Orbital Quantum Research Articles

Isolated core excitation of high-orbital-quantum-number Rydberg states of ytterbium

We study isolated core excitation of ultra cold ytterbium Rydberg atoms of high orbital quantum number. Measurements were performed on the $6s_{1/2} 40l \rightarrow 6p_{1/2} 40l $ transition with $l=5-9$. The extracted energy shifts and autoionization rates are in good agreement with a model based on independant electrons, taking into account interactions in a perturbative approach. We reveal a particularly long persistence of the autoionization rates with the orbital quantum number, explained by the strong coupling of the $6p_{1/2}nl$ autoionizing state with the $5d_{3/2}\epsilon l'$ continua compared to previously studied divalent atoms.

Locally Incompressible Spin State of the Fractional Quantum Hall Effect when v = 3/2

Neutral excitations in a two-dimensional electron system with an orbital and spin quantum number of 1 in the vicinity of filling factor v = 3/2 are studied experimentally. It is found that the rate of excitation relaxation to the ground state slows very strongly at v = 3/2, even though the number of vacancies in the ground state suitable for the relaxation of excitations is macroscopically large. It is shown that neutral excitations with orbital and spin quantum numbers of 1 in the state of v = 3/2 are an example of topologically protected excitation with different spin orderings in the ground and excited states. The state of v = 3/2 is an example of a locally incompressible fractional state of the quantum Hall effect, which is neither a Laughlin liquid nor an integer state of composite fermions.

Efficient energy resolved quantum master equation for transport calculations in large strongly correlated systems

We introduce a systematic approximation for an efficient evaluation of Born–Markov master equations for steady state transport studies in open quantum systems out of equilibrium: the energy resolved master equation approach. The master equation is formulated in the eigenbasis of the open quantum system and build successively by including eigenstates with increasing grandcanonical energies. In order to quantify convergence of the approximate scheme we introduce quality factors to check preservation of trace, positivity and hermiticity. Furthermore, we discuss different types of master equations that go beyond the commonly used secular approximation in order to resolve coherences between quasi-degenerate states. For the discussion of complete positivity we introduce a canonical Redfield–Bloch master equation and compare it to a previously derived master equations in Lindblad form with and without using the secular approximation. The approximate scheme is benchmarked for a six orbital quantum system which shows destructive quantum interference under the application of a bias voltage. The energy resolved master equation approach presented here makes quantum transport calculations in many-body quantum systems numerically accessible also beyond six orbitals with a full Hilbert space of the order of ∼106.

Difference in magnetic anisotropy of the ferromagnetic monolayers VI3 and CrI3

Concerning the magnetic anisotropy and magnetic moments of the ${M}^{3+}$ $(M=\mathrm{V}, \mathrm{Cr})$ ions in ferromagnetic $(\mathrm{FM}){M\mathrm{I}}_{3}$ monolayers, which have a honeycomb pattern of edge-sharing ${M\mathrm{I}}_{6}$ octahedra, conflicting observations have been reported in experimental and theoretical studies. We resolve these conflicts by determining the magnetic anisotropy energies for the ${M}^{3+}$ ions of ${M\mathrm{I}}_{3}$ monolayers, by analyzing their preferred spin orientations in terms of the selection rules based on the highest occupied molecular orbital--lowest unoccupied molecular orbital interactions of the ${M\mathrm{I}}_{6}$ octahedra, and by discussing whether or not the ${M}^{3+}$ ions are uniaxial. Here we show that the FM monolayer ${\mathrm{VI}}_{3}$ is uniaxial, but that of ${\mathrm{CrI}}_{3}$ is not. The magnetic anisotropy energy for the ${\mathrm{V}}^{3+}({d}^{2},S=1)$ ion of ${\mathrm{VI}}_{3}$ is greater than that for the ${\mathrm{Cr}}^{3+}$ $({d}^{3},$ $S=3/2)$ ion of ${\mathrm{CrI}}_{3}$ by more than an order of magnitude (i.e., \ensuremath{\sim}8 vs \ensuremath{\sim}0.6 meV). The ${\mathrm{V}}^{3+}$ ion exhibits uniaxial magnetism because its orbital quantum number L is not zero $(L=\phantom{\rule{0.16em}{0ex}}1)$, in contrast to the ${\mathrm{Cr}}^{3+}$ ion $(L=0)$.

