In a recent paper [Y. C. Ge and M. S. Child, Phys. Rev. Lett. 78, 2507 (1997)], by using a Gaussian wave function, Ge and Child presented a nonadiabatic relation between the quantum Berry phase and the classical Hannay angle for the time-dependent harmonic oscillator. In this paper, we present a perspective for this relation without the use of a trial wave function. In particular, an exact explicit formula for the cyclic evolution over the period T in the parameter space of action invariant is obtained; the $-\mathrm{}(n+1/2\mathrm{})\mathrm{}$ relation between the quantum geometric angle and the Hannay angle is rigorously established.

Quantum teleportation of a continuous-variable state is studied for the quantum channel of a two-mode squeezed vacuum influenced by a thermal environment. Each mode of the squeezed vacuum is assumed to undergo the same thermal influence. It is found that when the mixed two-mode squeezed vacuum for the quantum channel is separable, any nonclassical features, which may be imposed in an original unknown state, cannot be transferred to a receiving station. A two-mode Gaussian state, one of which is a mixed two-mode squeezed vacuum, is separable if and only if a positive well-defined P function can be assigned to it. The fidelity of teleportation is considered in terms of the noise factor given by the imperfect channel. It is found that quantum teleportation may give more noise than direct transmission of a field under the thermal environment, which is due to the fragile nature of quantum entanglement of the quantum channel.

We propose a scheme for quantum computing using high-$Q$ cavities in which the qubits are represented by single-cavity modes restricted in the space spanned by the two lowest Fock states. We show that single-qubit operations and universal multiple qubit gates can be implemented using atoms sequentially crossing the cavities.

In this study we consider Born-Oppenheimer coupled equations with the aim of deriving a single approximated Born-Oppenheimer-type equation which contains the effect of the nonadiabatic coupling terms. The derivation is done for a situation where N (⩾2) adiabatic surfaces, including the ground-state surface, have a degeneracy along a single line (e.g., conical intersection). The new equation can be considered as an extended version of the Born-Oppenheimer approximation. Although derived for a nongeneral case, the extension to a general case is also discussed. As special cases we treat, in the present paper, the two-state system and, in the following paper, the three-state system.

In this work is applied the extended-approximated Born-Oppenheimer (BO) equation, as derived in the preceding article [Phys. Rev. A 62, 032506, (2000)], to a tristate system. For this sake an appropriate scattering two-arrangement–two-coordinate model was devised. The calculations for each energy were done three times: once without doing any approximation, and two times by approximating the three coupled Schrödinger equations by two different, but gauge-related, single (extended) BO equation. State-to-state (reactive and nonreactive) transition probabilities were obtained, indicating that the new extended approximate BO equations yield relevant results for a tristate system.

We present angular basis functions for the Schrödinger equation of two-electron systems in hyperspherical coordinates. By using the hyperspherical adiabatic approach, the wave functions of two-electron systems are expanded in analytical functions, which generalizes the Jacobi polynomials. We show that these functions, obtained by selecting the diagonal terms of the angular equation, allow efficient diagonalization of the Hamiltonian for all values of the hyperspherical radius. The method is applied to the determination of the ${}^1{S}^e$ energy levels of the ${\mathrm{Li}}^{+}$ and we show that the precision can be improved in a systematic and controllable way.

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries ${\mathrm{SO}}_3$ and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry ${\mathrm{SO}}_4$ is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrödinger equation.

Ion-ion collision dynamics are studied by direct solution of the time-dependent Schrödinger and Dirac equations on a two-dimensional Cartesian lattice. The time-dependent Dirac equation is solved in both its two- and four-component forms using difference offsetting on the lattice to mitigate the fermion doubling pathology. For ${\mathrm{Pd}}^{46+}$ on ${\mathrm{Pd}}^{45+},$ which energetically corresponds to ${\mathrm{U}}^{92+}$ on ${\mathrm{U}}^{91+}$ in a three-dimensional space, total inelastic probabilities are calculated at a fixed ion velocity and several impact parameters. In this intermediate energy range, the total inelastic probabilities from the Schrödinger and two- and four-component Dirac equations are in reasonable agreement, although the detailed collision dynamics reveal interesting differences.

