Magnetic Dipole Polarizability Research Articles

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.

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules.

The electric dipole–magnetic dipole polarizability tensor , introduced to interpret the optical activity of chiral molecules, has been expressed in terms of a series of density functions , which can be integrated all over the three-dimensional space to evaluate components and trace . A computational approach to , based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of on the origin of the coordinate system has been investigated in connection with the corresponding change of . It is shown that only the trace of the density function defined via dynamic current density evaluated using the continuous translation of the origin of the coordinate system is invariant of the origin. Accordingly, this function is recommended as a tool that is quite useful for determining the molecular domains that determine optical activity to a major extent. A series of computations on the hydrogen peroxide molecule, for a number of different HO–OH dihedral angles, is shown to provide a pictorial documentation of the proposed method.

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.

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.

Second harmonic generation in metasurfaces with multipole resonant coupling

Abstract We report on the numerical demonstration of enhanced second harmonic generation (SHG) originating from collective resonances in plasmonic nanoparticle arrays. The nonlinear optical response of the metal nanoparticles is modeled by employing a hydrodynamic nonlinear Drude model implemented into Finite-Difference Time-Domain (FDTD) simulations, and effective polarizabilities of nanoparticle multipoles in the lattice are analytically calculated at the fundamental wavelength by using a coupled dipole–quadrupole approximation. Excitation of narrow collective resonances in nanoparticle arrays with electric quadrupole (EQ) and magnetic dipole (MD) resonant coupling leads to strong linear resonance enhancement. In this work, we analyze SHG in the vicinity of the lattice resonance corresponding to different nanoparticle multipoles and explore SHG efficiency by varying the lattice periods. Coupling of electric quadrupole and magnetic dipole in the nanoparticle lattice indicates symmetry breaking and the possibility of enhanced SHG under these conditions. By varying the structure parameters, we can change the strength of electric dipole (ED), EQ, and MD polarizabilities, which can be used to control the linewidth and magnitude of SHG emission in plasmonic lattices. Engineering of lattice resonances and associated magnetic dipole resonant excitations can be used for spectrally narrow nonlinear response as the SHG can be enhanced and controlled by higher multipole excitations and their lattice resonances. We show that both ED and EQ–MD lattice coupling contribute to SHG, but the presence of strong EQ–MD coupling is important for spectrally narrow SHG and, in our structure, excitation of narrow higher-order multipole lattice resonances results in five times enhancement.

Hadron Polarization in Strong Magnetic Field

The magnetic dipole polarizabilities and hyperpolarizabilities of the vector $${{\rho }^{0}}$$ and $${{\rho }^{ \pm }}$$ mesons have been calculated. The new characteristic of NPQCD in the strong magnetic field called tensor polarizability has been introduced, which is related to the tensor polarization of vector mesons. The contribution of the dipole magnetic polarizabilities to the tensor polarization of the vector mesons in the external abelian magnetic field has been explored.

Hadron polarization in strong magnetic field

The magnetic dipole polarizabilities and hyperpolarizabilities of the vector ρ0 and ρ± have been calculated. The new characteristic of the QCD vaccum in the strong magnetic field called tensor polarizability has been introduced, which is related to the tensor polarization. The contribution of the dipole magnetic polarizabilities to the tensor polarization of the vector mesons in the external abelian magnetic field has been explored.

Evaluation of Molecular Polarizability and of Intensity Carrying Modes Contributions in Circular Dichroism Spectroscopies

We re-examine the theory of electronic and vibrational circular dichroism spectroscopy in terms of the formalism of frequency-dependent molecular polarizabilities. We show the link between Fermi’s gold rule in circular dichroism and the trace of the complex electric dipole–magnetic dipole polarizability. We introduce the C++ code polar to compute the molecular polarizability complex tensors from quantum chemistry outputs, thus simulating straightforwardly UV-visible absorption (UV-Vis)/electronic circular dichroism (ECD) spectra, and infrared (IR)/vibrational circular dichroism (VCD) spectra. We validate the theory and the code by referring to literature data of a large group of chiral molecules, showing the remarkable accuracy of density functional theory (DFT) methods. We anticipate the application of this methodology to the interpretation of vibrational spectra in various measurement conditions, even in presence of metal surfaces with plasmonic properties. Our theoretical developments aim, in the long run, at embedding the quantum-mechanical details of the chiroptical spectroscopic response of a molecule into the simulation of the electromagnetic field distribution at the surface of plasmonic devices. Such simulations are also instrumental to the interpretation of the experimental spectra measured from devices designed to enhance chiroptical interactions by the surface plasmon resonance of metal nanostructures.

