Quadrupole Polarizabilities Research Articles

A comparative study of transition oscillator strengths and static polarizabilities of the hydrogen atom confined in Gaussian potential

Abstract The multipole (dipole, quadrupole, and octopole) photon-absorption transition oscillator strengths for the ground state of hydrogen atom confined in Gaussian potential are investigated for a great variety of potential depths and confining radii. It is interestingly found that at fixed potential depth the gradual increase of confining radius shows first destructive and then constructive effect on the multipole oscillator strengths. Such an effect can be understood from the overlap between the initial and final states. Multipole polarizabilities of the system are obtained through the sum-over-states formalism where the contributions from both the bound and continuum spectra of the system are included. Although the separate bound and continuum contributions can not be determined accurately, due to the long-range nature of the Coulomb potential introduced by the nucleus, their summations can be obtained to reasonably good accuracy, leading to fast convergence of numerical calculations of multipole polarizabilities. The present results are compared with previous calculations available in the literature. Although good agreement is observed for the dipole polarizability, significant differences exist in the quadrupole polarizability and orders-of-magnitude differences appear in the octopole polarizability. The possible reason for such large differences is analyzed by comparing the sum rule of corresponding oscillator strengths.

Interlayer Electric Multipoles Induced by In-Plane Field from Quantum Geometric Origins.

We show that interlayer charge transfer in 2D materials can be driven by an in-plane electric field, giving rise to electrical multipole generation in linear and second order in-plane field. The linear and nonlinear effects have quantum geometric origins in the Berry curvature and quantum metric, respectively, defined in extended parameter spaces characteristic of layered materials. We elucidate their symmetry characters and demonstrate sizable dipole and quadrupole polarizations, respectively, in twisted bilayers and trilayers of transition metal dichalcogenides. Furthermore, we show that this effect is strongly enhanced during the topological phase transition tuned by interlayer translation. The effects point to a new electric control on the layer quantum degree of freedom.

Comparative rotatory power of bent and twisted polyynes.

Linear polyynes of the formula C18 H2 (symmetry D∞h ) were bent in silico by progressively introducing CCC angles less than 180°. The bent structures (symmetry C2v ) were then twisted by introducing torsion angles across the CCCC segments by as much as 60°. The gyration tensors of these 19 structures (linear, bent, and twisted) were computed by linear response methods. Bending is massively generative of optical activity in oriented structures, even achiral structures, whereas twisting in conjunction with bending, serves to linearize the molecules and diminish maximally observable optical activity. This computational exercise is intended to unbind the infelicitous linkage of optical activity and chirality, which is only meaningful in isotropic media. Although bent structures are not optically active in solution-the spatial average of the optical activity is necessarily zero-solution measurements that deliver the spatial averages are a special class of measurements, albeit the overwhelmingly most common chiroptical measurements, that prejudice our common understanding of how π-conjugated structures generate gyration. Bending is far more effective than twisting at generating optical activity along some directions for oriented structures. The respective contributions from the transition electric dipole-magnetic dipole polarizability and the transition electric dipole-electric quadrupole polarizability are compared.

Dynamically generated quadrupole polarization using Floquet adiabatic evolution

We investigate the nonequilibrium dynamics of the $S=1$ quantum spin chain subjected to a time-dependent external drive, where the driving frequency is adiabatically decreased as a function of time (``Floquet adiabatic evolution''). We show that when driving the rhombic anisotropy term (known as the ``two-axis countertwisting'' in the context of squeezed spin states) of a N\'eel antiferromagnet, we are able to induce an overall enhancement in the quadrupole polarization, while at the same time suppressing the staggered magnetization order. The system evolves into a new state with a net quadrupole moment and antiferroquadrupolar correlations. This state remains stable at long times once the driving frequency is kept constant. On the other hand, we find that we cannot achieve a quadrupole polarization for the symmetry-protected Haldane phase, which remains robust against such driving.

