Full Wave Function Research Articles

Coherent State Evolution in a Superconducting Qubit from Partial-Collapse Measurement

Measurement is one of the fundamental building blocks of quantum-information processing systems. Partial measurement, where full wavefunction collapse is not the only outcome, provides a detailed test of the measurement process. We introduce quantum-state tomography in a superconducting qubit that exhibits high-fidelity single-shot measurement. For the two probabilistic outcomes of partial measurement, we find either a full collapse or a coherent yet nonunitary evolution of the state. This latter behavior explicitly confirms modern quantum-measurement theory and may prove important for error-correction algorithms in quantum computation.

Direct CP violation in hadronic B decays

There are different approaches for the hadronic B decay calculations, recently. In this paper, we upgrade three of them, namely factorization, QCD factorization and the perturbative QCD approach based on $k_T$ factorization, by using new parameters and full wave functions. Although they get similar results for many of the branching ratios, the direct CP asymmetries predicted by them are different, which can be tested by recent experimental measurements of B factories.

Investigation of the dynamics of two coupled oscillators with mixed quantum-classical methods

The dynamics of two coupled oscillators can become quite complex if anharmonic potential energy functions are employed. This type of system therefore represents a good model for an investigation of the performance of mixed quantum-classical methods. In this work, the motion of two coupled particles with a mass ratio of one to ten is studied with three different mixed quantum-classical methods in the presence of anharmonic potential terms for a comparison with exact quantum mechanical calculations. The mixed quantum-classical approaches include the multitrajectory Ehrenfest, the mixed quantum-classical Bohmian (MQCB), and the so-called coupled Schrödinger equations (CSE) formalisms. The analysis shows that while the description of a weakly anharmonic system by the Ehrenfest and MQCB schemes is accurate if proper sampling techniques are applied, both approximations break down rapidly if the anharmonic terms are increased. The performance of the simple CSE prescription, which corresponds to a reduction of the full two-dimensional wave function to two one-dimensional wave functions representing two quantum oscillators coupled via the potential energy in a classical fashion, decreases if the width of the initial wave packet is enlarged. The dependence of the CSE method on the diffuseness of the initial wave packet is therefore opposite to that of the MQCB method, which is more accurate for wide wave packets. Overall, the multitrajectory Ehrenfest ansatz is found to be most successful in reproducing the exact quantum results.

Nonadiabatic reactant-product decoupling calculation for the F(P1∕22)+H2 reaction

In this paper we present a theoretical study using time-dependent nonadiabatic reactant-product decoupling method for the state-to-state reactive scattering calculation of F((2)P(1/2))+H(2) (nu=j=0) reaction on the Alexander-Stark-Werner potential energy surface. In this nonadiabatic state-to-state calculation, the full wave function is partitioned into reactant component and a sum of all product components. The reactant and product components of the wave function are solved independently. For the excited state reaction, the state-to-state reaction probabilities for J=0.5 are calculated. Comparing the state-to-state reaction probabilities, it is found that the vibrational population of the HF product is dominated by vibrational levels nu=2 and 3. The rotation specific reaction probabilities of HF product in j=1 and 2 are larger than those in other rotational levels. As the rotation quantum number j increases, the positions of the peak in the rotational reaction probability of HF product in nu=3 shift to higher collision energy.

On the orbital dependence of compact, weight-selected configuration interaction and coupled-cluster wave functions

We recently reported that very compact coupled-cluster wave functions may be generated by selecting the most important configurations, by weight, from the full coupled-cluster wave function. Here, we consider how the choice of orbitals may affect these wave functions in the case of the symmetric dissociation of H2O. We employ unrestricted Hartree–Fock and complete-active-space self-consistent-field orbitals, as well as natural orbitals derived from a coupled-cluster singles and doubles wave function. For a given accuracy, some choices of orbitals can reduce the size of configuration interaction wave functions, but they have little effect on the weight-selected coupled-cluster wave functions.