Аналитическое решение уравнения Даффина - Кеммера - Петьо для суммы потенциала Маннинга - Розена и класс Юкавы

This paper presents an analytical bound-state solution to the Duffin - Kemmer - Petiau equation for the new putative combined Manning - Rosen and Yukawa class potentials. Using the developed scheme to approximate and overcome the difficulties arising in the centrifugal part of the potential, the bound-state solution of the modified Duffin - Kemmer - Petiau equation is found. Analytical expressions of energy eigenvalue and the corresponding radial wave functions are obtained for an arbitrary value of the orbital quantum number l . Also, eigenfunctions are expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are quite sensitive to the choice of radial and orbital quantum numbers.

Data for Beryllium–Hydrogen Charge Exchange in One and Two Centres Models, Relevant for Tokamak Plasmas

Data on the cross section and kinetic rate of charge exchange (CX) between the bare beryllium nucleus, the ion Be(+4) and the neutral hydrogen atom are of great interest for visible-range high-resolution spectroscopy in the ITER tokamak because beryllium is intended as the material for the first wall in the main chamber. Here an analysis of available data is presented, and the data needs are formulated. Besides the active probe signal produced by the CX of the diagnostic hydrogen neutral beam with impurity ions in plasma, a passive signal produced by the CX of impurity ions with cold edge plasma is also important, as it shows in observation data from the JET (Joint European Torus) tokamak with an ITER-like beryllium wall. Data in the range of a few eV/amu to ~100 eV/amu (amu stands for the atomic mass unit) needed for simulations of level populations for principal and orbital quantum numbers in the emitting beryllium ions Be(+3) can be obtained with the help of two-dimensional kinetic codes. The lack of literature data, especially for data resolved in orbital quantum numbers, has instigated us to make numerical calculations with the ARSENY code. A comparison of the results obtained for the one-centre Coulomb problem using an analytic approach and for the two-centre problem using numerical simulations is presented.

Wave function analysis with a maximum flow algorithm

An efficient algorithm for computing the maximum-flow path in a network is applied to the identification of the dominant configuration state functions (CSFs) in a graphically contracted function (GCF), configuration interaction, wave function. The flow network is a space of spin-adapted CSFs represented by a Shavitt graph, wherein the nodes correspond to orbital occupations and spin quantum numbers. The graph nodes are connected by arcs, and an arc density is defined as sums of the associated squared CSF coefficients. A max–min approach determines an upper bound to the maximum possible incoming flow for each graph node. A backtracking step generates a candidate walk and is followed by a limited search of alternative branching paths for the dominant CSF. The arc density contributions are removed from the graph, and the algorithm is reapplied to the updated graph. This list of generated walks can be partitioned in order to guarantee that the dominant CSFs have been identified. All of the steps in this algorithm are computationally efficient and do not depend on the potentially large dimension of the underlying linear CSF expansion space. An analysis of low-lying valence states of C2 illustrates the method.

Benchmarking Faddeev and transfer-to-the-continuum calculations for ( p,pN ) reactions

Nucleon-knockout reactions on proton targets (p, pN ) have experienced a renewed interest due to the availability of inverse-kinematics experiment with exotic nuclei. Various theoretical descriptions have been used to describe these reactions, such as the Distorted-Wave Impulse Approximation (DWIA), the Faddeev-type formalism and the Transfer to the Continuum method. Our goal is to benchmark the observables computed with the Faddeev and Transfer to the Continuum formalisms in the intermediate energy regime relevant for the experimental (p, pn) and (p, 2p) studies. In this paper, we analyze the 11 Be(p,pn)10Be reaction for different beam energies, binding energies and orbital quantum numbers with both formalisms to assess their agreement for different observables. We obtain a good agreement in all cases considered, within 10%, when the input potentials are taken consistently and realistically.

