Atomic Wave Functions Research Articles

Exploring unresolved sideband, optomechanical strong coupling using a single atom coupled to a cavity

A major trend within the field of cavity QED is to boost the interaction strength between the cavity field and the atomic internal degrees of freedom of the trapped atom by decreasing the mode volume of the cavity. In such systems, it is natural to achieve strong atom-cavity coupling, where the coherent interaction strength exceeds the cavity linewidth, while the linewidth exceeds the atomic trap frequency. While most work focuses on coupling of photons to the internal degrees of freedom, additional rich dynamics can occur by considering the atomic motional degree of freedom as well. In particular, we show that such a system is a natural candidate to explore an interesting regime of quantum optomechanics, where the zero-point atomic motion yields a cavity frequency shift larger than its linewidth (so-called single-photon optomechanical strong coupling), but simultaneously where the motional frequency cannot be resolved by the cavity. We show that this regime can result in a number of remarkable phenomena, such as strong entanglement between the atomic wave function and the scattering properties of single incident photons, or an anomalous mechanism where the atomic motion can significantly heat up due to single-photon scattering, even if the atom is trapped tightly within the Lamb-Dicke limit.

Efficient Adiabatic Spin-Dependent Kicks in an Atom Interferometer.

We present an atom interferometry technique in which the beam splitter is split into two separate operations. A microwave pulse first creates a spin-state superposition, before optical adiabatic passage spatially separates the arms of that superposition. Despite using a thermal atom sample in a small (600 μm) interferometry beam, this procedure delivers an efficiency of 99% per ℏk of momentum separation. Utilizing this efficiency, we first demonstrate interferometry with up to 16ℏk momentum splitting and free-fall limited interrogation times. We then realize a single-source gradiometer, in which two interferometers measuring a relative phase originate from the same atomic wave function. Finally, we demonstrate a resonant interferometer with over 100 adiabatic passages, and thus over 400ℏk total momentum transferred.

Construction of Fermi Potentials from Electronic Wave Functions.

The Fermi potential, vF(r), is the nonclassical part of the multiplicative effective potential appearing in the one-particle Schrödinger-type equation for the square root of the electron density. The usual way of constructing vF(r) by inverting that equation produces unsatisfactory results when applied to electron densities expanded in Gaussian basis sets. We suggest a different method that is based on an explicit formula for vF(r) in terms of the interacting one- and two-electron reduced density matrices of the system. This method is exact in the basis-set limit and yields accurate approximations to the basis-set-limit vF(r) when applied to reduced density matrices represented in terms of finite basis sets. Illustrative applications involve atomic and molecular wave functions generated at various levels of ab initio theory. It is also shown how to construct the Pauli and exchange-correlation potentials of any system starting with only vF(r).

Resonating valence bonds and spinon pairing in the Dicke model

Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms coupled to a common photon mode. In the lossy cavity limit, starting with an initial state with MM atoms excited and NN atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or ‘spinons’. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to an inchoate superconductor – mixed quantum state with a fluctuating number of spinon pairs. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization, the emission exhibits a continuous transition from a dark state to a bright state. This opens an exciting route to simulate RVB states and superconductivity.

Coulomb phase in high harmonic generation

We derive a regularized expression for the Coulomb term in the phase of high order harmonics emitted in the interaction of intense laser pulses with atoms. The calculation is based on the formalism of quantum orbits and on the imaginary time method and allows one to match the initially divergent Coulomb integral with the phases of the atomic wave function at the instants of ionization and recombination, leading to a finite and closed analytic formula. This complex-valued Coulomb phase can considerably modify both the yield and the interference structure of high harmonic spectra. Its possible implications for numerical calculations of the high harmonic signal are discussed.

Probing the mechanism of xanthine oxidase and 2-amino xanthine: an implication of energy, charge bond order and wave function.

Xanthine oxidase (XO) is an important molybdenum-containing enzyme catalyzing the hydroxylation of hypoxanthine to xanthine and xanthine to uricacid. The mechanistic action by which xanthine oxidase oxidizes purine derivatives is not well understood. A better understanding of the overall mechanism is supposed to enhance our ability to control the metabolic properties of potential drug molecules metabolized by this enzyme. In this work a model substrate, 2-Amino Xanthine has been used to study the mechanistic action of the enzyme. For this reason, the present theoretical work was intended to probe a unified mechanism for the oxidation of 2-Amino Xanthine by xanthine oxidase. Parameters like total electronic energy, Mulliken atomic charges, wave functions, and percent contribution of chemical fragments were generated using a DFT method employing B3LYP level of theory with 6-31G(d',p') basis set for nonmetals and LanL2DZ basis set for molybdenum. AOmix software package that employs single point energy output as an input file was employed for wave function and percent fragment analysis. From these result new reaction intermediates and plausible reaction mechanism root has been reported for reductive and oxidative half reaction using 2-Amino Xanthine as model substrate. In this work it can be concluded that a stepwise mechanistic route with hydrogen bonding reaction complex and active site resemble very rapid Mo (V) intermediate is most plausible.    Â

