilize a new one-body potential that accounts for intramolecular polarization by including an electric field-dependent correction to the Morse potential to ensure that CMM reproduces all physically relevant monomer properties including the dipole moment, molecular polarizability, and dipole and polarizability derivatives. The quality of CMM is illustrated through agreement of individual terms of the EDA and excellent extrapolation to energies and geometries of an extensive validation set of water cluster data.

Theory of angular momentum transfer from light to molecules

We present a theory describing the interaction of structured light, such as light carrying orbital angular momentum, with molecules. The light-matter interaction Hamiltonian we derive is expressed through couplings between spherical gradients of the electric field and the (transition) electric multipole moments of a particle of any nontrivial rotation point group. Our model can therefore accommodate an arbitrary complexity of the molecular and electric field structure, and it can be straightforwardly extended to atoms or nanostructures. Applying this framework to rovibrational spectroscopy of molecules, we uncover the general mechanism of angular momentum exchange between the spin and orbital angular momenta of light, molecular rotation, and its center-of-mass motion. We show that the nonzero vorticity of Laguerre-Gaussian beams can strongly enhance certain rovibrational transitions that are considered forbidden in the case of nonhelical light. We discuss the experimental requirements for the observation of these forbidden transitions in state-of-the-art spatially resolved spectroscopy measurements. Published by the American Physical Society 2024

Shot-noise-limited optical polarimetry with spin-alignment and magnetism decoupling

Quantum non-demolition measurement with an off-resonance polarized probe is a widely utilized technique for atomic sensors. We observe previously unexplored spin-alignment polarization induced by the far-detuned off-resonance linear probe in an ultrasensitive optical polarimetry. The evolution of probe-generated multipole moments exacerbates probe noise due to strong magnetic couplings. We demonstrate a method to decouple spin-alignment from magnetic fields by manipulating the multipole moments in zero-fields. The probe noise is suppressed by 10 dB with the proposed method, achieving a noise floor at the standard quantum limit. The realized shot-noise-limited optical polarimetry holds significant promise for atomic sensors aimed at ultra-sensitivity.

Secular dynamics and the lifetimes of lunar artificial satellites under natural force-driven orbital evolution

In this paper, we study the long-term (time scale of several years) orbital evolution of lunar satellites under the sole action of natural forces. In particular, we focus on secular resonances, caused either by the influence of the multipole moments of the lunar potential and/or by the Earth’s and Sun’s third-body effect on the satellite’s long-term orbital evolution. Our study is based on a simplified secular model obtained in ‘closed form’, i.e., without expansions in the satellite’s orbital eccentricity. Contrary to the case of artificial Earth satellites, in which many secular resonances compete in dynamical impact, we give numerical evidence that for lunar satellites only the 2g−resonance (ω̇=0) affects significantly the orbits at secular timescales. We interpret this as a consequence of the strong effect of lunar mascons. We show that the lifetime of lunar satellites is, in particular, nearly exclusively dictated by the 2g resonance. By deriving a simple analytic model, we propose a theoretical framework which allows for both qualitative and quantitative interpretation of the structures seen in numerically obtained lifetime maps. This involves explaining the main mechanisms driving eccentricity growth in the orbits of lunar satellites. In fact, we argue that the re-entry process for lunar satellites is not necessarily a chaotic process (as is the case for Earth satellites), but rather due to a sequence of bifurcations leading to a dramatic variation in the structure of the separatrices in the 2g resonance’s phase portrait, as we move from the lowest to the highest limit in inclination (at each altitude) where the 2g resonance is manifested.

Electronic Polarizability Tunes the Function of the Human Bestrophin 1 Cl- Channel.

Mechanisms of anion permeation within ion channels and nanopores remain poorly understood. Recent cryo-electron microscopy structures of the human bestrophin 1 Cl- channel (hBest1) provide an opportunity to evaluate ion interactions predicted by molecular dynamics (MD) simulations against experimental observations. Here, we implement the fully polarizable forcefield AMOEBA in MD simulations on different conformations of hBest1. This forcefield models multipole moments up to the quadrupole; therefore, it captures induced dipole and anion-π interactions. We show that key biophysical properties of the channel can only be simulated when electronic polarization is included in the molecular models and that Cl- permeation through the neck of the pore is achieved through hydrophobic solvation concomitant with partial ion dehydration. Furthermore, we demonstrate how such polarizable simulations can help determine the identity of ion-like densities within high-resolution cryo-EM structures and that neglecting polarization places Cl- at positions that do not correspond with their experimentally resolved location. Overall, our results demonstrate the importance of including electronic polarization in realistic and physically accurate models of biological systems, especially channels and pores that selectively permeate anions.

Topological‐Charge‐Dependent Dichroism and Birefringence of Optical Vortices

AbstractMaterial anisotropy and chirality produce polarization‐dependent light‐matter interactions. Absorption leads to linear and circular dichroism, whereas elastic forward scattering produces linear and circular birefringence. Here a form of dichroism and birefringence is highlighted whereby generic anisotropic media display locally different absorption and scattering of a focused vortex beam that depends upon the sign of the topological charge . The light‐matter interactions described in this work manifest purely through dominant electric‐dipole coupling mechanisms and depend on the paraxial parameter to first‐order. Previous topological‐charge‐dependent light‐matter interactions require the significantly weaker higher‐order multipole moments and are proportional to the paraxial parameter to second‐order. The result represents a method of probing the nano‐optics of advanced materials and the topological properties of structured light.

