We numerically solve the problem of a two-level system in a near-resonance time-dependent electric field of arbitrary amplitude. The obtained radiation spectrum of the dipole moment is compared both to that of a Landau-Lifshitz (LL) textbook solution [Quantum Mechanics (Pergamon, New York, 1987), p. 145] and to an off-resonance analytical solution [Dakhnovskii and Bavli (unpublished)] obtained recently for both optical and tunneling initial conditions. We show that the LL solution is valid at low field intensities while the off-resonance analytic solution qualitatively describes the intermediate- and high-intensity regimes.

From the experimental measurement of probability distributions of quadrature-field amplitudes, followed by numerical inversion (optical homodyne tomography), we have determined distributions and/or moments of the optical phase of small-photon-number fields for several definitions of the phase variable, including those based on Hermitian operators and on quasiprobability distributions. These measurements were performed on a vacuum field, and a weakly squeezed field. It is found that each definition of phase yields different distributions and/or moments for the experimental data. In addition, all of the experimentally determined quantities agree with the corresponding theoretical predictions.

We have studied the doubly charged ion yields and electron energy spectra (normal and coincidence) for double ionization of atoms in two different ionization regimes (perturbative and tunneling). In both cases, the double-ionization rates appear to be anomalously large in some intensity range and strongly reduced by circular polarization. It is argued that these similar behaviors must result from different physical mechanisms.

We consider a hidden-variable model for the Einstein, Podolsky, and Rosen experiment [Phys. Rev. 47, 777 (1935)] as modified by Bohm $[—Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951)]. We provide a nonlocal random-vector model that mimics the same statistical behavior as quantum mechanics and conforms with Bell’s theorem. Angular momentum conservation appears to require the nonlocal correlations.

In this paper we show that (a) all the known exact solutions of the problem of N anyons in oscillator potential precisely arise from the collective degrees of freedom, and (b) the system is pseudointegrable following Richens and Berry [Physica 2D, 495 (1981)]. We conclude that the exact solutions are trivial thermodynamically as well as dynamically.

In the following we discuss a recent experiment [H. Kaiser et al., Phys. Rev. A 45, 31 (1992)] on spectral filtering regarding its relevance to the wave-corpuscle dualism. An interpretation of the experiment is given, with the assumption, according to de Broglie, that a neutron is a real corpuscle traveling in space-time and surrounded by a guiding wave.

In this paper we discuss physical aspects of intractable (NP-complete) computing problems. We show, using a specific model, that a quantum-mechanical computer can in principle solve an NP-complete problem in polynomial time; however, it would use an exponentially large energy for that computation. We conjecture that our model reflects a complementarity principle concerning the time and the energy needed to perform an NP-complete computation.

The radiative correction to the electron charge-density distribution δρ(r) in the hydrogen atom due to the self-interaction and vacuum polarization is calculated in the leading order of perturbation theory. For large distances [r∼1/(mα)] this correction is small, whereas for small r∼1/m it is comparable to the relativistic corrections coming from the Dirac wave function.

The possibility of observing the Casimir force at macroscopic distances (a few centimeters) using a confocal optical resonator is discussed and a possible experimental apparatus is also suggested.

We present a model of continuous (in time) position measurements on a quantum system using a single pseudoclassical meter. The nonselective evolution of the system is described by a master equation which is identical to that obtained from previous models. The selective evolution is described by a stochastic nonlinear Schrödinger equation. The significance of this equation is that the stochastic term has a physical interpretaion. By carefully choosing the parameters which define the meter and the system-meter coupling, we obtain a meter pointer with well-defined position which undergoes fluctuations. This ‘‘jitter’’ in the pointer position gives rise to the stochastic dynamical collapse of the system wave function. By the inclusion of feedback on the meter, the pointer is made to relax towards an appropriate readout. We apply this model to the selective measurement of the position of a particle in a double-well potential. In contrast to a recent claim [H. Fearn and W. E. Lamb, Jr., Phys. Rev. A 46, 1199 (1992)] we show that truly continuous position measurements lead to a quantum Zeno effect in certain parameter regimes. This is manifest by the changing of the particle dynamics from coherent tunneling between the well minima to incoherent flipping, as in a random telegraph. As the measurement strength increases, the average length of time the particle remains stuck in one well increases proportionally.