Producing superfluid circulation states using phase imprinting

We propose a method to prepare states of given quantized circulation in annular Bose-Einstein condensates (BEC) confined in a ring trap using the method of phase imprinting without relying on a two-photon angular momentum transfer. The desired phase profile is imprinted on the atomic wave function using a short light pulse with a tailored intensity pattern generated with a Spatial Light Modulator. We demonstrate the realization of 'helicoidal' intensity profiles suitable for this purpose. Due to the diffraction limit, the theoretical steplike intensity profile is not achievable in practice. We investigate the effect of imprinting an intensity profile smoothed by a finite optical resolution onto the annular BEC with a numerical simulation of the time-dependent Gross-Pitaevskii equation. This allows us to optimize the intensity pattern for a given target circulation to compensate for the limited resolution.

Jj-Coupling-based atomic self-consistent-field calculations with relativistic effective core potentials and two-component spinors

A self-consistent-field (SCF) program for the calculation of atomic energies and wave functions defined in jj-coupling using two-component atomic spinors and relativistic effective core potentials (RECPs) is described. The code is based on the linear combination of atomic orbitals SCF algorithm for atomic states defined in LS-coupling developed by Roothaan and Bagus. Hamiltonian matrix elements with respect to one- and two-electron operators, including RECPs, are calculated for two-component atomic spinor basis functions of either Gaussian-type orbitals (GTOs) or Slater-type orbitals (STOs). Electronic states are defined as eigenfunctions of the total angular momentum squared operator and tables of the required vector coupling coefficients that define such pure states are provided. In addition, one or more GTO expansions of large- and small-core RECPs and their corresponding GTO basis sets are supplied for all elements Z=3 through Z=118. Optimized two-component basis sets of STOs or GTOs can be calculated for use in molecular structure codes based on RECPs and relativistic electronic structure theory. Atomic asymptotic state energies at the SCF level of theory for analysis of molecular dissociation limits can be studied. Program summaryProgram title: jjatomProgram Files doi:http://dx.doi.org/10.17632/zs4twp8r67.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: Relativistic atomic energies and wave functions; optimization of two component spinor basis sets.Solution method: Atomic spinors defined in jj-coupling and expansions in two-component spinor basis functions of Gaussian- or Slater-type functions. Self-consistent field optimization of the total energy. Used for optimization of two-component atomic spinor basis sets and calculations of valence spectra of heavy elements.

Simulating magnetic fields in Rydberg-dressed neutral atoms

A Rydberg interaction that can effectively exchange the states of two atoms may be used to transfer the optical phase of laser fields to the atomic pair wave function. A similar phase mapping may occur for many neutral atoms in a two-dimensional lattice when subjected to off-resonant optical Rydberg dressing fields, simulating the effect of a magnetic field. This all-optical method of simultaneously simulating magnetic fields and strong two-body interaction may have application to the study of quantum magnetism and topological physics.

The Stark Effect on the Wave Function of Tritium in Relativistic Condition

Tritium Atom is one of the isotopes of Hydrogen that has two Neutrons in the nucleus and an electron that surrounds the nucleus. The Stark Effect is an effect of a shift or polarization of the atomic spectrum caused by the external electrostatic field. The interaction between the electrons and the external electric field can be reviewed using an approximation method of perturbation theory. The perturbation theory used is a time Independent non-degenerate perturbation and reviewed to second order to obtain correction of Tritium Atomic wave function. The condition that used in the system is a relativistic condition by reviewing the movement of electrons within the Atom. The effects of relativity also affect the correction of the wave function of Atom Tritium in the ground state. Tritium is radioactive material that is still relatively safe, and one of the applications of Tritium Atom is on the battery of betavoltaics (Nano Tritium Battery).

Atomic spectroscopy with twisted photons: Separation of M1−E2 mixed multipoles

We analyze atomic photoexcitation into the discrete states by twisted photons, or photons carrying extra orbital angular momentum along their direction of propagation. From the angular momentum and parity considerations, we are able to relate twisted-photon photoexcitation amplitudes to their plane-wave analogues, independently of the details of the atomic wave functions. We analyzed the photo-absorption cross sections of mixed-multipolarity $E2-M1$ transitions in ionized atoms and found fundamental differences coming from the photon topology. Our theoretical analysis demonstrates that it is possible to extract the relative transition rates of different multipolar contributions by measuring the photo-excitation rate as a function of the atom's position (or the impact parameter) with respect to the optical vortex center. The proposed technique for separation of multipoles can be implemented if the target's atom position is resolved with sub-wavelength accuracy, for example, with Paul traps. Numerical examples are presented for Boron-like highly-charged ions (HCI).