Incorporating Noncovalent Interactions in Transfer Learning Gaussian Process Regression Models for Molecular Simulations.

FFLUX is a quantum chemical topology-based multipolar force field that uses Gaussian process regression machine learning models to predict atomic energies and multipole moments on the fly for fast and accurate molecular dynamics simulations. These models have previously been trained on monomers, meaning that many-body effects, for example, intermolecular charge transfer, are missed in simulations. Moreover, dispersion and repulsion have been modeled using Lennard-Jones potentials, necessitating careful parametrization. In this work, we take an important step toward addressing these shortcomings and show that models trained on clusters, in this case, a dimer, can be used in FFLUX simulations by preparing and benchmarking a formamide dimer model. To mitigate the computational costs associated with training higher-dimensional models, we rely on the transfer of hyperparameters from a smaller source model to a larger target model, enabling an order of magnitude faster training than with a direct learning approach. The dimer model allows for simulations that account for two-body effects, including intermolecular polarization and charge penetration, and that do not require nonbonded potentials. We show that addressing these limitations allows for simulations that are closer to quantum mechanics than previously possible with the monomeric models.

An approximate Kerr–Newman-like metric endowed with a magnetic dipole and mass quadrupole

Approximate all-terrain spacetimes for astrophysical applications are presented. The metrics possess five relativistic multipole moments, namely, mass, rotation, mass quadrupole, charge, and magnetic dipole moment. All these spacetimes approximately satisfy the Einstein–Maxwell field equations. The first metric is generated using the Hoenselaers–Perjés method from given relativistic multipoles. The second metric is a perturbation of the Kerr–Newman metric, which makes it a relevant approximation for astrophysical calculations. The last metric is an extension of the Hartle–Thorne metric that is important for obtaining internal models of compact objects perturbatively. The electromagnetic field is calculated using Cartan forms for locally non-rotating observers. These spacetimes are relevant for inferring properties of compact objects from astrophysical observations. Furthermore, the numerical implementations of these metrics are straightforward, making them versatile for simulating potential astrophysical applications.

Retraction Note to: Comparative Measurements of Plasma Position Using Multipole Moments Method and Analytical Solution of Grad–Shafranov Equation in IR-T1 Tokamak

Retraction Note to: Comparative Measurements of Plasma Position Using Multipole Moments Method and Analytical Solution of Grad–Shafranov Equation in IR-T1 Tokamak

Machian fractons, Hamiltonian attractors, and nonequilibrium steady states

We study the N fracton problem in classical mechanics, with fractons defined as point particles that conserve multipole moments up to a given order. We find that the nonlinear Machian dynamics of the fractons is characterized by late-time attractors in position-velocity space for all N, despite the absence of attractors in phase space dictated by Liouville's theorem. These attractors violate ergodicity and lead to nonequilibrium steady states, which always break translational symmetry, even in spatial dimensions where the Hohenberg-Mermin-Wagner-Coleman theorem for equilibrium systems forbids such breaking. We provide a conceptual understanding of our results using an adiabatic approximation for the late-time trajectories and an analogy with the idea of “order-by-disorder” borrowed from equilibrium statistical mechanics. Altogether, these fracton systems host a paradigm for Hamiltonian dynamics and nonequilibrium many-body physics. Published by the American Physical Society 2024

Electromagnetic properties of nuclei from first principles: a case for synergies between experiment and theory.

One of the overarching goals in nuclear science is to understand how the nuclear chart emerges from the underlying fundamental interactions. The description of the structure of nuclei from first principles, using ab initio methods for the solution of the many-nucleon problem with inputs from chiral effective field theory, has advanced dramatically over the past two decades. We present an overview over the available ab initio tools with a specific emphasis on electromagnetic observables, such as multipole moments and transition strengths. These observables still pose a challenge for ab initio theory and are one of the most exciting domains to exploit synergies with modern experiments. Precise experimental data are vital for the validation of the theory predictions and the refinement of ab initio methods. We discuss some of the past and future experimental efforts highlighting these synergies. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Developing a Differentiable Long-Range Force Field for Proteins with E(3) Neural Network-Predicted Asymptotic Parameters.

Accurately describing long-range interactions is a significant challenge in molecular dynamics (MD) simulations of proteins. High-quality long-range potential is also an important component of the range-separated machine learning force field. This study introduces a comprehensive asymptotic parameter database encompassing atomic multipole moments, polarizabilities, and dispersion coefficients. Leveraging active learning, our database comprehensively represents protein fragments with up to 8 heavy atoms, capturing their conformational diversity with merely 78,000 data points. Additionally, the E(3) neural network (E3NN) is employed to predict the asymptotic parameters directly from the local geometry. The E3NN models demonstrate exceptional accuracy and transferability across all asymptotic parameters, achieving an R2 of 0.999 for both protein fragments and 20 amino acid dipeptide test sets. The long-range electrostatic and dispersion energies can be obtained using the E3NN-predicted parameters, with an error of 0.07 and 0.02 kcal/mol, respectively, when compared to symmetry-adapted perturbation theory (SAPT). Therefore, our force fields demonstrate the capability to accurately describe long-range interactions in proteins, paving the way for next-generation protein force fields.

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains.

The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.