Quadrupole Research Articles

Quantum phase transition in even-even Molybdenum isotopes using Von Neumann entropy

In this study, the Von Neumann entropy (entanglement entropy) of s - d bosons and proton (π) - neutron (ν) bosons in the even-even Molybdenum (94-42 102Mo) isotopes, within the framework of the Interacting Boson Model-2 (IBM-2), has been calculated and analyzed. In order to compare the results, the energy spectra, quadrupole moment, and the expectation value of the s-boson number operator of Mo isotopes have been obtained. The results showed that 94Mo has the minimum entanglement of s and d bosons and 102Mo nucleus has the maximum entanglement of s and d bosons. Therefore, these nuclei are spherical (U(5)) and γ-unstable (SO(6)) nuclei, respectively, and other observables confirm this result. Also, the value of the entanglement entropy of the π and ν bosons is constant by changing the control parameter. So, it does not show any transition.

Aspects of rotating anisotropic dark energy stars

By employing modified Chaplygin fluid prescription for the dark energy, we construct slowly rotating isotropic and anisotropic dark energy stars. The slow rotation is incorporated via general relativistic Hartle–Thorne formalism; whereas the anisotropy is introduced through Bowers–Liang prescription. We consider both the monopole and quadrupole deformations and present a complete analysis of rotating dark energy stars. By numerically solving the rotating stellar structure equations in presence of anisotropy, we analyse and quantify various properties of dark energy stars such as mass (M), radius, mass deformation, angular momentum (J), moment of inertia, and quadrupole moment (Q), for three different equation of state parameters. We find that anisotropic slow rotation results in significant deformation of stellar mass and thereby affects other global properties studied. For the values of angular frequencies considered, the effect of anisotropy on the stellar structure is found to be more prominent than that due to rotation. The dimensionless quadrupole moment QM/J2 measuring deviation from a Kerr metric black hole was obtained for anisotropic dark energy stars. We observe that dark energy stars with higher anisotropic strength tend to approach the Kerr solution more closely. We report that our results have considerable agreement with various astrophysical observational measurements. We also find that the dimensionless quadrupole moments of anisotropic dark energy stars corresponding to the canonical mass q¯1.4 have a similar range of values as that of isotropic neutron stars and strange stars.

Interferometric Near-field Fano Spectroscopy of Single Halide Perovskite Nanoparticles.

Semiconducting halide perovskite nanoparticles support Mie-type resonances that confine light on the nanoscale in localized modes with well-defined spatial field profiles yet unknown near-field dynamics. We introduce an interferometric scattering-type near-field microscopy technique to probe the local electric field dynamics at the surface of a single MAPbI3 nanoparticle. The amplitude and phase of the coherent light scattering from such modes are probed in a broad spectral range and with high spatial resolution. In the spectral domain, we uncover a Fano resonance with a 2π phase jump. In the near-field dynamics, this Fano resonance gives rise to a destructive interference dip after a few femtoseconds. Mie theory suggests that the interference between electric quadrupole and magnetic dipole modes of the particle, with spectra affected by resonant interband absorption of MAPbI3, lies at the origin of this effect. Our results open up a new approach for probing local near-field dynamics of single nanoparticles.

Electroweak Parameters from Mixed SU(2) Yang–Mills Thermodynamics

Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius r0∼a0, where a0 is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of Tc=7.95 keV. The monopole is in the Bogomolny–Prasad–Sommerfield (BPS) limit. It is interpreted in an electric–magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet’s charge at a value of the electromagnetic fine-structure constant α of α−1∼134 for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle θW∼30°, which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales (Λe=3.6 keV and ΛCMB∼10−4 eV). Here, the condition that the droplet’s bulk thermodynamics is stable determines the value of θW. The core radius of the monopole, whose inverse equals the droplet’s mass in natural units, is about 1% of r0.