Frustrated ionization of atoms in the multiphoton regime

A semiclassical analytic theory which describes the excitation of atomic Rydberg states by intense laser radiation is formulated in the multiphoton limit of ionization. The theory is based on the separation of the electron motion in fast oscillations in the laser field and slow scattering in the Coulomb field of the nucleus. It allows one to calculate classical cut-off positions in the distribution of excited atoms in principal and orbital quantum numbers, and to identify the effect of quantum interference.

Penningionization processes involving cold Rydberg alkali metal atoms

This paper investigates the Penning ionization (PI) processes in cold gas media of alkali atoms. The PI autoionization widths of atomic pairs show a drastic dependence (by orders of magnitude) on the orbital quantum numbers of Rydberg atoms involved in a long-range dipole-dipole interaction. The nontrivial dependence of the PI efficiency on the size of colliding particles was considered, with a particular accent to the applications in the research of cold matter created in the experiments with magneto-optical traps. We have analytically described the optimal, highly asymmetric configurations of atomic Rydberg pairs, which lead to an explosive intensification (by several orders of magnitude) of a free-electron escaping due to PI. The excited states of atoms in the optimal pairs turn out to have a strong difference in atomic shell sizes. The optimal pairs’ properties may be favorable for the generation of primary (seeding) charged particles when a cold Rydberg medium evolves into a cold plasma. Within the framework of the semiclassical approach, we have obtained universal analytical formulas containing two adjustable parameters and present here their values in tabulated form, which allows estimating the PI rate constants for various pairs of alkali metal atoms.

Tunable magnetic properties and magnetocaloric effect of TmGa by Ho substitution

The influence of Ho substitution for Tm atoms on the magnetic properties and magnetocaloric effect (MCE) of TmGa compound was systematically investigated according to magnetic measurements and neutron powder diffraction (NPD) experiments. The magnetic transitions of ${\mathrm{Tm}}_{1\ensuremath{-}x}{\mathrm{Ho}}_{x}\mathrm{Ga}$ compounds show different types by Ho substitution due to the variation of spin and orbital angular momentum quantum number and the complete magnetic diagram of ${\mathrm{Tm}}_{1\ensuremath{-}x}{\mathrm{Ho}}_{x}\mathrm{Ga}$ compounds was obtained. The spin reorientation (SR) transition of ${\mathrm{Tm}}_{0.1}{\mathrm{Ho}}_{0.9}\mathrm{Ga}$ compound was directly confirmed by variable-temperature NPD experiments. Results show that the magnetic moment orders along the $c$ axis at the temperatures between ${T}_{\mathrm{SR}}$ and ${T}_{\mathrm{C}}$ and it cants away from the $c$ axis towards the $ab$ plane upon cooling below ${T}_{\mathrm{SR}}$. Furthermore, Ho substitution plays a dominant role in MCE of ${\mathrm{Tm}}_{1\ensuremath{-}x}{\mathrm{Ho}}_{x}\mathrm{Ga}$ compounds. When $x=0.15$, the peak value of magnetic entropy change reaches the maximum value of 18.0 J/kg K under field change of 0--2 T. The refrigerant temperature span ($\ensuremath{\delta}{T}_{\mathrm{FWHM}}$) and refrigeration capacity of ${\mathrm{Tm}}_{0.85}{\mathrm{Ho}}_{0.15}\mathrm{Ga}$ compound show enhancement of 23.0 and 21.6%, correspondingly, compared with TmGa compound. The giant MCE of ${\mathrm{Tm}}_{0.85}{\mathrm{Ho}}_{0.15}\mathrm{Ga}$ compound results from the optimization of spin and total angular momentum quantum number by Ho substitution.

Efficient local energy evaluation for multi-Slater wave functions in orbital space quantum Monte Carlo.