Tensor polarizability of the vector mesons from SU(3) lattice gauge theory

The magnetic dipole polarizabilities of the vector ρ0 and ρ± mesons in SU(3) pure gauge theory are calculated in the article. Based on this the authors explore the contribution of the dipole magnetic polarizabilities to the tensor polarization of the vector mesons in external abelian magnetic field. The tensor polarization leads to the dilepton asymmetry observed in non-central heavy ion collisions and can be also estimated in lattice gauge theory.

Partial-wave analysis of proton Compton scattering data below the pion-production threshold

Low-energy Compton scattering off the proton is used as an experimental tool for determination of the proton polarizabilities. However, the present empirical determinations rely heavily on the theoretical description(s) of the experimental cross sections in terms of polarizabilities. The state-of-art determinations are based on either the fixed-t dispersion relations (DR) or chiral perturbation theory in the single-baryon sector (χPT). The two approaches obtain rather different results for proton polarizabilities, most notably for βM1 (magnetic dipole polarizability). We attempt to resolve this discrepancy by performing a partial-wave analysis of the world data on proton Compton scattering below threshold. We find a large sensitivity of the extraction to a few “outliers”, leading us to conclude that the difference between DR and χPT extraction is a problem of the experimental database rather than of “model-dependence”. We have specific suggestions for new experiments needed for an efficient improvement of the database. With the present database, the difference of proton scalar polarizabilities is constrained to a rather broad interval: αE1−βM1=(6.8…10.9)×10−4fm3, with their sum fixed much more precisely [to 14.0(2)] by the Baldin sum rule.

On the magnetic polarizability tensor of US coinage

The magnetic dipole polarizability tensor of a metallic object gives unique information about the size, shape and electromagnetic properties of the object. In this paper, we present a novel method of coin characterization based on the spectroscopic response of the absolute tensor. The experimental measurements are validated using a combination of tests with a small set of bespoke coin surrogates and simulated data. The method is applied to an uncirculated set of US coins. Measured and simulated spectroscopic tensor responses of the coins show significant differences between different coin denominations. The presented results are encouraging as they strongly demonstrate the ability to characterize coins using an absolute tensor approach.

Electric Dipole-Magnetic Dipole Polarizability and Anapole Magnetizability of Hydrogen Peroxide as Functions of the HOOH Dihedral Angle.

The trace of tensors that account for chiroptical response of the H2O2 molecule is a function of the HO-OH dihedral angle. It vanishes at 0° and 180°, due to the presence of molecular symmetry planes, but also for values in the range 90-100° of this angle, in which the molecule is unquestionably chiral. Such an atypical effect is caused by counterbalancing contributions of diagonal tensor components with nearly maximal magnitude but opposite sign, determined by electron flow in open or closed helical paths, and associated with induced electric and magnetic dipole moments and anapole moments. For values of dihedral angle external to the 90-100° interval, the helical paths become smaller in size, thus reducing the amount of cancellation among diagonal components. Shrinking of helical paths determines the appearance of extremum values of tensor traces approximately at 50° and 140° dihedral angles.

Broadband suppression of backscattering at optical frequencies using low permittivity dielectric spheres

The exact suppression of backscattering from rotationally symmetric objects requires dual symmetric materials where εr = μr. This prevents their design at many frequency bands, including the optical one, because magnetic materials are not available. Electromagnetically small non-magnetic spheres of large permittivity offer an alternative. They can be tailored to exhibit balanced electric and magnetic dipole polarizabilities a1 = b1, which result in approximate zero backscattering. In this case, the effect is inherently narrowband. Here, we put forward a different alternative that allows broadband functionality: Wavelength-sized spheres made from low permittivity materials. The effect occurs in a parameter regime where approximate duality is met for all multipolar order an ≈ bn, in a weakly wavelength dependence fashion. In addition, and despite of the low permittivity, the overall scattering response of these spheres is still significant. Scattering patterns are shown to be highly directive across an octave spanning band. The effect is analytically and numerically shown using the Mie coefficients.