Important configurations in configuration interaction and coupled-cluster wave functions

Using a new general-order determinant-based program, we construct compact configuration interaction and coupled-cluster wave functions by selecting the most important configurations, by weight, from a full configuration interaction or full coupled-cluster wave function. Our results show that for the symmetric dissociation of water, chemical accuracy can be achieved across the surface with ∼2% of the full coupled-cluster expansion compared to ∼10% of the full configuration interaction expansion.

Hamiltonian for coupled flux qubits

An effective Hamiltonian is derived for two coupled three-Josephson-junction (3JJ) qubits. This is not quite trivial, for the customary "free" 3JJ Hamiltonian is written in the limit of zero inductance L. Neglecting the self-flux is already dubious for one qubit when it comes to readout, and becomes untenable when discussing inductive coupling. First, inductance effects are analyzed for a single qubit. For small L, the self-flux is a "fast variable" which can be eliminated adiabatically. However, the commonly used junction phases are_not_ appropriate "slow variables", and instead one introduces degrees of freedom which are decoupled from the loop current to leading order. In the quantum case, the zero-point fluctuations (LC oscillations) in the loop current diverge as L->0. Fortunately, they merely renormalize the Josephson couplings of the effective (two-phase) theory. In the coupled case, the strong zero-point fluctuations render the full (six-phase) wave function significantly entangled in leading order. However, in going to the four-phase theory, this uncontrollable entanglement is integrated out completely, leaving a computationally usable mutual-inductance term of the expected form as the effective interaction.

Repulsive double many-body expansion potential energy surface for the reactions N(4S)+ H2⇌ NH(X3Σ–)+ H from accurate ab initio calculations

A single-sheeted DMBE potential energy surface is reported for the reactions N(4S)+H2<-->NH(X3Sigma-)+H based on a fit to accurate multireference configuration interaction energies. These have been calculated using the aug-cc-pVQZ basis set of Dunning and the full valence complete active space wave function as reference, being semi-empirically corrected by scaling the two-body and three-body dynamical correlation energies. The topographical features of the novel global potential energy surface are examined in detail, including a conical intersection involving the two first 4A'' potential energy surfaces which has been transformed into an avoided crossing in the present single-sheeted representation.

Collectivity, shell openness indices, and complexity measures of multiconfigurational states: Computations within full CI scheme

AbstractIt is shown that the multiconfigurational character of the N‐electron wave function can be treated by a new quantitative index, N, computed as a special matrix invariant of the full wave function. Along with N, a simpler index N is given due to the Kutzelnigg and Smith open‐shell theory. The indices are compared with an effective number of unpaired electrons introduced by Takatsuki, Fueno, and Yamaguchi. Full configuration interaction (FCI) computations on such quantities realized in the present work for atoms and dissociation reactions lead to the conclusion that all indices give a qualitatively similar picture. It is stressed that N as a more complicated quantity reflects a global complexity of the electronic state, while other indices represent the electron structure peculiarities only at the one‐electron level. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Exact Solutions of the Duffin–Kemmer–Petiau Equation for the Deformed Hulthen Potential

Using the Nikiforov–Uvarov method, an application of the relativistic Duffin–Kemmer–Petiau equation in the presence of a deformed Hulthen potential is presented for spin zero particles. We derived first-order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunctions to be evaluated by using the Nikiforov–Uvarov method that can be written in terms of hypergeometric polynomials.

Total atomic scattering factors for the ground states of the lithium isoelectronic sequence from Na8+ to Ca17+

In this work, total atomic scattering factors for the ground states of the lithium isoelectronic sequence are calculated by using the full core plus correlation wave function. For the ground state of the lithium atom, our results are compared with the previous theoretical values in the literature; the influence of electron correlation on total atomic scattering factors is analyzed systematically and our results agree with previous configuration interaction calculations very well. For the ground states of the lithium isoelectronic sequence from Na8+ to Ca17+, the general functional behavior of total atomic scattering factors is analyzed together for each state of the isoelectronic sequence.