The broad $(\approx 700$ meV) C $1\overrightarrow{s}{\pi }_u^{*}$ resonance in the absorption spectrum of ${\mathrm{CO}}_2$ has been decomposed into contributions from two Renner-Teller split core-excited states with bent and linear equilibrium geometries using resonant Auger spectroscopy. The C ${1s}^{-1}\hspace{0.5em}{\pi }^{*}$ excited state was found to decay primarily via participator Auger transitions to the $A{}^2{\Pi }_u$ state of ${\mathrm{CO}}_2^{+}.$ Analysis of the vibrational structure in the high-resolution Auger spectra, measured at several photon energies across the broad C $1\overrightarrow{s}{\pi }_u^{*}$ resonance, was accomplished using calculated Franck-Condon factors for the electronic excitation and de-excitation processes. Estimations of the geometries of the Renner-Teller split core-excited states were obtained from a comparison of the calculations with the resonant Auger spectra. Transitions to the bent core-excited state were found to contribute to the absorption profile exclusively at the photon energies below the maximum of the C $1\overrightarrow{s}{\pi }_u^{*}$ resonance, whereas the linear core-excited state becomes accessible at higher photon energies. The symmetric stretch vibrational progression of the linear core-excited state was identified and assigned. The minimum of the potential energy surface of the C ${1s}^{-1}{\pi }^{*}$ core-excited state at its linear configuration was estimated to be 290.4 eV above the ground vibrational level of the ground electronic state of ${\mathrm{CO}}_2.$

Quantum electrodynamics is used to calculate the angle- and energy-resolved triple differential cross section for double photoionization of He by circularly polarized light for electrons emitted in a plane perpendicular to the incident beam direction. In the present work, the effect of chirality of the circularly polarized light in producing dichroism is obtained. Results are compared with the existing experimental results and theoretical calculations.

Changes in Kr $4s$ photoelectron satellite intensities caused by interference with the Auger decay of inner-shell doubly excited ${3d}^9{4p}^5{\mathrm{nln}}^{\prime }{l}^{\prime }$ states are studied by high-resolution experiment and one-step calculations. The calculations predict pronounced interference effects in the relative intensity of the most intense satellite line ${4p}^4{(}^1{D\left)4d\right(}^2{S}_{1/2})$ as a function of photon energy, in good agreement with experiment.

“Thomas process” is a name used for a family of singular two-step processes that can lead to electron transfer. The Thomas process of the “second kind,” occurring in reactions with both transfer and ionization, utilizes the $e-e$ scattering in the second step, so this Thomas process requires the dynamics of the electron-electron interaction. We calculate numerically the second order element of an S matrix and corresponding cross sections for the transfer ionization process. We find that the position and shape of the Thomas peak depend on both electron-electron and the electron-nucleus interaction. Also the direct and exchange amplitudes are equal at the peak position. We test the peaking approximation used for transfer ionization. Our results can be compared to experimental results for $p^{+}+\mathrm{He}\to {\mathrm{H}+\mathrm{H}\mathrm{e}}^{2+}{+e}^{-}.$

A modified freezing full-core method is introduced and applied to calculations of lithium in strong magnetic fields up to ${10}^{10}$ G. The accuracy of results is higher than that from unrestricted Hartree-Fock calculations. In the absence of magnetic fields, our results agree with the most accurate calculations to within 0.02%. We also discussed the effect of strong magnetic fields on core electrons.

In this paper, we present a practical numerical technique for calculating both the ionization rate and the wave function of an atom in high-frequency laser fields. This method permits the replacement of the exact final-state wave function by its asymptotic form in the matrix elements, which is shown to extremely simplify the numerical calculations. This approach is compared with the high-frequency Floquet theory and an exact numercical Floquet calculation, and proved to be very efficient and reliable. Moreover, this method is successfully applied to investigate the two-color interference effect in the stabilization regime. We find a significant enhancement or suppression on the ionization rate and the high-order harmonic generation through adjusting the relative phase between the two frequency components.