Be optical lattice clocks with the fractional Stark shift up to the level of 10−19

The energy levels and electric dipole () matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic , magnetic dipole () and electric quadrupole () polarizabilities as well as the hyperpolarizabilities of the and states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity I is in the range of 14.3–15.9 kW cm−2 and the detuning δ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7–40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 × 10−18. While, when I is in the range of 15.01–15.46 kW cm−2 and δ is in the range of 40.73–40.76 MHz, the fractional Stark shifts are lower than 1.0 × 10−19.

Computational Study of the Adsorption of Small Gas Molecules on Pillar[5]arenes

AbstractThe anthropogenic carbon dioxide (CO2) that is the main cause of the greenhouse effect has become subject to many studies of gas capture, storage, and separation. P[n]A‐based supramolecular organic frameworks (SOF) have emerged as a promising candidate for capturing and separation of CO2. Experimental studies show high adsorption rates and selectivity for CO2 over other gases such as methane (CH4) and nitrogen (N2). [Advanced Materials 26, 7027 (2014)] However, a full understanding of CO2 adsorption in P[n]A is still missing. Using density functional theory (DFT) based calculations, we found that CO2 can be adsorbed by P[5]A in different positions. The most favorable adsorption position is within the cavity of P[5]A. The CO2 molecule adsorbs by forming hydrogen bonds or by π‐π interaction with the benzene rings of P[5]A. Also CH4 and N2 can be physisorbed by P[5]A, but with lower binding energies, which can be explained by the weaker quadrupole moments and polarizabilities of CH4 and N2. Our investigations are the basis for targeted design and optimization of a potential application of P[5]A in CO2 capture, storage, and separation.

Wannier topology and quadrupole moments for a generalized Benalcazar-Bernevig-Hughes model

We analyze a special separable and chiral-symmetric model with a quantized quadrupole moment, extending the Benalcazar-Bernevig-Hughes model [Science 357, 61 (2017)]. Using nested-Wilson loop formalism, we give an exact expression for Wannier centers, sector polarizations, and quadrupole moments. These are connected to the winding numbers of the constitutive one-dimensional chains. We prove that these winding numbers can characterize the model's Wannier topology as a $\mathbb{Z}\times\mathbb{Z}$ set. These results clearly show that the quantization of the quadrupole moment can arise without additional spatial symmetry (except for translation symmetry) for the bulk. By switching from the Wannier representation to the Bloch representation, we derive an alternative expression for the bulk quadrupole moment and obtain its exact value. Combining the bulk quadrupole and edge polarizations, we analytically calculate the corner charge in a large square system and make the bulk-boundary correspondence explicit in an edge-consistent gauge. Our work reveals the relationship between zero-energy states at the boundary, charge localization, and the bulk quadrupole of the extended model.

Generalized Many-Body Dispersion Correction through Random-Phase Approximation for Chemically Accurate Density Functional Theory.

We extend our recently proposed Deep Learning-aided many-body dispersion (DNN-MBD) model to quadrupole polarizability (Q) terms using a generalized Random Phase Approximation (RPA) formalism, thus enabling the inclusion of van der Waals contributions beyond dipole. The resulting DNN-MBDQ model only relies on ab initio-derived quantities as the introduced quadrupole polarizabilities are recursively retrieved from dipole ones, in turn modeled via the Tkatchenko-Scheffler method. A transferable and efficient deep-neuronal network (DNN) provides atom-in-molecule volumes, while a single range-separation parameter is used to couple the model to Density Functional Theory (DFT). Since it can be computed at a negligible cost, the DNN-MBDQ approach can be coupled with DFT functionals, such as PBE, PBE0, and B86bPBE (dispersionless). The DNN-MBQ-corrected functionals reach chemical accuracy while exhibiting lower errors compared to their dipole-only counterparts.

Derivation and implementation of the optical rotation tensor for chiral crystals.

