We show how quantum instability is displayed in the von Neumann entropy and in the Wigner function. For this purpose, an intracavity second-harmonic generation close to the Hopf bifurcation range is studied. We examine the role of dissipation in unstable dynamics and the formation of the quantum states of the cavity modes, and discuss contrast ensemble behavior with that of individual realization on the basis of a quantum-jump simulation method. Namely, it is found that the Wigner functions for fundamental and second-harmonic modes prepared initially in a vacuum state acquire the three-hump structure due to phase symmetry breaking in the bifurcation range. The time evolution of coherent states leads to long-lived swing of the system between two side humps in a phase space.

The degenerate optical parametric oscillator may generate very high-intensity two-dimensional localized structures. A quantitative comparison of the propagation and the mean-field models is presented for different mistunings, corresponding to monostable and bistable homogeneous solutions. In both models, we study the circular domain walls as an example of localized structures. The peak intensities are comparable; the difference lies mainly in their domain of existence as a function of the pump amplitude parameter.

Laser systems with nonorthogonal eigenmodes have a linewidth that is broader than the usual Schawlow-Townes value, by a factor that is known as the Petermann excess noise factor. In a recent quantum analysis, this excess noise was attributed to loss-induced coupling betwen the laser modes. Using the same approach, we show here that the Petermann excess noise also appears on the laser quantum intensity noise. The calculation is shown to be in good agreement with an experiment using a laser diode with two contributing transverse modes.

Energy levels of the ground state and $n=2\mathrm{}$ excited states of heliumlike ions with $22<~Z<~36$ are calculated using a large-scale, relativistic configuration-interaction method. Quantum electrodynamic corrections are evaluated in Dirac-Kohn-Sham (DKS) potentials to account for screening and relaxation effects, and results are shown to be quite reliable as long as the Latter correction to the DKS potentials is excluded. We also find good agreements among different high-precision calculations and between theory and experiment in this Z range.

The resonant double photoionization of Ne has been studied via an electron-electron coincidence experiment at a photon energy of 92.21 eV. At this energy, the kinetic energy of the photoelectrons matches exactly the energy of the Auger electrons. The overall experimental energy resolution, narrower than the natural linewidth of the intermediate state, has allowed us to observe angular- and energy-dependent interference effects due to the indistinguishability of the two electrons.

It is found that systematic errors in phase inversions and random errors in Hadmard-Walsh transformations are the dominant gate imperfection in Grover’s quantum search algorithm. They lead to reductions in the maximum probability of the marked state and affect the efficiency of the algorithm. Given the degree of inaccuracy, we find that to guarantee a half-rate of success, the size of the database should be on the order of $O(1/{\delta }^2),$ where $\delta$ is the uncertainty.

For a three-body system, a quantum wave function ${\Psi }_m^l$ with definite l and m quantum numbers may be expressed in terms of an internal wave function ${\chi }_k^l,$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on ${\chi }_k^l$ to ensure that the external wave function ${\Psi }_m^l$ is analytic. These constraints effectively amount to boundary conditions on ${\chi }_k^l$ and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.

The carbon $1s$ photoelectron spectrum has been measured for ${\mathrm{CO}}_2$ at photon energies of 308, 320, and 330 eV with an instrumental resolution about half the natural linewidth. These spectra have been analyzed to obtain vibrational spacings, vibrational intensities, and the lifetime, τ, of the carbon $1s$ core-hole state. Theoretical calculation of the lifetime width, ħ/τ, using a one-center model, which assumes that only the valence electrons localized on the atom with the core hole can participate in Auger deexcitation of the core hole, predicts a value of 66 meV, considerably smaller than that predicted for ${\mathrm{CH}}_4$ (96 meV). Experimental measurements indicate, however, that the ${\mathrm{CO}}_2$ carbon $1s$ width is, in fact, much larger than expected—$99\pm 2\mathrm{meV}$—and is approximately the same as that found experimentally for ${\mathrm{CH}}_4$ (95±2 meV). This result indicates that valence electrons on the oxygen atoms may play a role in the Auger decay the carbon $1s$ core hole in ${\mathrm{CO}}_2,$ and, hence, that a multicenter model may be necessary to describe the Auger process.

