Atomic Wave Functions Research Articles

Wave Function Engineering on Superconducting Substrates: Chiral Yu-Shiba-Rusinov Molecules.

Magnetic adatoms on superconductors give rise to Yu-Shiba-Rusinov (YSR) states that hold considerable interest for the design of topological superconductivity. Here, we show that YSR states are also an ideal platform to engineer structures with intricate wave function symmetries. We assemble structures of iron atoms on the quasi-two-dimensional superconductor 2H-NbSe2. The Yu-Shiba-Rusinov wave functions of individual atoms extend over several nanometers enabling hybridization even at large adatom spacing. We show that the substrate can be exploited to deliberately break symmetries of the adatom structure leading to hybridized YSR states exhibiting symmetries that cannot be found in orbitals of iso-structural planar molecules in the gas phase. We exploit this potential by designing chiral YSR wave functions of triangular adatom structures. Our results significantly expand the range of interesting quantum states that can be engineered using arrays of magnetic adatoms on superconductors.

Front Cover: Commentary on “A simple, practical experiment to investigate atomic wavefunction reduction within a Stern‐Gerlach magnet” by Michael Devereux, published in J. Phys. B: At. Mol. Opt. Phys. 57, 152501 (2024), https://doi.org/10.1088/1361‐6455/ad5992

Front Cover: Commentary on “A simple, practical experiment to investigate atomic wavefunction reduction within a Stern‐Gerlach magnet” by Michael Devereux, published in <i>J. Phys. B: At. Mol. Opt. Phys</i>. 57, 152501 (2024), https://doi.org/10.1088/1361‐6455/ad5992

Ab Initio Manganese Kα and Kβ Energy Eigenvalues, Shake-Off Probabilities, Auger Rates, with Convergence Tests.

This work presents ab initio calculations for the Kα spectrum of manganese (Z = 25, [Ar]3d54s2), a highly complex system due to the five open orbitals in the 3d shell. The spectrum is composed of the canonical diagram line [1s]→[2p] and shake-off satellite lines [1snl]→[2pnl] (nl∈{2s,2p,3s,3p,3d,4s}), where square brackets denote a hole state. The multiconfiguration Dirac-Hartree-Fock method with the active set approach provides the initial and final atomic wavefunctions. Results are presented as energy eigenvalue spectra for the diagram and satellite transitions. The calculated wavefunctions include over one hundred million configuration state functions and over 280,000 independent transition energies for the seven sets of spectra considered. Shake-off probabilities and Auger transition rates determine satellite intensities. The number of configuration state functions ensures highly-converged wavefunctions. Several measures of convergence demonstrate convergence in the calculated parameters. We obtain convergence of the transition energies in all eight transitions to within 0.06 eV and shake-off probabilities to within 4.5%.

Commentary on “A simple, practical experiment to investigate atomic wavefunction reduction within a Stern‐Gerlach magnet” by Michael Devereux, published in J. Phys. B: At. Mol. Opt. Phys. 57, 152501 (2024), https://doi.org/10.1088/1361‐6455/ad5992

Commentary on “A simple, practical experiment to investigate atomic wavefunction reduction within a Stern‐Gerlach magnet” by Michael Devereux, published in <i>J. Phys. B: At. Mol. Opt. Phys</i>. 57, 152501 (2024), https://doi.org/10.1088/1361‐6455/ad5992

A simple, practical experiment to investigate atomic wavefunction reduction within a Stern–Gerlach magnet

For nearly one hundred years most quantum-mechanics texts have depicted a continuous, spin-direction superposition of the wavefunction of the silver atom traversing a Stern–Gerlach (S–G) magnet. But there are sound scientific arguments which deny that understanding. Schrodinger’s equation for that continuous wavefunction development cannot describe the transfer of energy from the magnetic field to that atom. Modern micro-fabrication techniques now make it possible to implement a simple, accessible experiment testing whether a spin superposition does continue in the magnet. Because the S–G experiment is the prototype for quantum measurement, that observation is crucial to implementing a realistic quantum theory of measurement.

