Quadrupole Polarizabilities Research Articles

Noncompact atomic insulators

We study the conditions for Bloch bands to be spanned by symmetric and strictly compact Wannier states that have zero overlap with all lattice sites beyond a certain range. Similar to the characterization of topological insulators in terms of an algebraic (rather than exponential) localization of Wannier states, we find that there may be impediments to the compact localization even of topologically "trivial" obstructed atomic insulators. These insulators admit exponentially-localized Wannier states centered at unoccupied orbitals of the crystalline lattice. First, we establish a sufficient condition for an insulator to have a compact representative. Second, for $\mathcal{C}_2$ rotational symmetry, we prove that the complement of fragile topological bands cannot be compact, even if it is an atomic insulator. Third, for $\mathcal{C}_4$ symmetry, our findings imply that there exist fragile bands with zero correlation length. Fourth, for a $\mathcal{C}_3$-symmetric atomic insulator, we explicitly derive that there are no compact Wannier states overlapping with less than $18$ lattice sites. We conjecture that this obstruction generalizes to all finite Wannier sizes. Our results can be regarded as the stepping stone to a generalized theory of Wannier states beyond dipole or quadrupole polarization.

Dual-band metamaterial absorber with a low-coherence composite cross structure in mid-wave and long-wave infrared bands.

The atmospheric window in the infrared (IR) band primarily consists of mid-wave (MWIR, 3-5 μm) and long-wave IR (LWIR, 8-12 μm) bands, also known as the working bands in most of the IR devices. The main factor affecting the device capability includes the absorption efficiency, hence, the absorption material. Herein, a dual-band absorber based on the composite cross structure (CCS) in both MWIR and LWIR bands was proposed, with absorption peaks of 4.28 μm and 8.23 μm. The obtained absorber is with high scalability in the MWIR and LWIR region respectively by tuning the structural parameters. A quadrupole polarization model is proposed for further understanding of the uneven distribution of electromagnetic field that was caused by the change of the center spacing of the embedded structure. Meanwhile, it was shown that the two absorption peaks exhibited good incident angle stability. In addition, as the incident angle of the TM mode increases, a waveguide is formed between the embedded structure and the surface structure, leading to another strong absorption in the LWIR band. The results showed that absorption increases as the incident angle increases. The proposed absorber can be a good candidate for applications in thermal emission, detection and solar energy harvesting.

Observation of second- and higher-order electric quadrupole interactions with an atomic ion

The response of matter to fields underlies the physical sciences, from particle physics to astrophysics, and from chemistry to biophysics. We observe an atom's response to an electric quadrupole field to second- and higher orders; this arises from the atom's electric quadrupole polarizability and hyperpolarizabilities. We probe a single atomic ion which is excited to Rydberg states and confined in the electric fields of a Paul trap. The quadrupolar trapping fields cause atomic energy level shifts and give rise to spectral sidebands. The observed effects are described well by theory calculations.

Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge.

This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10%-20% with CAM-B3LYP and 20%-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(-)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistent with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials.

Multipole polarizabilities for hydrogen-like atoms in Hulthén potential with and without spherical confinement

The multipole polarizabilities for hydrogen-like atoms with Hulthen potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthen potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthen, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations.

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

Optically pumped NMR oscillator based on 131Xe nuclear spins

A 131Xe nuclear magnetic resonance (NMR) oscillator can be used in the measurement of rotation rates, CPT and Lorentz violation tests, etc. To improve the measurement precision of devices based on a 131Xe NMR oscillator, its characteristics need to be fully understood. Under the conditions where the Zeeman interaction is much larger than the quadrupolar interaction, the characteristics of the 131Xe NMR oscillator involving the magnetic resonance, free induction decay, and closed-loop oscillation are investigated both experimentally and theoretically. The main findings are as follows. The 131Xe NMR oscillator consists of six oscillators, three of which can be directly observed by a magnetometer. When the polarization of the 131Xe spin ensemble can be described by a spin temperature, the ensemble exhibits both spin orientation and spin alignment. The spin alignment breaks the symmetry of the three main oscillators. The free induction decay signal of 131Xe depends on parameters such as the spin alignment and the driving magnetic field, which make the measurement of the relaxation time difficult. In the closed-loop mode under self-excitation, the 131Xe NMR oscillator may oscillate with more than one frequency at certain feedback gain and phase. If the quadrupole splitting is much smaller than the spin relaxation rate, then the 131Xe oscillator can be described by the Bloch equations, and the 131Xe oscillator will have a large amplitude. The oscillation frequency of the closed-loop oscillator depends on the quadrupole splitting, polarization, and various relaxation times, which should be considered in designing a high-precision NMR sensor. The results are significant for optimizing and improving the performance of the 131Xe NMR oscillator as a sensor for precision measurement.