This paper reports the derivation and implementation of the electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability tensors at the density functional theory level with periodic boundary conditions (DFT-PBC). These tensors are combined to evaluate the Buckingham/Dunn tensor that describes the optical rotation (OR) in oriented chiral systems. We describe several aspects of the derivation of the equations and present test calculations that verify the correctness of the tensor formulation and their implementation. The results show that the full OR tensor is completely origin invariant as for molecules and that PBC calculations match molecular cluster calculations on 1D chains. A preliminary investigation on the choice of density functional, basis set, and gauge indicates a similar dependence as for molecules: the functional is the primary factor that determines the OR magnitude, followed by the basis set and to a much smaller extent the choice of gauge. However, diffuse functions may be problematic for PBC calculations even if they are necessary for the molecular case. A comparison with experimental data of OR for the tartaric acid crystal shows reasonable agreement given the level of theory employed. The development presented in this paper offers the opportunity to simulate the OR of chiral crystalline materials with general-purpose DFT-PBC methods, which, in turn, may help to understand the role of intermolecular interactions on this sensitive electronic property.

Determination of quadrupolar dispersion coefficients of the alkali-metal atoms interacting with different material media

In the present work, we determine the ${C}_{5}$ coefficients along with their uncertainties due to quadrupole polarization effects of all the alkali atoms interacting with a metal (Au), a semiconductor (Si), and four dielectric materials (${\mathrm{SiO}}_{2}, {\mathrm{SiN}}_{x}$, yttrium aluminum garnet, and sapphire). The required dynamic electric quadrupole ($E2$) polarizabilities are evaluated by calculating $E2$ matrix elements of a large number of transitions in the alkali atoms by employing a relativistic coupled-cluster method. A significant contribution towards the long-range van der Waals potential is made by the quadrupole polarization effects. Our finding shows that contributions from the ${C}_{5}$ coefficients to the atom-wall interaction potentials are pronounced at short distances (1--10 nm). The ${C}_{3}$ coefficients of a Fr atom interacting with the above material media are also reported. These results could be useful in understanding the interactions of alkali atoms trapped in different material bodies during high-precision measurements.

Constructing Electron-Atom Elastic Scattering Potentials Using Relativistic Coupled-Cluster Theory: A Few Case Studies

In light of the immense interest in understanding the impact of an electron on atoms in the low-energy scattering phenomena observed in laboratories and astrophysical processes, we propose an approach to construct potentials using relativistic coupled-cluster (RCC) theory for the determination of electron-atom (e-A) elastic scattering cross-sections (eSCs). The net potential of an electron, scattered elastically by an atom, is conveniently expressed as the sum of the static (Vst) and exchange (Vex) potentials due to interactions of the scattered electron with the electrons of the atom and potentials due to polarization effects (Vpol) on the scattered electron by the atomic electrons. The Vst and Vex potentials for the e-A eSC problems can be constructed with a knowledge of the electron density function of the atom, while the Vpol potential can be obtained using the polarizabilities of the atom. In this paper, we present the electron densities and electric polarizabilties of Be, Mg, Ne and Ar atoms using two variants of the RCC method. Using these quantities, we construct potentials for e-A eSC problems. To obtain Vpol accurately, we evaluate the second- and third-order electric dipole and quadrupole polarizabilities using a linear response approach.

Magic wavelength for a rovibrational transition in molecular hydrogen

Molecular hydrogen, among other simple calculable atomic and molecular systems, possesses a huge advantage of having a set of ultralong living rovibrational states that make it well suited for studying fundamental physics. Further experimental progress will require trapping cold H2 samples. However, due to the large energy of the first electronic excitation, the conventional approach to finding a magic wavelength does not work for H2. We find a rovibrational transition for which the AC Stark shift is largely compensated by the interplay between the isotropic and anisotropic components of polarizability. The residual AC Stark shift can be completely eliminated by tuning the trapping laser to a specific “magic wavelength” at which the weak quadrupole polarizability cancels the residual dipole polarizability.