The dynamics of a classical electron in the field of a nucleus and the electrical and magnetical components of a superintense laser field is investigated analytically. Particular emphasis is placed on the motion in the propagation direction of the laser field which is governed in a competitive manner by a laser induced drift away from the nucleus and an attractive Coulomb force towards it. In order to characterize the ionization and recombination/rescattering dynamics we develop an approximate mapping of the space and momentum coordinates in phase space each time the electron crosses the axis of the laser field propagation. For a certain fraction of the initial phase-space coordinates of the electron in the vicinity of the nucleus we find that the drift can be compensated for due to the attraction of the nucleus. A large number of substantial and almost periodic bursts of acceleration by the nucleus is then possible in the direction of propagation of the laser field. We evaluate the corresponding harmonic spectrum and explain the features deviating from those in the laser parameter regime where the magnetic-field component can be neglected.

We present predictions for temperature-dependent shifts and damping rates. They are obtained by applying the dielectric formalism to set up a self-consistent model of a trapped Bose gas which can be shown to satisfy generalized Ward identities. Within the framework of the model we use lowest-order perturbation theory to determine the first-order correction to the results of Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation frequencies, and present numerical results for the temperature dependence of the damping rates and the frequency shifts. Good agreement with the experimental values measured by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)] are found for the $m=2\mathrm{}$ mode, while we find disagreements in the shifts for $m=0.\mathrm{}$ The latter point to the necessity of a nonperturbative treatment for an explanation of the temperature dependence of the $m=0\mathrm{}$ shifts.

Quantum-statistical properties of light propagating in a coupler with third order nonlinearity are investigated. The stochastic equations describing the dynamics of the system are derived in positive-P and Wigner representations. The possibility to generate quadrature-squeezed states is shown numerically.

With a wall-stabilized high-current arc, we have measured the transition probabilities of several multiplet pairs of C I, N I, and O I. Pairs have been selected for which two recent ab initio calculations have produced widely different results. All chosen multiplets are among the prominent, strong features of their respective spectra, and the pairing is in each case done for multiplets that hardly differ in their excitation energies. Our results do not favor either of the calculations, but are consistent with an earlier experiment.

Laser-photoelectron spectroscopy has been used to determine the electron affinity of atomic thallium. Photoelectron kinetic-energy spectra of ${\mathrm{Tl}}^{-}$ were obtained and compared to those of ${\mathrm{Na}}^{-}$ obtained in the same manner. Using this technique, the electron affinity of thallium was determined to be 0.377±0.013 eV. This value is compared to several recent calculations of the electron affinity of thallium. In addition, a summary of experimental values and several systematic theoretical predictions of the electron affinities of the other group-13 elements is presented.

We have performed photoassociation spectroscopy to study the doubly excited states of ${\mathrm{Na}}_2$ involved in the associative ionization of colliding $\mathrm{Na}\mathrm{}\left(3P\right)\mathrm{}$ atoms. Rovibrational levels of two doubly excited potentials connected to the $P_{3/2}{+P}_{3/2}$ asymptote, one of $0_u^{-}$ and one of $1_u$ symmetry, have been identified. These two doubly excited potentials dominate the route to ionization used in photoassociation experiments of cold Na. Binding energies and rotational constants for all the vibrational levels with binding energies $<50\mathrm{}\mathrm{GHz}$ have been measured. The asymptotic potentials and short-range ionization probabilities are extracted from the data.