Radiative decay rates for magnetic dipole (M1) and electric quadrupole (E2) transitions between low-lying levels within the 4f3 ground configuration of Pr III

Abstract A new set of theoretical radiative decay rates characterizing forbidden transitions in doubly charged praseodymium (Pr III) is reported in the present paper. More precisely, transition probabilities were computed for all magnetic dipole (M1) and electric quadrupole (E2) lines involving the lowest energy levels of the 4f$^3$ ground configuration located below 20000 cm$^{-1}$ since the levels above this limit are preferentially depopulated by allowed electric dipole (E1) transitions. The calculations were carried out using different computational strategies based firstly on the pseudo-relativistic Hartree-Fock (HFR) method and secondly on the fully relativistic Multiconfiguration Dirac-Hartree-Fock (MCDHF) method. The comparison between the results obtained by these independent approaches makes it possible to estimate their reliability. Comparisons with the few previously published data were also made. In addition, some astrophysical implications were deduced from the new atomic parameters computed in the present work, such as the possible presence of [Pr III] lines in the infrared spectra recorded by the {\it James Webb Space Telescope} ($JWST$) in the context of the investigation of kilonovae in their nebular phase, i.e. several days after neutron star mergers.

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core–shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3%–6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

Metastable doubly charged Rydberg trimers

We examine an effectively one-electron system with three positive nuclei composed of a Rb*87 Rydberg atom interacting with a pair of Rb+87 ions and predict the existence of metastable vibrationally bound states of Rb32+87. These molecules are long-range trimers whose stability rests on the presence of core-shell electrons and favorable scaling of the Rydberg atom's quadrupole moment with the principal quantum number n. Unlike recently observed ion-Rydberg dimers, whose binding is due to internal flipping of the Rydberg atom's dipole moment, the binding of Rb32+87 arises from the interaction of the ions with the Rydberg atom's quadrupole moment. The stability of these trimers is highly sensitive to n. For n≤35, we estimate that the lifetime of the bound states should be limited by intercore tunneling of the Rydberg electron, which creates an instability in the system. However, we predict that the rate of this process decreases significantly with n, such that already for n=38 it is comparable in magnitude to the rate of spontaneous emission of the Rydberg state. The decreasing depth of the binding potential at larger n will further lead to an increase in the tunneling rate of the vibrational states from the molecular binding potential to dissociative regions of the adiabatic potential energy surface. Nonetheless, at n=38, this mechanism is only relevant for the highest-excited vibrational states in the binding potential. Published by the American Physical Society 2024

Concept for a geometry-insensitive high-field magnetic resonance detector

AbstractWe introduce an inverse design methodology for a new class of eigenfrequency-invariant metamaterial-resonators, targeting nuclear magnetic resonance detection at ultra-high $$\mathbf {B_0}$$ B 0 field, and operating at two specified frequencies selected from within the 100-1500 MHz range. The primary optimisation goal is to maximise the magnetic field intensity and uniformity within a liquid sample, while the electric energy should be kept to a minimum level to reduce dielectric heating or quadrupolar moment excitation effects. Due to the symmetric geometry requirement of the cavity, a demultiplexer is also designed to direct each discrete resonant signal to another predetermined output port of the resonator. In order to reduce the geometrical dependency of the resonance frequency, a bespoke metamaterial is used for the cavity host. Therefore, an additional optimisation problem for a unit cell domain is defined to seek a proper material layout for the host region of the resonators. Given the sensitivity of the frequency domain, the optimisation process is effectively regulated through the utilisation of both a Helmholtz filter and a projection method. It is found that considerable improvements of the resonator quality factor can be obtained through this optimisation process.

Molecular models of PM6 for non-fullerene acceptor organic solar cells: How DAD and ADA structures impact charge separation and charge recombination.