Relativistic normal coupled-cluster theory analysis of second- and third-order electric polarizabilities of Zn I

We present precise values of electric polarizabilities for the ground state of Zn due to second-order dipole and quadrupole interactions, and due to third-order dipole-quadrupole interactions. These quantities are evaluated in the linear response theory framework by employing a relativistic version of the normal coupled-cluster (NCC) method. The calculated dipole polarizability value is compared with available experimental and other theoretical results including those are obtained using the ordinary coupled-cluster (CC) methods in both finite-field and expectation value evaluation approaches. We also give a term-by-term comparison of contributions from our CC and NCC calculations in order to show differences in the results from these two methods. Moreover, we present results from other lower-order methods to understand the role of electron correlation effects in the determination of the above quantities. A machine learning based scheme to generate optimized basis functions for atomic calculations is developed and applied here. From the analysis of the dipole polarizability result, accuracy of the calculated quadrupole and third-order polarizability values are ascertained, for which no experimental values are currently available.

Tailoring higher-order topological phases via orbital hybridization

Higher-order topological insulators (HOTIs) have attracted much attention in photonics due to the tightly localized disorder-robust corner and hinge states. Here, we reveal an unconventional HOTI phase with vanishing dipole and quadrupole polarizations. This phase arises in the array of evanescently coupled waveguides hosting degenerate $s$- and $d$-type orbital modes arranged in a square lattice with four waveguides in the unit cell. As we prove, the degeneracy of the modes with the different symmetry gives rise to the nontrivial topological properties rendering the system topologically equivalent to the two copies of the anisotropic two-dimensional Su-Schrieffer-Heeger model rotated by ${90}^{\ensuremath{\circ}}$ with respect to each other and based on $s\ifmmode\pm\else\textpm\fi{}d$ hybridized orbitals. We probe the unusual topology of the model by constructing a quantized Fu-Kane-type pseudospin pump. Our results introduce a route to tailor higher-order band topology leveraging both crystalline symmetries and accidental degeneracies of the different orbital modes.

Additional light waves in atomic cryocrystals in the frequency vicinity of a quadrupole-allowed excitonic resonance

The paper is devoted to propagation of exciton–polariton excitations in atomic cryocrystals in the frequency vicinity of a quadrupole-allowed excitonic resonance. The unit volume quadrupole polarizability tensor is obtained for a cubic crystal. A number of peculiar features of exciton polariton dispersion are discussed, related to the presence of additional light waves.

Polarization effects, shape resonances and bound states in low energy positron elastic scattering by Zinc and Cadmium vapours

Low energy elastic positron scattering from Zn and Cd atoms was studied using model correlation potential. Special attention is given to the study of polarization effects through the incorporation of quadrupole polarizabilities and hyperpolarizabilities in the scattering potential. Resonant p-wave shape structures are found for both systems. Results show that these become sharper and move to lower energies as the level of polarization of the potential is increased. Resonance was suppressed in Cd when the second hyperpolarizability γ was taken greater than 46000 a.u. and true p-wave bound states were formed. Comparison to previous calculations and dependence of the results with the scheme adopted to match the correlation and polarization components of the potential is discussed. We find that the elastic cross sections and the resonant effects do not depend on the specific form of the correlation potential but strongly depend on the polarization parameters and the matching point determined by the crossing between the correlation and polarization components of the potential. The value for the dipole–dipole–quadrupole polarizability B for Cd was specifically calculated using the relativistic coupled-cluster approach and is reported for the first time in this work.