Probability of He+ Ion at Quantum Number 3 ≤ n ≤ 4 in Momentum Space

Ions resulting from the ionization of helium atoms are known as helium ions. Atom of Helium The probability distribution of the particle locations and velocities inside a helium atom is referred to as probability. Using theoretical study methods, the goal of this research is to find the probability of an electron's position in a helium atom at the quantum number 3 ≤ n ≤ 4. This type of research is non-experimental research by developing previously existing theories. This type of research is non-experimental research by transforming the radial wave function of hydrogenic atoms in position space into a radial wave function in momentum space using the Fourier transformation, then including a number of Gegenbauer functions and using the probability equation of finding an electron in a Helium ion in momentum space. The results of this research provide information regarding the position and probability of the existence of electrons in the helium atom. The probability value for the Helium ion is obtained using the equation P(p) = which is used to indicate the probability of finding an electron in a helium atom is directly proportional to the principal quantum number (n) and the value of the electron's momentum. The larger the electron momentum interval, the greater the probability.

Effects of higher-order Casimir-Polder interactions on Rydberg atom spectroscopy

In the extreme near field, when the spatial extension of the atomic wavefunction is no longer negligible compared to the atom-surface distance, the dipole approximation is no longer sufficient to describe Casimir-Polder interactions. Here we calculate the higher-order, quadrupole and octupole, contributions to Casimir-Polder energy shifts of Rydberg atoms close to a dielectric surface. We subsequently investigate the effects of these higher-order terms in thin-cell and selective reflection spectroscopy. Beyond its fundamental interest, this regime of extremely small atom surface separations is relevant for quantum technology applications with Rydberg or surface-bound atoms interfacing with photonic platforms. Published by the American Physical Society 2024

Persistent currents of ultrarelativistic plasma-encased endofullerene molecules entrapping a H atom

In this work, for the first time in the relevant literature, the persistent currents (PC) and induced magnetic fields (IMF) of an endofullerene molecule entrapping a hydrogen atom, under spherical confinement, are investigated. The endofullerene molecule is enclosed within a spherical region and embedded in a plasma environment. The plasma environment is depicted with the more general exponential cosine screened Coulomb potential, and its relevant effects are analyzed by considering plasma screening parameters. The relevant model for endohedral confinement is the Woods–Saxon confinement potential, which is compatible with experimental data. The effects of various forms of C n are thoroughly elucidated via the analysis of the confinement depth, spherical shell thickness, the inner radius, and the smoothing parameters. To find the bound states in the spherically confined endofullerene, the decoupling of the second-order Dirac equation for the large and small components of the radial atomic wave functions is considered. The Dirac equation with the interaction potential is solved numerically by using the Runge–Kutta–Fehlberg method via the decoupling formalism. The influence of spin orientations on the PC and IMF is also elucidated. The effects of spherical confinement, plasma shielding, and the structural properties of the fullerene on the PC and IMF are thoroughly viewed. Moreover, under given physical conditions, the optimal ranges of these effects are determined.

Refinement of X-ray and electron diffraction crystal structures using analytical Fourier transforms of Slater-type atomic wavefunctions in Olex2.

An implementation of Slater-type spherical scattering factors for X-ray and electron diffraction for elements in the range Z = 1-103 is presented within the software Olex2. Both high- and low-angle Fourier behaviour of atomic electron density and electrostatic potential can thus be addressed, in contrast to the limited flexibility of the four Gaussian plus constant descriptions which are currently the most widely used method for calculating atomic scattering factors during refinement. The implementation presented here accommodates the increasing complexity of the electronic structure of heavier elements by using complete atomic wavefunctions without any interpolation between precalculated tables or intermediate fitting functions. Atomic wavefunctions for singly charged ions are implemented and made accessible, and these show drastic changes in electron diffraction scattering factors compared with the neutral atom. A comparison between the two different spherical models of neutral atoms is presented as an example for four different kinds of X-ray and two electron diffraction structures, and comparisons of refinement results using the existing diffraction data are discussed. A systematic but slight improvement in R values and residual densities can be observed when using the new scattering factors, and this is discussed relative to effects on the atomic displacement parameters and atomic positions, which are prominent near the heavier elements in a structure.