The quadrupole moment of a non-fullerene acceptor (NFA) generated by the constituent electron donor (D) and acceptor (A) units is a significant factor that affects the charge separation (CS) and charge recombination (CR) processes in organic photovoltaics (OPVs). However, its impact on p-type polymer domains remains unclear. In this study, we synthesized p-type molecules, namely acceptor-donor-acceptor (ADA) and donor-acceptor-donor (DAD), which are components of the benchmark PM6 polymer (D: benzodithiophene and A: dioxobenzodithiophene). Planar heterojunction films, a model of bulk heterojunction, were prepared using ADA, DAD, and PM6 as the bottom p-type layers and Y6 NFA as the top n-type layer. Flash-photolysis time-resolved microwave conductivity, femtosecond transient absorption spectroscopy, and quantum mechanical calculations were employed to probe the charge carrier dynamics. Our findings reveal that while the subtle difference in quadrupole moment and energy gradient of the p-type materials has a minimal influence on CS, the molecular type (ADA or DAD) significantly affects the bulk CR. This study expands the understanding of how the p-type component and its conformation at the p/n interface impact the CS and CR in OPVs, highlighting the critical role of molecular donors in optimizing device performance.

Comprehensive Analysis of Optical Resonances and Sensing Performance in Metasurfaces of Silicon Nanogap Unit

Metasurfaces composed of silicon nanogap units have a variety of optical resonances, including bound states in the continuum (BIC). We show comprehensive numerical results on metasurfaces of Si-nanogap units, analyze the optical resonances, and clarify optically prominent resonances as well as symmetry-forbidding resonances that are the BIC, based on the numerical analyses of optical spectra and resonant electromagnetic field distributions. Introducing asymmetry in the unit cell, the BIC become optically allowed, being identified as magnetic dipole, electric quadrupole, and magnetic quadrupole resonances. Moreover, the optical resonances are examined in terms of refractive index sensing performance. A pair of the resonances associated with electric field localization at the nanogap was found to be sensitive to the refractive index in contact with the metasurfaces. Consequently, the gap mode resonances are shown to be suitable for a wide range of refractive index sensing over 1.0–2.0.

A quadrupole oscillator as an integrable model

A quadrupole oscillator is presented as an integrable model in the Born-Oppenheimer formalism with an electronic Hamiltonian being the quadrupole tensor. The electronic states of present concern are associated with a doubly degenerate positive eigenvalue of the electronic Hamiltonian, and accordingly the nuclear Hamiltonian takes a 2×2 matrix form. While the potential function for nuclear motion is proportional to r2, the kinetic energy operator is rather complicated, containing coupling terms with a Berry connection through adiabatic approximation. The energy eigenvalues, which receive a modification by a Chern number, get closer to those for the 3D isotropic harmonic oscillator if the angular momentum quantum number becomes sufficiently large.

Non-resonant picosecond three-wave mixing in the gas phase.

We report on the experimental observation of non-resonant, second-order optical sum-frequency generation (SFG) in five different atomic and molecular gases. The measured signal is attributed to a SFG process by characterizing its intensity scaling and its polarization behavior. We show that the electric quadrupole mechanism cannot explain the observed trends and suggest a mechanism based on symmetry breaking along the incident beam path arising from laser-induced species ground state number density gradients. Our results demonstrate that the SFG is about four orders of magnitude stronger than the third-harmonic generation (THG) and independent from any externally applied electric fields. These features make this method suitable for gas number density measurements at the picosecond time scale in reactive flows and plasmas.

Diffusion and Spectroscopy of H2 in Myoglobin

The diffusional dynamics and vibrational spectroscopy of molecular hydrogen (H2) in myoglobin (Mb) is characterized. Hydrogen has been implicated in a number of physiologically relevant processes, including cellular aging or inflammation. Here, the internal diffusion through the protein matrix was characterized, and the vibrational spectroscopy was investigated using conventional empirical energy functions and improved models able to describe higher-order electrostatic moments of the ligand. Depending on the energy function used, H2 can occupy the same internal defects as already found for Xe or CO (Xe1 to Xe4 and B-state). Furthermore, four additional sites were found, some of which had been discovered in earlier simulation studies. Simulations using a model based on a Morse oscillator and distributed charges to correctly describe the molecular quadrupole moment of H2 indicate that the vibrational spectroscopy of the ligand depends on the docking site it occupies. This is consistent with the findings for CO in Mb from experiments and simulations. For H2, the maxima of the absorption spectra cover ∼20 cm−1 which are indicative of a pronounced Stark effect of the surrounding protein matrix on the vibrational spectroscopy of the ligand. Electronic structure calculations show that H2 forms a stable complex with the heme iron (stabilized by ∼−12 kcal/mol), but splitting of H2 is unlikely due to a high activation energy (∼50 kcal/mol).