Determination of quadrupole polarizabilities of the excited states of alkali-metal atoms

The scalar and tensor components of the electric quadrupole (E2) polarizabilities of the first two excited states of all the alkali-metal atoms are determined. To validate the calculations, we have evaluated the ground state E2 polarizabilities of these atoms and compared them with the literature values. We could not find the ground state E2 polarizability value for Fr in the literature to compare with our result. The dominant parts of these quantities are estimated by combining the precisely calculated E2 transition matrix elements of many low-lying transitions with the experimental energies, while the other contributions are estimated using lower-order methods. Our estimated values for the ground states of the above atoms are in good agreement with the literature values suggesting that our estimated E2 polarizabilities for the excited states of the alkali atoms, which were not known earlier except for the Li atom, are also quite accurate. These reported E2 polarizabilities could be useful in guiding many precision measurements in the alkali atoms.

Дисперсия поляритонных возбуждений в атомарных криокристаллах в окрестности частоты квадрупольно разрешенного экситонного резонанса

The paper is devoted to the propagation of exciton-polariton excitations in atomic cryocrystals in the frequency vicinity of a quadrupole resolved exciton resonance. The structure of the local electromagnetic field in a molecular crystal in the frequency vicinity of an isolated quadrupole transition in the spectrum of the molecule is investigated; the tensor of the quadrupole polarizability of the unit volume of a cubic crystal is obtained. The features of the exciton polaritons dispersion reflecting the presence of additional light waves in the investigated frequency neighborhood are studied.

Possible Observational Evidence for the Existence of a Parallel Universe

Many totally different kinds of astrophysical observations demonstrated that, in our universe, there exists a preferred direction. Specifically, from observations in a wide range of frequencies, the alignment of various preferred directions in different data sets was found. Moreover, the observed Cosmic Microwave Background (CMB) quadrupole, CMB octopole, radio and optical polarizations from distant sources also indicate the same preferred direction. While this hints at a gravitational pull from the “outside”, the observational data from the Plank satellite showed that the bulk flow velocity was relatively small: much smaller than was initially thought. In the present paper we propose a configuration where two three-dimensional universes (one of which is ours) are embedded in a four-dimensional space and rotate about their barycenter in such a way that the centrifugal force nearly (but not exactly) compensates their mutual gravitational pull. This would explain not only the existence of a preferred direction for each of the three-dimensional universes (the direction to the other universe), but also the fact that the bulk flow velocity, observed in our universe, is relatively small. We point out that this configuration could also explain the perplexing features of the Unidentified Aerial Phenomena (UAP), previously called Unidentified Flying Objects (UFOs), recorded by various detection systems—the features presented in the latest official report by the US Office of the Director of National Intelligence. Thus, the proposed configuration of the two rotating, parallel three-dimensional universes seems to explain both the variety of astrophysical observations and (perhaps) the observed features of the UAP.

Higher-order topological insulators in two-dimensional Dirac materials

As a novel topological state, a higher-order topological insulator has attracted enormous interest, which in d spatial dimensions has gapless boundary states at (d−n) dimensions (integer n is larger than 1). Until now, merely few two-dimensional (2D) materials have been identified as higher-order topological insulators and their experimental confirmations are still absent. Here we propose a universal strategy of antidot engineering to realize second-order topological insulators (SOTIs) in 2D Dirac materials. Based on symmetry analysis, tight-binding model, and first-principles calculations, we demonstrate SOTIs in antidot-decorated Xene (X=C, Si,and Ge) by displaying its finite bulk quadrupole moment, weak topological edge states, and in-gap topological corner states. An inherent connection is established for the existing various mechanisms of the SOTIs, including quadrupole polarization, filling anomaly, and generalized Su-Schrieffer-Heeger model on a Kekulé lattice. The robustness of topological corner states of the SOTIs against edge perturbations and bulk disorders is explicitly demonstrated, rendering our strategy appealing to experimental realization of topological corner states.Received 5 September 2021Accepted 30 November 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L042044Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEdge statesFirst-principles calculationsTopological materialsPhysical SystemsGermaneneGrapheneHoneycomb latticeTechniquesDensity functional theorySymmetriesTight-binding modelWannier function methodsCondensed Matter, Materials & Applied Physics