Topological atom optics and beyond with knotted quantum wavefunctions

Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realization of structured light fields hosting complex singularities and topologically non-trivial characteristics. However, analogous studies are still in their infancy in the field of atom optics. Here, we investigate and experimentally create knotted quantum wavefunctions in spinor Bose–Einstein condensates which display non-trivial topologies. In our work we construct coordinated orbital and spin rotations of the atomic wavefunction, engineering a variety of discrete symmetries in the combined spin and orbital degrees of freedom. The structured wavefunctions that we create map to the surface of a torus to form torus knots, Möbius strips, and a twice-linked Solomon’s knot. In this paper we demonstrate close connections between the symmetries and underlying topologies of multicomponent atomic systems and of vector optical fields—a realization of topological atom-optics.

Static field ionization of the spherically confined hydrogen atom

AbstractThe ionization of the hydrogen atom confined in a spherical potential well and subjected to a static electric field is studied, using the diffusion Monte Carlo (DMC) method. Atomic ionization within a potential well is found to be a stationary, gradual, and reversible process. The value of the electric field at the onset of ionization is of the order of 0.1 atomic units, and depends on the symmetry of the atomic wave function and on the confinement dimension. By decreasing the confinement sphere, the difference between the bound and ionized states disappears, showing that strict confinement leads to pressure ionization of the atom. The off‐center case is studied characterizing the potential energy surface (PES), and the transition between field‐induced and pressure‐induced ionization is confirmed. Except for very weak fields, the minimum of the PES is reached when the proton is in contact with the boundary of the well.

A model of the spin Hall effect in polycrystalline nonmagnetic metals

In this paper, we theoretically investigated the effect of the polycrystalline structure of metal samples on the magnitude of the spin Hall effect. The equation for the dynamics of the averaged over the crystallite momentum of the collectivized conduction electron in the crystalline field of a homogeneous and isotropic polycrystalline metal is obtained. Averaging the obtained equation over all randomly oriented crystallites resulted in an expression for the electric field of the spin Hall effect. It significantly depends on the form of the single-electron atomic radial wave function and on the Hall coefficient. The coefficients of the spin Hall effect for some metals of 3rd–6th periods are calculated. It is shown that the results for nonmagnetic d- and f-metals within the measurement error are consistent with the experimental data. The best match is observed for Pt, [Formula: see text]-W, [Formula: see text]-W, Pd, Nb, Ag, Mo, Cu and Al. A discrepancy of less than 20% was obtained for Au, Ti, Mn. For the considered rare-earth metals (Lu, Ho, Dy, Gd) only for paramagnetic Lu the correspondence of calculation results and experimental data is obtained. For Ho, Dy, and Gd, which exhibit ferromagnetic and antiferromagnetic states at low temperatures, the discrepancy is more than 35%. Based on the obtained results, the limitations of the developed approach are formulated.