Resonance energy transfer mediated by a chiral molecule.

The problem of resonant energy transfer (RET) between an electric dipole donor, D, and an electric dipole acceptor, A, mediated by a passive, chiral third-body, T, is considered within the framework of molecular quantum electrodynamics theory. To account for the optical activity of the mediator, magnetic dipole and electric quadrupole coupling terms are included in addition to the leading electric dipole interaction term. Fourth-order diagrammatic time-dependent perturbation theory is used to obtain the matrix element. It is found that the Fermi golden rule rate depends on pure multipole moment polarizabilities and susceptibilities of T, as well as on various mixed electric and magnetic multipole moment response functions. The handedness of T manifests through mixed electric-magnetic dipole and mixed electric dipole-quadrupole polarizabilities, which affect the rate and, respectively, require the use of fourth-rank and sixth-rank Cartesian tensor averages over T, yielding non-vanishing isotropic rate formulae applicable to a chiral fluid medium. Terms of a similar order of magnitude proportional to the product of electric dipole polarizability and either magnetic dipole susceptibility or electric quadrupole polarizability of T are also computed for oriented and freely tumbling molecules. Migration rates dependent upon the product of the pure electric dipole or magnetic dipole polarizability with the mixed electric-magnetic or electric dipole-quadrupole analogs, which require fourth- and fifth-rank Cartesian tensor averaging, vanish for randomly oriented systems. Asymptotically limiting rate expressions are also evaluated. Insight is gained into RET occurring in complex media.

Electric dipole and quadrupole properties of the Cd atom for atomic-clock applications

We present accurate values of the atomic properties that are sensitive to an external electric field in an experiment, such as static electric dipole and quadrupole polarizabilities, hyperpolarizabilities, and quadrupole moments of the low-lying $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$, $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}$, and $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ states of the Cd atom. The four-component relativistic coupled-cluster theory is employed to determine the atomic wave functions and energies. The finite-field approach is adopted to estimate the above quantities from the evaluated energies. The roles of electron correlation effects in the calculations are demonstrated by giving results that are obtained with different approximations. Precise knowledge of the above spectroscopic properties is useful for estimating typical systematics of the optical clocks built using the Cd atoms.

Core polarizability of rubidium using spectroscopy of the ng to nh, ni Rydberg transitions

We present a precise measurement of the rubidium ionic core polarizability. The results can be useful for interpreting experiments such as parity violation or black-body radiation shifts in atomic clocks since the ionic core electrons contribute significantly to the total electrical polarizability of rubidium. We report a dipole polarizability $\alpha_d$ = $9.116 \pm 0.009$ $a_0^3$ and quadrupole polarizability $\alpha_q$ = $38.4 \pm 0.6$ $a_{0}^{5}$ derived from microwave and radio-frequency spectroscopy measurements of Rydberg states with large angular momentum. By using a relatively low principal quantum number ($17 \leq n \leq 19$) and high angular momentum ($4 \leq \ell \leq 6$), systematic effects are reduced compared to previous experiments. We develop an empirical approach to account for non-adiabatic corrections to the polarizability model. The corrections have less than a 1\% effect on $\alpha_d$ but almost double $\alpha_q$ from its adiabatic value, bringing it into much better agreement with theoretical values.

Dynamic Multipole Polarizabilities of Helium and Screened-Helium Atoms

The precise estimation of atomic polarizabilities impinges upon a number of areas and processes in physical science. We calculate precisely the dynamic multipole polarizabilities of the helium and screened-helium atoms using highly correlated exponential wavefunctions based on the pseudo-state summation method. For screened environments, we consider the Debye–Hückel potential (DHP) as the interaction potentials between the charged particles. The dynamic multipole (quadrupole, octupole, and hexadecapole) polarizabilities for the ground state of the helium atom and the multipole (quadrupole and octupole) polarizabilities of the screened-helium atom for different screening parameters are reported along with magic-zero wavelengths. The reported results for hexadecapole polarizability of the helium atom and dynamic multipole polarizability of the screened-helium atom are new and would be useful for future investigation on this topic.

Reduced resonance line-width and enhanced figure of merit in Ag/Si/SiO2 nanopillar array sensors

Ag/Si/SiO2 nanopillar array sensors are presented to reduce the line-width and enhance the figure of merit (FOM). In Ag/Si/SiO2 nanopillar arrays, each Ag nanopillar is on top of each Si nanopillar, and each Si nanopillar is on top of each SiO2 nanopillar, which sits on quartz substrates. The simulated results show that the line-width can be as small as 7 nm, 2.4 times narrower than that of the periodic arrays of Ag nanopillars on SiO2 nanopillars, which sit on quartz substrates. This can be attributed to the reduced line-width of the plasmonic lattice resonance (PLR), which is due to the coupling between the localized surface plasmon quadrupole polarization of Ag nanopillars and the diffraction of the periodic arrays. The period of the arrays, the diameter of Ag nanopillars, the thickness of Ag nanopillars, Si nanopillars and SiO2 nanopillars have important effects on the PLR. Benefiting from the narrower line-width, the FOM is enhanced. This provides a possible way to improve the application of plasmonic array sensors.