Classical limit of position matrix elements for Rydberg atoms

In this work we discuss Bohr’s correspondence principle in a particular physical system, namely the hydrogen atom. It is shown that while diagonal elements of the position operator are equal to zero, off-diagonal elements between two states of different but close energies have a classical limit. The classical limit is reached when both principal quantum numbers, and hence both energies, are large but their difference is small. In this case the matrix elements of the position operator tend to the Fourier component of a classical trajectory, whose parameters are found. The classical limit is proved by finding numerical values of the matrix elements and also by exact treatment of the analytical formulas. This discussion provides a deeper understanding of the correspondence between quantum and classical mechanics and contributes to a better understanding of hydrogen atom wave functions.

Electron-assisted magnetization tunneling in single spin systems

Magnetic excitations of single atoms on surfaces have been widely studied experimentally in the past decade. Lately, systems with unprecedented magnetic stability started to emerge. Here, we present a general theoretical investigation of the stability of rare-earth magnetic atoms exposed to crystal or ligand fields of various symmetry and to exchange scattering with an electron bath. By analyzing the properties of the atomic wavefunction, we show that certain combinations of symmetry and total angular momentum are inherently stable against first or even higher order interactions with electrons. Further, we investigate the effect of an external magnetic field on the magnetic stability.

Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

AbstractThe spectrum of the hydrogen atom confined in a spherical impenetrable box of radius Rc has been investigated by many authors up to date, but not at the level of relativistic corrections. It is well known that, as Rc diminishes, all energy levels and the pressure increase very rapidly, whereas the polarizability goes to zero. In this report, we have computed the relativistic corrections that underlie the fine structure of the confined hydrogen atom, as a function of Rc. Such corrections correspond to relativistic kinetic energy, spin‐orbit coupling and the Darwin term, which are calculated in the frame of time‐independent perturbation theory, for which, use was made of the exact confined hydrogen atom wave functions. We show that for a confinement radius of 0.5 au the relativistic corrections increase up to three orders of magnitude with respect to those corresponding to the free atom. As Rc decreases, the kinetic energy correction and the spin‐orbit coupling for become negative whereas their absolute value and the Darwin term, which is positive, increase very rapidly.

The fractal geometry of Hartree-Fock.

The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.

Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal

A constructive theoretical platform for the description of quantum space-time crystals uncovers for $N$ interacting and ring-confined rotating particles the existence of low-lying states with proper space-time crystal behavior. The construction of the corresponding many-body trial wave functions proceeds first via symmetry breaking at the mean-field level followed by symmetry restoration using projection techniques. The ensuing correlated many-body wave functions are stationary states and preserve the rotational symmetries, and at the same time they reflect the point-group symmetries of the mean-field crystals. This behavior results in the emergence of sequences of select magic angular momenta $L_m$. For angular-momenta away from the magic values, the trial functions vanish. Symmetry breaking beyond mean field can be induced by superpositions of such good-$L_m$ many-body stationary states. We show that superposing a pair of adjacent magic angular momenta states leads to formation of special broken-symmetry states exhibiting quantum space-time-crystal behavior. In particular, the corresponding particle densities rotate around the ring, showing undamped and nondispersed periodic crystalline evolution in both space and time. The experimental synthesis of such quantum space-time-crystal wave packets is predicted to be favored in the vicinity of ground-state energy crossings of the Aharonov-Bohm-type spectra accessed via an externally applied magnetic field. These results are illustrated here for Coulomb-repelling fermionic ions and for a lump of contact-interaction attracting bosons.

Constructing “Designer Atoms” via Resonant Graphene-Induced Lamb Shifts

The properties of an electron in an atom or molecule are not fixed; rather they are a function of the optical environment of the emitter. Not only is the spontaneous emission a function of the optical environment, but also the underlying wave functions and energy levels, which are modified by the potential induced by quantum fluctuations of the electromagnetic field. In free space, this modification of atomic levels and wave functions is very weak and generally hard to observe due to the prevalence of other perturbations like fine structure. Here, we explore the possibility of highly tailorable electronic structure by exploiting large Lamb shifts in tunable electromagnetic environments such as graphene, whose optical properties are dynamically controlled via doping. The Fermi energy can be chosen so that the Lamb shift is very weak, but it can also be chosen so that the shifts become more prominent than the fine structure of the atom and even potentially the Coulomb interaction with the nucleus. Potential...