Electron impact fine-structure cross-section calculations of Cu and their applications in the diagnostics of laser-produced Cu-plasma through the collisional radiative model

We present the calculations of electron impact excitation cross-sections for the transitions from the ground state of Cu 3d104sS1/22 to the excited fine structure energy levels of the configurations 3d94s2,3d94s4p,3d104l,(l=p,d,f),3d105l,(l=s,p,d),3d10nl,(n=6,7;l=s,p) using the fully relativistic distorted wave theory. In addition, cross-sections for the transitions from the metastable states 3d94s2D5/2,3/22 to the upper excited levels are also presented. For calculating these cross-sections, we have obtained the atomic wave functions of copper using the multi-configuration Dirac–Fock approximation theory. To ensure the accuracy of these wave functions, we compared our calculated oscillator strengths of some dipole-allowed transitions of Cu with the available earlier reported values. We have utilized all the calculated electron impact fine-structure level excitation cross-sections from the ground as well as the metastable states of Cu to develop a fine structure-resolved collisional-radiative (CR) model for the diagnostics of laser-produced Cu plasma at atmospheric pressure. The model has been applied for diagnostics by coupling it with the spatially resolved optical emission spectroscopy (OES) measurements of Singh and Sharma [Phys. Plasmas 23 122104 (2016)] in the presence and absence of a static magnetic field. For diagnostics, the intensities of three OES observed strong atomic emission lines of Cu viz, 510.5, 515.3, and 521.8 nm have been utilized in the absence and presence of a magnetic field at different axial lengths (z = 0.5–6.5 mm) from the Cu target. Also, these intensities are corrected using the internal reference self-absorption method to overcome the effect of radiation trapping. The normalized intensities of the considered lines obtained from the CR model have been compared with their corresponding OES-measured values to extract the plasma parameters, i.e., electron temperature and electron density. Further, the obtained electron temperatures from the CR model are compared with the corresponding values reported in the experimental paper of Singh and Sharma [Phys. Plasmas 23 122104 (2016)] obtained using the Boltzmann plot method.

Dielectric Environment Sensitivity of Carbon Centers in Hexagonal Boron Nitride.

A key advantage of utilizing van-der-Waals (vdW) materials as defect-hosting platforms for quantum applications is the controllable proximity of the defect to the surface or the substrate allowing for improved light extraction, enhanced coupling with photonic elements, or more sensitive metrology. However, this aspect results in a significant challenge for defect identification and characterization, as the defect's properties depend on the the atomic environment. This study explores how the environment can influence the properties of carbon impurity centers in hexagonal boron nitride (hBN). It compares the optical and electronic properties of such defects between bulk-like and few-layer films, showing alteration of the zero-phonon line energies and their phonon sidebands, and enhancements of inhomogeneous broadenings. To disentangle the mechanisms responsible for these changes, including the atomic structure, electronic wavefunctions, and dielectric screening, it combines ab initio calculations with a quantum-embedding approach. By studying various carbon-based defects embedded in monolayer and bulk hBN, it demonstrates that the dominant effect of the change in the environment is the screening of density-density Coulomb interactions between the defect orbitals. The comparative analysis of experimental and theoretical findings paves the way for improved identification of defects in low-dimensional materials and the development of atomic scale sensors for dielectricenvironments.

Lithium Ion Wave Function (3Li2+) in a Momentum Chamber at n?3

Lithium ion (3Li2+) is a light alkali metal which is reactive and flammable when exposed to water or air. Lithium becomes ionic when lithium metal loses two of its three valence electrons. The wave function is a complex quantity that shows the characteristics of the de Broglie wave. The wave function in question is the radial wave function in the particle, because to find the probability that the electron is in the particle, only the radial part of the wave function is needed. However, there is no literature that discusses the wave function in the momentum space in the case of hydrogenic ions. Therefore, this research will examine the wave function of Lithium ion (3Li2+) in the momentum space. This type of research in the preparation of this article uses non-experimental research. Based on the results of the research that has been done, the wave function of Lithium ion (3 Li2+) in the momentum space at n 3 is obtained. The wave function consists of a radial, angular (polar and azimuth) wave function, as well as the wave function of Lithium ion (3Li2+) as a whole. The fundamental difference between the wave function of Lithium ion (3Li2+) in the momentum space and the wave function of hydrogenic atoms in the other momentum space is the value of the radial function caused by the difference in the value of (z) or atomic number.