One-Dimensional Models for Atoms in Strong Magnetic Fields, II: Anti-Symmetry in the Landau Levels

Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these type, we show that the maximum number of electrons that can be bound is less than a Z + Z f(Z). The function f(Z) represents a small non-linear growth which is quadratic in log Z when the magnetic field strength grows polynomially with the nuclear charge Z. In contrast to earlier work, the models considered here include those arising from realistic cases in which the full trial wave function for N-electrons is the product of an N-electron trial function in one-dimension and an antisymmetric product of states in the lowest Landau level.

Model Study of Three-Body Forces in the Three-Body Bound State

The Faddeev equations for the three-body bound state with two- and three-body forces are solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar Fujita-Miyazawa type three-body forces. The influence of the strength and range of the three-body force on the wave function, single particle momentum distributions and the two-body correlation functions are studied in detail. The extreme case of pure three-body forces is investigated as well.

Accurate Single-Valued Double Many-Body Expansion Potential Energy Surface for Ground-State HN2

A single-valued double many-body expansion potential energy surface is reported for ground-state HN2 by fitting accurate ab initio energies that have been suitably corrected by scaling for the H−N2 and N−NH regions. The energies of ∼900 geometries have been calculated at the multireference configuration interaction level, using aug-cc-pVQZ basis sets of Dunning and the full valence complete active space wave function as reference. The topographical features of the novel global potential energy surface are examined in detail.

Confined quantum systems: dipole polarizability of the two-electron quantum dot,the hydrogen negative ion and the helium atom

The dipole polarizabilities of the electronic ground state of three two-electronquantum systems, namely the two-electron quantum dot, the hydrogen negativeion and the helium atom, confined by an anisotropic harmonic oscillatorpotential have been studied for different confinement strengths ωby using the quantum chemical configuration interaction (CI) methodemploying a Cartesian anisotropic Gaussian basis set supplemented by aquantum-chemical standard Cartesian Gaussian basis set, respectively,and a full CI wavefunction. The dipole polarizability of the harmonicoscillator quantum dot may be calculated analytically. It is proportional tothe number of electrons, inversely proportional to the square of ω andhas no electron correlation contribution. This is valid for all states includingthe excited states. The situation is different for quantum systems witha finite nuclear charge, like the hydrogen negative ion and the heliumatom. In general the dipole polarizability of the two-electron quantumdot decreases strongly with increasing confinement strength ω, thepolarizability of the helium atom varying slowly with increasing ω,while the behaviour of the polarizability of the hydrogen negativeion lies between both. Except for the two-electron quantum doteach component of the dipole polarizability tensor, i.e. αxx, αyy andαzz,depends on the confinement along all axes. The electron correlation contributionto the dipole polarizability of the helium atom and of the hydrogen negativeion behaves differently for the different Cartesian components αzz andαxxof the tensor. The different behaviour observed for different Cartesian componentsmay be rationalized by the reduced dimensionality of the systems.

Coupled-channel integral equations for quasi-one-dimensional systems

An integral equation approach is developed for the propagation of electrons in two-dimensional quantum waveguides. The original two-dimensional problem is transformed into a set of one-dimensional coupled equations by expanding the full wave function in terms of simple transverse basis functions. The equivalence of the Schrödinger equation with suitable boundary conditions in configuration space to an integral equation approach in momentum space can thus be illustrated in a coupled channel situation with a minimum of geometrical complications. The application to scattering from a point defect embedded in a waveguide is considered. In this case the scattering integral equations reduce to a set of algebraic equations, and typical coupled channel phenomena can be discussed through straightforward mathematical techniques. The convergence problems due to a singular perturbation are briefly considered, and the differences between genuine one-dimensional problems and the present two-dimensional case are discussed.