We present an algorithm for calculating the local energy of a multi-Slater wave function in orbital space quantum Monte Carlo (QMC). Recent developments in selected configuration interaction methods have led to increased interest in using multi-Slater trial wave functions in various QMC methods. For an ab initio Hamiltonian, our algorithm has a cost scaling of O(n5 + nc), as opposed to the O(n4nc) scaling of existing orbital space algorithms, where n is the system size and nc is the number of configurations in the wave function. We present our method using variational Monte Carlo calculations with the Jastrow multi-Slater wave function, although the formalism should be applicable for auxiliary field QMC. We apply it to polyacetylene and demonstrate the possibility of using a much larger number of configurations than possible using existing methods.

Unconventional magnetic excitations and spin dynamics of exotic quantum spin systems BaCo$$_2$$V$$_2$$O$$_8$$ and Ba$$_3$$CuSb$$_2$$O$$_9$$

We review terahertz (THz) electron spin resonance studies of two types of exotic quantum spin systems, namely, the spin(S)-1/2 one-dimensional (1D) Ising-like antiferromagnet BaCo $$_2$$ V $$_2$$ O $$_8$$ and the S=1/2 two-dimensional (2D) honeycomb-like antiferromagnet Ba $$_3$$ CuSb $$_2$$ O $$_9$$ in magnetic fields of up to 50 T. For the former subject, unconventional magnetic excitations were identified below a critical magnetic field $$H_c$$ ( $$\sim $$ 4 T), where the exotic field-induced order-to-disorder transition occurs, and magnetic excitations in a Tomonaga-Luttinger liquid state were observed above $$H_c$$ . The novel magnetic excitations were analyzed with an S=1/2 1D XXZ model by considering the peculiar structure of this compound. For the latter subject, the orbital quantum dynamics of the spin liquid candidate Ba $$_3$$ CuSb $$_2$$ O $$_9$$ was revealed using multifrequency electron spin resonance ranging from 9.3 GHz to 0.73 THz. The g-factor of the hexagonal Ba $$_3$$ CuSb $$_2$$ O $$_9$$ single crystal possesses a weak six-fold symmetry at low frequencies, while two-fold symmetry is manifested at high frequencies. From the critical point between the two frequency regions, the frequency of the dynamic Jahn-Teller distortion is determined to be approximately 10 GHz. This dynamic distortion, accompanied by orbital quantum tunneling, proves the spin-orbital liquid state in Ba $$_3$$ CuSb $$_2$$ O $$_9$$ .

Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl–Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl–Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods

Carrier multiplication in semiconductor quantum dots

The creation of many electron–hole (e–h) pairs in semiconductors under the absorption of a single photon was named as carrier multiplication (CM) process. The probabilities of the creation of two and three e–h pairs under the absorption of a single photon in semiconductor quantum dots (QDs) were investigated in the second and in the third orders of the perturbation theory using as the perturbations the Hamiltonians of the electron–radiation and electron–electron Coulomb interactions. It was supposed that the photon in the initial state has a sufficient energy to create two or three e–h pairs with the electrons in the lowest conduction band and with the holes in the valence band on the lowest levels of the size quantization. Their envelope wave functions were determined as the solutions of the Schrödinger equation for the electron inside the impenetrable sphere with the radius R0 of the QD. They are expressed through the spherical Bessel functions. It was shown that the lowest energy level of the size quantization with orbital quantum number l=0 in the QDs with small radii R→0 has the wave function similar with the 3D Dirac delta function. In this approximation the probabilities of the CM were estimated.

Vortex Beam Detection Based on Plasmonic in Plane Zone-Plate

A plasmonic in-plane zone-plate (IPZP) is analytically proposed and numerically analyzed. The proposed scheme consists of several discretely metallic nano-slits, which couple incident vortices into SPP and form focal spots. Wave front information of incident beam is reflected in the field distribution along “focal plane” of IPZP, and therefore, the proposed structure can be used for topological charge detection. Besides, an orthogonal slit array IPZP achieving simultaneous spin and orbital angular momentum detection is elaborated. IPZP structure has relatively high fabrication tolerance and the parameters can be adjusted to fit various operating wavelength. The proposed structure is expected to find potential applications in orbital angular momentum communication and high-dimensional quantum entanglement.