Traditional beam-foil methods for measuring lifetimes of low-lying atomic levels are generally impractical beyond $Z\sim 35$ because of the correspondingly shorter flight times when lifetimes become less than a few tens of picoseconds. We recently reported the results of an experiment using a novel two-foil method to measure the 9.5-psec lifetime of the $2{}^3{P}_2$ level in heliumlike krypton. We describe here the results of an extension of that work in which we measured the time evolution of the $N>~2$ excited state population between the foils by observing the dependence upon foil separation of the charge-state distributions emerging from the second foil. The results are consistent with the well-known power-law dependence of Rydberg-fed atomic transitions observed in beam-foil studies, but probe a much shorter time scale than has hitherto been accessible.

We present results from a study of the coherence properties of a system involving three discrete states coupled to each other by two-photon processes via a common continuum. This tripod linkage is an extension of the standard laser-induced continuum structure (LICS), which involves two discrete states and two lasers. We show that in the tripod scheme, there exist two population trapping conditions; in some cases these conditions are easier to satisfy than the single trapping condition in a two-state LICS. Depending on the pulse timing, various effects can be observed. We derive some basic properties of the tripod scheme, such as the solution for coincident pulses, the behavior of the system in the adiabatic limit for delayed pulses, the conditions for no ionization and for maximal ionization, and the optimal conditions for population transfer between the discrete states via the continuum. In the case when one of the discrete states is strongly coupled to the continuum, the population dynamics reduces to a standard two-state LICS problem (involving the other two states) with modified parameters; this provides the opportunity to customize the parameters of a given two-state LICS system.

For a gas of N bosons interacting through a two-body Morse potential a variational bound of the free energy of a confined system is obtained. The calculation method is based on the Feynman-Kac functional projected on the symmetric representation. Within the harmonic approximation a variational estimate of the effect of the interaction range on the existence of many-particle bound states, and on the $N-T$ phase diagram is obtained.

In a recent paper [Phys. Rev. A 59, R3149 (1999)] Lamoreaux reported calculations of the Casimir force. The experimentally found permittivity was used in the calculations. Large deviations were found between numerically evaluated forces and forces derived from a series expanded plasma model. We would like to comment on a few results presented in this work. First, we claim that important features of the imaginary component of the permittivity of copper, presented in Fig. 1(a) are due to the interpolation procedure and are not caused by physical phenomena. These features influence the calculated permittivity for imaginary frequencies, which is the quantity used to calculate the Casimir attraction. Second, we discuss the extrapolation procedure used for low frequencies. The results depend substantially on how this extrapolation is performed.

We describe a method that is well suited to analysis of the bound states of the alkali-metal dimers near their dissociation limit. The method combines inverse perturbation theory, coupled-channel bound-state theory, and the accumulated phase method to treat the short-range part of the molecular potentials. We apply this method to analyze the bound-state energies measured in a two-color photoassociation experiment in an ultracold ${}^{85}\mathrm{Rb}$ gas. This analysis yields information on the interactions between ultracold ${}^{85}\mathrm{Rb}$ atoms that is important to the understanding of ultracold Rb collisions and Bose-Einstein condensation.

Thomas-Fermi theory for Bose-Einstein condensates in inhomogeneous traps is revisited. The phase-space distribution function of the condensate in the Thomas-Fermi limit $\left(\overrightarrow{ħ}0\right)$ is $f_0(\mathit{R},\mathit{p})\propto \delta \left(\mu -H_{\mathrm{cl}}\right)$ where $H_{\mathrm{cl}}$ is the classical counterpart of the self-consistent Gross-Pitaevskii Hamiltonian. Starting from this distribution function the Thomas-Fermi kinetic energy is calculated for any number of particles. Good agreement between the Gross-Pitaevskii and Thomas-Fermi kinetic energies is found even for low and intermediate particle numbers N. Application of this Thomas-Fermi theory to the attractive case and to the calculation of the frequencies of the monopole and quadrupole excitations in the sum rule approach yields conclusive results as well. The difference with the usual Thomas-Fermi approach to the Bose-Einstein condensates (large-N limit) is discussed in detail.