Active Plasmonics and Active Chiral Plasmonics through Orientation-Dependent Multipolar Interactions

While most active plasmonic efforts focus on responsive metamaterials to modulate optical response, we present a simple alternative based on applied orientation control that can likely be implemented for many passive plasmonic materials. Passive plasmonic motifs are simpler to prepare but cannot be altered post-fabrication. We show that such systems can be easily manipulated through substrate orientation control to generate both active plasmonic and active chiral plasmonic responses. Using gold nanocrescents as our model platform, we demonstrate tuning of optical extinction from -21% to +36% at oblique incidence relative to normal incidence. Variation of substrate orientation in relation to incident polarization is also demonstrated to controllably switch chiroptical handedness (e.g., Δg = ±0.55). These active plasmonic responses arise from the multipolar character of resonant modes. In particular, we correlate magnetoelectric and dipole-quadrupole polarizabilities with different light-matter orientation-dependence in both near- and far-field localized surface plasmon activity. Additionally, the attribution of far-field optical response to higher-order multipoles highlights the sensitivity offered by these orientation-dependent characterization techniques to probe the influence of localized electromagnetic field gradients on a plasmonic response. The sensitivity afforded by orientation-dependent optical characterization is further observed by the manifestation in both plasmon and chiral plasmon responses of unpredicted structural nanocrescent variance (i.e., left- and right-tip asymmetry) not physically resolved through topographical imaging.

Calculation of higher-order corrections to the light shift of the 5s2 S01−5s5p P0o3 clock transition in Cd

In the recent work [A.~Yamaguchi et. al, Phys. Rev. Lett. {\bf 123}, 113201 (2019)] Cd has been identified as an excellent candidate for a lattice clock. Here, we carried out computations needed for further clock development and made an assessment of the higher-order corrections to the light shift of the $5s^2\, ^1\!S_0$--$5s5p\, ^3\!P_0^o$ clock transition. We carried out calculations of the magnetic dipole and electric quadrupole polarizabilities and linear and circular hyperpolarizabilities of the $5s^2\, ^1\!S_0$ and $5s5p\, ^3\!P_0^o$ clock states at the magic wavelength and estimated uncertainties of these quantities. We also evaluated the second-order Zeeman clock transition frequency shift.

Accurate calculation of multipole polarizabilities for one-electron atom in Debye plasmas

The electric multipole polarizabilities of one-electron atoms embedded in weakly coupled Debye plasmas are calculated in the non-relativistic framework. The static dipole, quadrupole, octopole, and hexadecapole polarizabilities for hydrogen atoms in both ground and excited states at a variety of Debye screening parameters are calculated in high precision based on the sum-over-states method, where the system bound and continuum states are produced by employing the generalized pseudospectral method. It is shown that the contribution of bound states to the polarizability decreases with increasing the plasma screening strength, whereas the contribution of continuum states is enhanced. At very small screening parameters where the plasma environment starts to take effect, it is found that the 2l-pole polarizability for s-wave states with principle quantum number n≥l+1 has an abrupt change from its non-screening value to infinity. We attribute such a phenomenon to the sudden non-degeneracy of different angular momentum states in the n shell. With continuously increasing the screening strength, the polarizabilities for n≥l+1 states decrease to certain values and, eventually, they approach to infinity at the critical screening parameter. For states with n≤l, the 2l-pole polarizabilities show regular enhancement from the non-screening value to infinity. The present results are compared with other theoretical calculations available in the literature and it is shown that our work has established by now the most accurate predictions of multipole oscillator strengths and polarizabilities for one-electron atoms in Debye plasmas.

Molecular multipoles and (hyper)polarizabilities of water by ab initio calculations

The dipole, quadrupole, octopole, hexadecapole, dipole polarizability, first hyperpolarizability, second hyperpolarizability, dipole-quadrupole polarizability, dipole–dipole-quadrupole polarizability, quadrupole–quadrupole polarizability, and dipole-octopole polarizability of water molecule are calculated by CCSD(T) level of theory and complete basis set limit (CBS) with finite field method. Comparisons with previous ab initio calculations as well as the known experimental measurements are also made. It is shown that the calculated dipole, quadrupole, and dipole polarizability are in good agreements with the experimental measurements. Considering the nuclear vibration and dispersion effect, the average first and second hyperpolarizabilities at CCSD(T)/CBS level are also in reasonable agreement with experimental measurements.