Synthesis, DFT computational insights on structural, optical, photoelectrical characterizations and spectroscopic parameters of the novel (2E)-3-(4-methoxy-5-oxo-5H-furo[3, 2-g]chromen-6-yl)acrylonitrile(MOFCA)

Reaction of 6-formylvisnagin (1) with cyanoacetic acid in dry pyridine afforded the novel (2E)-3-(4-methoxy-5-oxo-5H-furo[3,2-g]chromen-6-yl)acrylonitrile (2, MOFCA). The chemical structure of the prepared compound was determined by the elemental analysis and spectral data. The individual emulation characteristics of compound (2, MOFCA), were accomplished by DFT, and TD-DFT/B3LYP, at 6-311 ++ G (d, p). The computational results detect the most stable structure of MOFCA, depending on the positions of the methoxy (O-CH3) group, within change in dihedral angle. FT-IR spectroscopy was applied for the vibrational spectral analysis. Using frontier molecular orbital (FMO) analysis, various spectroscopic and quantum chemical parameters are discussed. The absorption energies, oscillator strength, and electronic transitions of compound (2, MOFCA), have been derived at TD-DFT/CAM-B3LYP/6-311++G (d,p) computations utilizing a PCM and measured in different polar and non-polar solvents experimentally in UV-Vis spectra. The output of the computation shows accurate agreement between theoretical spectra and practical spectra for the title compound. NLO analysis was computed at the identical plane of theory which are, α; Δα, and first-order β, the hyper-Rayleigh scattering (βHRS) and the depolarization ratio (DR), were shown promising optical properties. The plots of natural bonding orbital (NBO), thermochemical parameters and the molecular electrostatic potential surfaces (MEPS) have been computed. All the computations in the gas phase have been completed.

Some aspects related to the transformation of the three body wave function built on the Gaussian basis

The three-body wave function built on the basis of the Gaussian function, calculated using the three-body Hamiltonian with the Pauli blocking operator is studied. As an example, the wave function of the ground state of the 9 Be was taken. Analytical expressions are presented for the overlap matrix elements of the basis function for both basic and alternative set of relative Jacobi coordinates. The correlation densities of the wave function are calculated and illustrated depending on the set of orbital quantum numbers.

Analytical evaluation of relativistic molecular integrals: III. Computation and results for molecular auxiliary functions

This work describes the fully analytical method for the calculation of the molecular integrals over Slater-type orbitals with non-integer principal quantum numbers. These integrals are expressed through relativistic molecular auxiliary functions derived in our previous paper (Bagci and Hoggan in Phys Rev E 91(2):023303, 2015). The procedure for computation of the molecular auxiliary functions is detailed. It applies both in relativistic and non-relativistic electronic structure theory. It is capable of yielding highly accurate molecular integrals for all ranges of orbital parameters and quantum numbers.

On the geometric quantization of the ro-vibrational motion of homonuclear diatomic molecules

In the framework of geometric quantization we extend the harmonic oscillator rules to rotation and vibration of molecules. First, the geometric quantization of the rigid rotor is introduced. The novelty is that we found an explicit relation giving the impulse along the third axes, which takes discrete values and found that it depends not only on the principal quantum number, but also on the orbital and magnetic quantum numbers. Geometric quantization is further extended to the class of vibrational (damped) systems. The theory is sought as mathematical requirement, which can be traced in the analysis of integrable systems. It is shown that properties of the critical points of the momentum map can be the key to the integrability. A C⁎ isomorphism of the momentum map between the Lie algebra of physical observables and that of the harmonic oscillator induces the geometric quantization on former. We show how the method works, taking into account the Lennard-Jones' potential, which characterizes the interaction between molecules. A second example shows a physical system having the energy levels depending on the magnitude of the frequencies.