Large-scale atom interferometry for fundamental physics

Atom interferometers measure quantum interference patterns in the wave functions of cold atoms that follow superpositions of different space-time trajectories. These can be sensitive to phase shifts induced by fundamental physics processes such as interactions with ultralight dark matter or the passage of gravitational waves. The capabilities of large-scale atom interferometers are illustrated by their estimated sensitivities to the possible interactions of ultralight dark matter with electrons and photons, and to gravitational waves in the frequency range around 1 Hz, intermediate between the peak sensitivities of the LIGO and LISA experiments. Atom interferometers can probe ultralight scalar couplings with much greater sensitivity than is currently available from probes of the Equivalence Principle. Their sensitivity to mid-frequency gravitational waves may open a window on mergers of masses intermediate between those discovered by the LIGO and Virgo experiments and the supermassive black holes present in the cores of galaxies, as well as fundamental physics processes in the early Universe such as first-order phase transitions and the evolution of networks of cosmic strings.

Suppressed electric quadrupole moment of thulium atomic clock states

A method for highly accurate calculations of atomic electric quadrupole moments (EQM) is presented, using relativistic general-excitation-rank configuration interaction wave functions based on Dirac spinors. Application to the clock transition states of the thulium atom employing up to full Quadruple excitations for the atomic wave function yields a final value of ${Q}_{zz}({^{2}F}_{7/2})=0.07\begin{array}{c}+0.07\\ \ensuremath{-}0.00\end{array}$ a.u., establishing that the thulium electronic ground state has an exceptionally small EQM. A detailed analysis of this result is presented which has implications for EQMs of other atoms with unpaired $f$ electrons.

Precise predictions and new insights for atomic ionization from the Migdal effect

The scattering of neutral particles by an atomic nucleus can lead to electronic ionisation and excitation through a process known as the Migdal effect. We revisit and improve upon previous calculations of the Migdal effect, using the Dirac-Hartree-Fock method to calculate the atomic wavefunctions. Our methods do not rely on the use of the dipole approximation, allowing us to present robust results for higher nuclear recoil velocities than was previously possible. Our calculations provide the theoretical foundations for future measurements of the Migdal effect using neutron sources, and searches for dark matter in direct detection experiments. We show that multiple ionisation must be taken into account in experiments with fast neutrons, and derive the semi-inclusive probability for processes that yield a hard electron above a defined energy threshold. We present results for the noble elements up to and including xenon, as well as carbon, fluorine, silicon and germanium. The transition probabilities from our calculations are publicly available.

Empirical Determination of the Bohr-Weisskopf Effect in Cesium and Improved Tests of Precision Atomic Theory in Searches for New Physics.

The finite distribution of the nuclear magnetic moment across the nucleus gives a contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic ^{133}Cs. This value is found from historical muonic-atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the precision heavy-atom community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

Off-resonant modulated driving gate protocols for two-photon ground-Rydberg transition and finite Rydberg blockade strength.

Recently, the concept of two-qubit controlled phase gate via off-resonant modulated driving has been introduced into the neutral atom qubit platform, with respect to both single-photon and two-photon ground-Rydberg transitions. In order to reach a better performance practically, further developments are in need to overcome a few known limitations in previous discussions. Here, we thoroughly analyze a variety of modulation styles for two-photon transitions, demonstrating the versatility of off-resonant modulated driving protocols. Furthermore, we show that it is possible to refine the designing process for improved performances for specific finite Rydberg blockade strength values. In particular, a reduced requirement on the blockade strength can be directly linked to an improvement of connectivity in qubit array of neutral atoms. These progress are closely related to the core feature that the atomic wave function acquires a geometric phase from the time evolution, which begins and finishes at the same quantum state. Under reasonable experimental conditions readily available nowadays, we anticipate that the fidelity of such protocols can reach as high as the essential requirement of NISQ even if the effects of technical errors and cold atoms' nonzero temperatures are considered.