Faraday rotation method improves the upper limit of the electron electric-dipole-moment sensitivity.

The electron electric-dipole-moment (eEDM) is a powerful tool for exploring new particles. The candidates for eEDM search are heavy atoms and their molecules, which are well known for the obvious relativistic effect. Lead atom is considered to be the most ideal relativistic atom [Park et al., Nat. Commun. 11(1), 815 (2020)]. PbH molecule is an important representative of the Pb compound and is considered a cold candidate molecule due to the high diagonal Franck-Condon factors. We systematically investigated the (eEDM) searches of PbH using a two-component approach. The parity- and time-reversal symmetry violation constants of ground and excited states, including internal effective electric field Eeff, electron-nucleon scalar-pseudoscalar interaction constant WP,T, and nuclear magnetic quadrupole moment, were obtained and compared to other molecules. In addition, we designed two experimental methods to measure the sensitivity of the eEDM, indicating that the Faraday rotation method could greatly improve its sensitivity.

Manipulating reflection-type all-dielectric non-local metasurfaces via the parity of a particle number.

The parity of a particle number is a new degree of freedom for manipulating metasurface, while its influence on non-local metasurfaces remains an unresolved and intriguing question. We propose a metasurface consisting of periodically arranged infinite-long cylinders made from multiple layers of SiO2 and WS2. The cylinder exhibits strong backward scattering due to the overlapping magnetic dipole and electric quadrupole resonances. Without non-local coupling in unit cells, the infinite-size metasurface manifests high reflection across all instances. However, with non-local coupling in supercells, parity-dependent reflectivity diverges, exhibiting either increased logarithmic or decreased exponential behavior, with significant distinctions at small particle numbers. Interestingly, equal magnitude reflection and transmission reversals are achievable through alternation between adjacent odd and even particle numbers. The finite-size non-local metasurfaces behave similarly to the infinite-size counterparts, yet high reflection disappears at small particle numbers due to energy leakage. Essentially, high reflection arises from strong backward scattering and effective suppression of lateral multiple scatterings. Our work aids in the actual metasurface design and sheds new light on photonic integrated circuits and on-chip optical communication.

Corner and edge states in topological Sierpinski Carpet systems

Fractal lattices, with their self-similar and intricate structures, offer potential platforms for engineering physical properties on the nanoscale and also for realizing and manipulating high order topological insulator states in novel ways. Here we present a theoretical study on localized corner and edge states, emerging from topological phases in Sierpinski Carpet within a $\pi$-flux regime. A topological phase diagram is presented correlating the quadrupole moment with different hopping parameters. Particular localized states are identified following spatial signatures in distinct fractal generations. The specific geometry and scaling properties of the fractal systems can guide the supported topological states types and their associated functionalities. A conductive device is proposed by coupling identical Sierpinski Carpet units providing transport response through projected edge states which carry on the details of the system's topology. Our findings suggest that fractal lattices may also work as alternative routes to tune energy channels in different devices.