Determination of the properties of vector mesons in external magnetic field by quenched SU(3) lattice QCD

We investigate the ground state energies of vector ρ± and K±∗ mesons depending on the magnetic field value in the SU(3) lattice gauge theory. It has been shown that the energy of a vector particle depends on its spin projection on the field axis. The magnetic dipole polarizability and hyperpolarizabilities give significant contributions to the energy value which prevents the formation of the charged vector meson condensate at high magnetic fields. We calculate the g-factor of ρ± and K±∗ mesons and the dipole magnetic polarizability of ρ± mesons.

Dipole-dipole dispersion interactions between neutrons

We investigate the long-range interactions between two neutrons utilizing recent data on the neutron static and dynamic electric and magnetic dipole polarizabilities. The resulting long-range potentials are used to make quantitative comparisons between the collisions of a neutron with a neutron and a neutron with a proton. We also assess the importance of the first pion production threshold and first excited state of the nucleon, the $\Delta$-resonance ($J^{\pi}$ = + 3/2, I = 3/2). We found both dynamical effects to be quite relevant for distances r between ~ 50 fm up to ~$10^3$ fm in the nn system, the neutron-wall system and in the wall-neutron-wall system, reaching the expected asymptotic limit beyond that. Relevance of our findings to the confinement of ultra cold neutrons inside bottles is discussed.

Magnetic Polarizability Tensor Spectroscopy for Low Metal Anti-Personnel Mine Surrogates

The magnetic dipole polarizability tensor is an object-specific property possessing information about the size, shape, and material. This information could be used by electromagnetic induction sensors typically used for demining operations to discriminate between buried mines and clutter, reducing false alarm rates, and improving demining throughput and safety. This paper presents a methodology capable of obtaining the spectroscopic tensors of small metallic objects and low metal anti-personnel mine surrogates. The experimental results are validated against simulated and analytical solutions to ensure that the obtained tensor truly represents the absolute object tensor. Absolute tensors for a number of typical clutter items and mine surrogates are presented, with significant variance observed between those of mine and clutter.

Van der Waals and Casimir-Polder interactions between neutrons

We investigate the van der Waals interaction between neutrons using the theory of Casimir and Polder, wherein the potential for asymptotically large separations falls off as the inverse seventh power, and compare it to the similar interaction between a neutron and a proton, for which the asymptotic interaction falls off as the inverse fourth power. Modifications of the formalism to extend the validity to smaller separations using dynamic electric and magnetic dipole polarizability data are discussed

Aromaticity and Optical Activity.

The relationship between aromaticity and optical activity is investigated in comparisons of heterocycles with 4n + 2 and 4n π-electrons, in cyclic ketones with and without aromatic resonance structure representations, in tautomers and pericyclic reaction partners in which only one compound of each pair is aromatic, and in partially hydrogenated cyclo-C18 derivatives with both radial and tangential π-orbitals. In all comparisons, aromaticity is correlated to diminished optical activity. A heuristic explanation of this observation is grounded in the electric dipole-magnetic dipole polarizability contribution to optical activity in which the sense of electric dipoles and magnetic dipoles become uncoupled when electrons can circulate around a ring with either sense. These observations form a basis for making broad structure-optical activity correlations from inspection of molecular structure.

Magnetic polarizability of pion

We explore the energy dependence of $\pi$ mesons off the background abelian magnetic field on the base of quenched SU(3) lattice gauge theory and calculate the magnetic dipole polarizability of charged and neutral pions for various lattice volumes and lattice spacings. The contribution of the magnetic hyperpolarizability to the neutral pion energy has been also found.

Evaluation of the forward Compton scattering off protons: Spin-independent amplitude

We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits. For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\alpha_{E1}+\beta_{M1}=14.0(2)\times 10^{-4}\,\mathrm{fm}^3$. An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We remark on sum rules for the elastic component of polarizabilities.