We present a generalization of the variationally stable method of Gao and Starace [B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988); Phys. Rev. A 39, 4550 (1989)] for two-electron atoms and ions that incorporates a coupled-channel adiabatic hyperspherical approach. Using this approach, we report results for two-photon detachment of ${\mathrm{H}}^{-},$ in which we have coupled one, two, three, and four adiabatic hyperspherical channels within each term level of the initial, intermediate, and final states. We present results also for the dynamic polarizability of ${\mathrm{H}}^{-}$ as well as for the one-photon detachment cross section. Comparisons are given with results of prior work.

We investigate the scattering of intense short laser pulses off trapped cold fermionic atoms. We discuss the sensitivity of the scattered light to the quantum statistics of the atoms. The temperature dependence of the scattered light spectrum is calculated. Comparisons are made with a system of classical atoms that obey Maxwell-Boltzmann statistics. We find the total scattering increases as the fermions become cooler but eventually tails off at very low temperatures (far below the Fermi temperature). At these low temperatures the fermionic degeneracy plays an important role in the scattering, as it inhibits spontaneous emission into occupied energy levels below the Fermi surface. We demonstrate that temperature dependent qualitative changes in the differential and total spectrum can be utilized to probe the quantum degeneracy of a trapped Fermi gas when the total number of atoms is sufficiently large $(>~{10}^6).\mathrm{}$ At smaller numbers of atoms, incoherent scattering dominates and it displays weak temperature dependence.

We consider the criterion for Bose-Einstein condensation for particles in a harmonic trap. For a fixed angular momentum, the lowest energy state for a cloud of bosons with attractive interactions is the ground state of the cloud with all the angular momentum in the center-of-mass motion, and the one-particle reduced density matrix generally does not have a single large eigenvalue, but a number of them, suggesting that the state is an example of a fragmented condensate [N. K. Wilkin, J. M. F. Gunn, and R. A. Smith, Phys. Rev. Lett. 80, 2265 (1998)]. We show that a convenient way to describe correlations in the system is by defining an internal one-particle reduced density matrix, in which the center-of-mass motion is eliminated, and that this has a single eigenvalue equal to the number of particles for the problem considered here. Our considerations indicate that care is necessary in formulating a criterion for Bose-Einstein condensation.

We develop a multiscale technique to describe excitations of a Bose-Einstein condensate, whose characteristic scales are comparable to the healing length, thus going beyond the conventional hydrodynamical approximation. As an application of the theory, we derive an approximate explicit vortex and other solutions. The dynamical stability of the vortex is discussed on the basis of the mathematical framework developed here, the result being that its stability is granted at least up to times on the order of seconds, which is the condensate lifetime. Our analytical results are confirmed by numerical simulations.

The dynamics of a quantum soliton propagating in nonlinear optical fibers is analyzed in the second-quantized picture in a fully canonical way. The quantum nonlinear Schrödinger equation with equal-time commutation relations for the field operators is solved using the formalism developed by Haus and Lai [J. Opt. Soc. Am. B $7,$ 386 (1990)]. The canonical approach is compared with the treatment of Haus and Lai based on phenomenological equal-space commutation relations. The two theories are shown to provide similar outcomes of a homodyne measurement. This result justifies the use of equal-space commutation relations in quantum studies of soliton propagation.

We study two types of coherent states for two-mode realizations of the direct product group $\mathrm{SU}(1,1)\mathrm{}\otimes \mathrm{SU}(1,1)\mathrm{}$ [which is locally isomorphic to SO(2,2)] constructed from the coupling of two single-mode realizations of SU(1,1). The basis states for the relevant representations of $\mathrm{SU}(1,1)\mathrm{}\otimes \mathrm{SU}(1,1)\mathrm{}$ are constructed from the SU(1,1) Clebsch-Gordon coefficients. From these, Perelomov and Barut-Giradello coherent states are constructed. Various properties of the states are discussed, and methods for generating them are proposed. Some of the states can be generated by the operation of beam splitters with two-mode squeezed vacuum states or pair coherent states as inputs. We show that a competitive two-channel two-photon process gives rise to states of the Barut-Girardello type as the steady-state solutions of the associated master equation for appropriate initial conditions.