Confined quantum systems: a comparison of the spectral properties of thetwo-electron quantum dot, the negative hydrogen ion and the heliumatom

The spectrum, the electron density distribution and the character of threetwo-electron quantum systems, namely the two-electron quantum dot, thenegative hydrogen ion and the helium atom, confined by an anisotropic harmonicoscillator potential, have been studied for different confinement strengths, ω,by using the quantum chemical configuration interaction (CI) methodemploying a Cartesian anisotropic Gaussian basis set supplemented by aquantum chemical standard Cartesian Gaussian basis set, respectively,and a full CI wavefunction. Energy level diagrams and electron densitydistributions are displayed for low lying electronic singlet states and selectedconfinement parameters. The results for the three confined quantum systems arecompared with each other: in general, the absolute energies of the states andthe interval between states increase with increasing confinement, ω.The ordering of states may vary for different values of ω.The shape of the electron density distribution differs among the threesystems. Its size increases in the order He < H− < two-electronquantum dot. Electron distributions in prolate type confinement are stretched alongthe zaxis, while those in oblate type are compressed with respect to this axis.The CI wavefunction of most of the low lying states for the helium atomand the negative hydrogen ion is dominated by one configuration, whilesome of the CI wavefunctions corresponding to states of the two-electronquantum dot have more than one leading configuration. The ground state CIwavefunctions of the negative hydrogen ion and the helium atom confined in aspherical potential are dominated by harmonic oscillator functions up to82.4 and 47.1%, respectively, for the smallest confinement of ω = 0.1.These values increase to 98.8 and 89.0%, respectively, for ω = 0.5.

Confined quantum systems: spectral properties of the atoms helium and lithiumin a power series potential

The potential energy curve and the electron density distribution forlow-lying electronic states of the helium and lithium atoms confined byan anisotropic harmonic oscillator potential have been studied fordifferent confinement parameters (ωx, ωy, ωz)by using the quantum chemical configuration interaction (CI) method employing aCartesian anisotropic Gaussian basis set supplemented by a quantum chemicalstandard Cartesian Gaussian basis set, respectively. In the case of thehelium atom full CI wavefunctions have been used, and in the case of thelithium atom multi-reference CI wavefunctions have been employed. Theresults for the two confined quantum systems are compared to each other:parabolic-and non-parabolic-type potential energy curves are observed forstates of both atoms in different type harmonic oscillator confinement. Thenon-parabolic potentials always appear in pairs, one with a double minimumand the other with a sharp edge at the minimum. They result from theinteraction of energetically nearby states of the same symmetry. The electrondensity distributions of the states of the two atoms show deformation fromspherical symmetry according to the symmetry and strength of the confiningpotential at the position of the atoms. The electron distribution of thestates having non-parabolic potential energy curves is strongly deformedand occasionally shows curvilinear nodal planes of parabolic shape.

Transitions in ZnS and CdSe quantum dots and wave-function symmetry

Excitation energies for wurtzite spherical ZnS and CdSe quantum dots in the range of 40–4000 atoms were calculated using empirical pseudopotentials and a real-space basis. The energies are compared to experiments and other pseudopotential models. For ZnS quantum dots, squared transition dipole sums were computed efficiently, without the need for full wave functions of the excited states; and some transition dipole calculations include the effects of an approximate electron-hole Coulomb potential. Squared transition dipole sums from the highest energy linear dipole like valence states to the lowest excited state were computed as a function of dot size. The model predicts that the per atom dipole transition sum decreases with quantum dot size for those transitions. The mixing of even and odd angular components and charge asymmetry of the wave functions affect the dipole transition strengths. The total oscillator strength for the lowest energy transition region increases with size at small radii, resembling the pattern recently observed experimentally for CdSe quantum dots. We examined the role of wave-function angular momentum for transitions to conduction band surface states.

Theoretical molecular Auger spectra with electron population analysis

An approximation method is proposed to simulate the molecular Auger spectra. Auger transition rates are estimated with atomic populations of valence orbitals on an excited atom by Mulliken and Löwdin population analyses. Normal Auger energies and relative rates for H 2O and NH 3 molecules are evaluated using a full CI wave functions among the valence orbitals constructed from SCF orbitals for the neutral ground state and for the core-hole excited state. Theoretical spectra show fairly good correspondence with the experimental spectra. It is demonstrated that the present approach is applicable for qualitative assignment and analysis of Auger spectra for larger molecules.