Electric quadrupole transitions of 98–112Ru atomic nuclei via conformable fractional Bohr Hamiltonian

In this paper, we investigate the energy spectra, wave functions and the [Formula: see text] transition rates for [Formula: see text]Ru atomic nuclei, using the conformable fractional Bohr Hamiltonian model. For the [Formula: see text]-part of the potential, the newly proposed Yukawa plus modified exponential potential is considered and the harmonic oscillator potential in [Formula: see text]-part, with [Formula: see text] fixed around [Formula: see text]. By using the conformable fractional Nikiforov–Uvarov method, energy spectra and wave functions are obtained analytically. The sensitivity of the potential parameters and the spectra with respect to the fractional order parameter is investigated. The normalized fractional energies and fractional electric quadrupole transition rates are compared with the available experimental predictions and those from existing theoretical studies. Comparisons are made at different values of the fractional derivative order. The results are presented across a broader range of values of [Formula: see text], providing a systematic analysis of how variations in this parameter influence the energy spectra, wave functions, and [Formula: see text] transition rates in Ru nuclei. Overall, the comparison of our results with experimental data shows the good accuracy of our model, especially when the fractional parameter goes to lower values. It can be concluded that the order of fractional derivative plays a crucial role in refining theoretical predictions of electric quadrupole transition rates, especially for transitions involving higher multipolarities.

Topological phase transitions and flat bands on a square-octagon lattice

We construct a square-octagon lattice model by considering the nearest-neighbor (NN) hoppings with staggered magnetic fluxes and the next-nearest-neighbor (NNN) hoppings, where zero-Chern-number topological insulator (ZCNTI) phases emerge. At 1/4 filling, by tuning the staggered fluxes and NNN hopping potential, this model supports the phase transition from a Chern insulator (CI) with Chern number C = 2 to a ZCNTI phase. At half filling, we observe that staggered magnetic fluxes can induce a higher-order topological insulator (HOTI) state. Interestingly, the ZCNTI appears at 3/4 filling when considering the NN and NNN hoppings in the absence of staggered fluxes, which has been rarely reported in previous work. Contrary to conventional HOTIs, this ZCNTI phase hosts both robust corner states and gapless edge states which can be identified based on the quantized dipole and quadrupole moments. Additionally, a topological flat band (TFB) with flatness ratio about 24 appears. We further investigate ν = 1/2 fractional Chern insulator (FCI) state when hard-core bosons fill into this TFB model.

Role of biquadratic exchange on thermodynamic quantities in anisotropic Heisenberg model

The magnetic and thermodynamic properties of the spin-1 anisotropic Heisenberg system are studied within Oguchi approximation. The system contains both the bilinear and biquadratic exchange interactions between the nearest neighboring spins located on a centered honeycomb lattice. For the positive biquadratic exchange interaction parameters, the phase transition in the Heisenberg case is of both second and first order where there is a discontinuity in the thermodynamic properties at this transition temperature. For some negative biquadratic exchange interaction parameters, in both the Heisenberg and Ising cases, the ferromagnetic state changes in favor of the antiferromagnetic state. The frustrated antiferromagnetic structure created by the biquadratic exchange parameter with negative sign was shown significantly influence the magnetization, quadrupolar moment, internal energy, heat capacity, entropy and free energy of the system, where the system has an oscillating chaotic phase regime. A double peak behavior was observed in the specific heat, with one at the critical temperature and another at a low temperature.

Realization of robust high-Q resonances of BICsvia eigenfield perturbations in a multiple-notched nanocube metasurface.

Non-radiative bound states in the continuum (BICs) allow the construction of resonances with high-quality (Q) factors and have emerged as an attractive platform for manipulating light-matter interactions on the nanoscale. However, current studies on symmetry-protected BICs (SP-BICs) suffer from a fundamental trade-off between the Q factor and asymmetric parameters, presenting a significant hurdle for practical applications. Here, utilizing the eigenfield perturbations, we successfully break the conventional inverse quadratic law of the SP-BICs and realize the robust high-Q resonances against the asymmetric parameters. We find the introductions of the central notch can efficiently boost the resonance of the electric quadrupole, which results in the enhancement of multiple-mode interference, and thus improving Q factors, while the constant effective refractive index guarantees the resonance with a stable wavelength. Our findings provide a promising strategy for modulating the light-matter interaction and may pave the way for applications in future high-performance optoelectronic devices.