Photoionization of S3+ using the Breit-Pauli R-matrix method

Sulphur is one of the most abundant chemical elements in the universe and a large number of lines have been observed in the spectra of astrophysical object. The S IV and SV ions considered in this work have received much interest in the last decade. The main objective of the present work is to report on photoionization cross-sections of S IV using the Breit-Pauli R-matrix (BPRM) method. We have carried out extensive non-relativistic and relativistic calculations of the photoionization cross sections to focus on relativistic effects. The reliability of the atomic data presented here has been carefully tested. We have exploited the BPRM code to describe the atomic wavefunctions and generate the energy levels for the SV 81 fine-structure bound target states and the corresponding A-values for transitions between these levels. The partial and total cross sections for the photoionization of the Al-like S3+ ground and excited states are determined for photon energy ranging from the S4+ 3s2 threshold up to the S4+ 4s threshold. We present statistically weighted, level resolved ground photoionization cross sections for the S IV ion. Both resonance positions and the oscillator strengths are presented. Extensive comparison of the present calculated values with those obtained from direct theoretical scattering calculation is also presented. To the best of our knowledge, the work reported herein describes for the first time a detailed relativistic photoionization calculation for this system, and the results are relevant to the laboratory and astrophysical plasmas.

ARC: An open-source library for calculating properties of alkali Rydberg atoms

We present an object-oriented Python library for the computation of properties of highly-excited Rydberg states of alkali atoms. These include single-body effects such as dipole matrix elements, excited-state lifetimes (radiative and black-body limited) and Stark maps of atoms in external electric fields, as well as two-atom interaction potentials accounting for dipole and quadrupole coupling effects valid at both long and short range for arbitrary placement of the atomic dipoles. The package is cross-referenced to precise measurements of atomic energy levels and features extensive documentation to facilitate rapid upgrade or expansion by users. This library has direct application in the field of quantum information and quantum optics which exploit the strong Rydberg dipolar interactions for two-qubit gates, robust atom-light interfaces and simulating quantum many-body physics, as well as the field of metrology using Rydberg atoms as precise microwave electrometers. Program summaryProgram Title: ARC: Alkali Rydberg CalculatorProgram Files doi:http://dx.doi.org/10.17632/hm5n8w628c.1Licensing provisions: BSD-3-ClauseProgramming language: Python 2.7 or 3.5, with C extensionExternal Routines: NumPy [1], SciPy [1], Matplotlib [2]Nature of problem: Calculating atomic properties of alkali atoms including lifetimes, energies, Stark shifts and dipole–dipole interaction strengths using matrix elements evaluated from radial wavefunctions.Solution method: Numerical integration of radial Schrödinger equation to obtain atomic wavefunctions, which are then used to evaluate dipole matrix elements. Properties are calculated using second order perturbation theory or exact diagonalisation of the interaction Hamiltonian, yielding results valid even at large external fields or small interatomic separation.Restrictions: External electric field fixed to be parallel to quantisation axis.Supplementary material: Detailed documentation (.html), and Jupyter notebook with examples and benchmarking runs (.html and .ipynb).[1] T.E. Oliphant, Comput. Sci. Eng. 9, 10 (2007). http://www.scipy.org/.[2] J.D. Hunter, Comput. Sci. Eng. 9, 90 (2007). http://matplotlib.org/.

Neutrino mass, electron capture, and the shake-off contributions

Electron capture can determine the electron neutrino mass, while the beta decay of Tritium measures the electron antineutrino mass and the neutrinoless double beta decay observes the Majorana neutrino mass. Electron capture e. g. on 163Ho plus bound electron to 163Dy* plus neutrino can determine the electron neutrino mass from the upper end of the decay spectrum of the excited Dy*, which is given by the Q-Value minus the neutrino mass. The Dy* states decay by X-ray and Auger electron emissions. The total decay energy is measured in a bolometer. These excitations have been studied by Robertson and by Faessler et al.. In addition the daughter atom Dy can also be excited by moving in the capture process one electron into the continuum. The escape of these continuum electrons is automatically included in the experimental bolometer spectrum. Recently a method developed by Intemann and Pollock was used by DeRujula and Lusignoli for a rough estimate of this shake-off process for "s" wave electrons in capture on 163Ho. The purpose of the present work is to give a more reliable description of "s" wave shake-off in electron capture on Holmium. For that one needs very accurate atomic wave functions of Ho in its ground state and excited atomic wave functions of Dy* including a description of the continuum electrons. In the present approach the wave functions of Ho and Dy* are determined selfconsistently with the antisymmetrized relativistic Dirac-Hartree-Fock approach. The relativistic continuum electron wave functions for the ionized Dy* are obtained in the corresponding selfconsistent Dirac-Hartree-Fock-Potential. In this improved approach shake-off can hardly be seen after electron capture in 163Ho and thus can probably not affect the determination of the electron neutrino mass.