Profiles of Static Quadrupole Polarizability of Impurity‐Doped Quantum Dots Driven by Gaussian White Noise

Herein, the influence of Gaussian white noise on static quadrupole polarizability (SQP) of the impurity‐doped quantum dots (QDs) is studied. The SQP profiles are critically analyzed as several physical quantities are varied over a range in the absence and presence of noise. The introduction of noise to the system is accomplished via two different routes viz. “additive” and “multiplicative.” SQP profiles consist of noticeable features like maximization, minimization, and saturation in the absence of noise and presence of additive noise. However, on most occasions, the SQP profile becomes devoid of any noticeable characteristics in the presence of multiplicative noise. The multiplicative noise plays some noticeable role only during the direct variation in confinement energy. Herein, the exclusive role of additive noise having strength around a typical value for the generation of large SQP is highlighted. The findings bear mentionable importance on the nonlinear optical properties of QD‐based devices under the aegis of noise.

Polarizabilities, dispersion coefficients, and retardation functions at the complete basis set CCSD limit: From Be to Ba plus Yb.

Static and dynamic polarizabilities of alkaline earth metal atoms Be-Ba and of the Yb atom, as well as dispersion coefficients and retardation functions for their long-range interactions, are used as a benchmark for the restricted coupled cluster method with singles and doubles (CCSD) and noniterative triples added [CCSD(T)] and related polarization propagator CCSD(3) methods at the complete basis set limit. The latter is attained through the sequence of the augmented correlation-consistent polarized weighted core valence n-zeta basis sets with the exact 2-component approximation for the scalar relativistic effects and with the small-core effective core potentials (for Ca, Sr, and Ba). At the converged level of core correlation treatment, the finite-field CCSD(T) method reproduces the best available data for the static dipole and quadrupole polarizabilities better than 1% and 4%, respectively. Systematic cancelation of the triple contribution in the CCSD(3) calculations of the dynamic polarizabilities of alkaline earth metal atoms makes their dispersion coefficients accurate within 3%. The retardation functions are computed and used for the analysis of the long-range interactions in the homonuclear dimers. Implications to accurate ab initio calculations of the global interaction potentials are discussed.

Dissolution of shell structures and the polarizability of dripline nuclei

Nuclear matter and finite nuclei at extreme isospin are studied within the microscopical Giessen energy density functional (GEDF). The structure of the GEDF is discussed. Quasiparticle wave equations and the residual interactions are derived by variational methods. Applications to nuclear ground and excited states by HFB and QRPA methods and extensions to multi-phonon theory are indicated. Pairing effects are described by the Gorkov coupled channels approach by which wave function effects are accounted for. Pairing self-energies for continuum states and the resulting additional scattering phase shifts are introduced. It is shown that pairing and polarization self-energies can induce narrow resonances in continuum spectra. Dipole and quadrupole response functions and polarizabilities are discussed as signatures for halo and skin dynamics in lithium and in carbon isotopes. The recently established new pygmy dipole (PDR) and quadrupole (PQR) modes are considered as signatures for nuclear skin dynamics. Their importance for astrophysical reaction rates and stellar nucleo-synthesis is investigated.

Kramers-Heisenberg dispersion formula for scattering of twisted light

An extremely active research topic of modern optics is studying how light can be engineered to possess forms of structure such as a twisting or a helical phase and the ensuing optical orbital angular momentum (OAM) and its interactions with matter. In such circumstances, the plane-wave description no longer suffices and both paraxial and nonparaxial solutions to the wave equation are desired. Within the framework of molecular QED theory, a general formulation is developed for the scattering of twisted light beams by molecular systems through the Kramers-Heisenberg dispersion formula and ensuing scattering cross section, which takes account of the effects of the phase and intensity structure of twisted light, revealing scattering effects not exhibited by unstructured, plane-wave light. The theory is applicable to linear scattering as well as to nonlinear optical effects for both chiral and nonchiral species, and explicit results are derived for Rayleigh and Raman scattering (including second-order contributions), Rayleigh and Raman optical activity, and their circular-vortex differential scattering analogs. These processes necessitate the inclusion of magnetic-dipole and electric-quadrupole coupling terms, as well as the usual leading electric-dipole interaction term. It is seen that the coupling of electric quadrupole moments to structured light affords a unique sensitivity to the phase properties of the beam, most importantly, its optical OAM, and its inclusion permits the contribution to the scattering cross section proportional to the square of the mixed electric dipole-quadrupole polarizability to be evaluated for which interesting features result. These include its discriminatory behavior arising from circularly polarized input radiation and its dependence on the topological charge, which can also serve to enhance scattering. Also presented are results for a contribution of identical order proportional to the pure electric-dipole and quadrupole polarizabilities.