A Sagnac experiment with electron waves in vacuum is reported. The phase shift caused by rotation of an electron biprism interferometer placed on a turntable has been measured. It was found to agree with prediction within error margins of about 30%. A compact ruggedized electron interferometer was used. It is based on a high-precision optical bench of 36-cm length. This interferometer is less sensitive by orders of magnitude to mechanical vibrations and electromagnetic stray fields than conventional electron interferometers. A beam of low-energy electrons (150–3000 eV) emitted by a field-emission electron source was used. For the most part, electrostatic electron optical components were employed. The magnified interference fringe pattern was intensified by a dual-stage multichannel-plate intensifier, recorded by a charge-coupled-device video camera, transmitted from the turntable to the laboratory system via a slip ring, and evaluated by an image-processing system. Both the rotation rate and the area enclosed between the two partial waves were varied (up to values of 0.5 ${\mathrm{s}}^{\mathrm{-}1}$ and 3.9 ${\mathrm{mm}}^2$, respectively). Fringe shifts on the order of 5% of a fringe period were attained. Some historical aspects of the Sagnac effect as well as some aspects of its interpretation are mentioned. A brief informal discussion is included of the interpretation of the Sagnac phase shift as a geometric phase (‘‘Berry phase’’) caused by the global anholonomy of the local phase factor that is produced by the gauge field induced by rotation.

Longitudinal coherence in two-beam interferometers means that the two partial wave packets arrive in the plane of interference simultaneously. In charged-particle interferometers, this simultaneity can be lost due to a difference in the geometrical path lengths, a difference in the optical path length, or a difference in the group velocities for the two wave packets on parts of or all of the beam paths. Several of those influences can combine to yield a net relative spatial delay between the wave packets in the interference plane, thus causing a reduction of the interference fringe contrast. A Wien filter can be used in charged-matter-wave interferometry to compensate for this relative delay and thus to reestablish longitudinal coherence. A Wien filter consists of an electric and a magnetic field perpendicular both to each other and the beam path. In its matched state, i.e., when the electrostatic and the magnetic forces on the electrons exactly cancel each other, the Wien filter neither deflects the beams nor exerts any phase shift on the wave packets. However, wave packets traveling through the Wien filter on laterally separated paths propagate in regions of different electric potentials and in turn with different group velocities, which leads to a longitudinal shift of the wave packets relative to each other. Maximum longitudinal coherence (and thereby fringe contrast) can be restored by choosing the compensating delay caused by the Wien filter exactly opposite to the net relative delay caused by the influences mentioned.

An experiment is presented that demonstrates this property of a Wien filter. The coherence-reviving action of a Wien filter is discussed in the context of the incoherent superposition in the registration plane of the plane waves corresponding to different wavelengths in the electron spectrum. It demonstrates that the quantum-mechanical coherence of the self-interacting plane-wave components of the wave packets describing the particle ensemble is more robust than the experimental loss of interference-fringe contrast often suggests. The availability of such a contrast-restoring device is especially important for very-low-energy (a few keV or less) electron interferometry. It is also likely to become important for future ion-beam interferometers.

Dynamic dipole and quadrupole polarizabilities of the 2 ${}_{}{}^1{}_{}{}^{}$S and 2 ${}_{}{}^3{}_{}{}^{}$S metastable states of He are calculated using our time-dependent gauge-invariant method and compared with previous theoretical results. Dispersion coefficients for the He(2 ${}_{}{}^1{}_{}{}^{}\mathrm{S}$)-${\mathrm{H}}_2$ and He(2 ${}_{}{}^3{}_{}{}^{}$S)-${\mathrm{H}}_2$ systems, and their dependence on the intramolecular H-H distance are reported.

The full configuration-interaction (CI) method using elliptical basis functions has been used to calculate the wave function for a few of the lower ${}_{}{}^{1,3}{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{}{}_{}{}^{}$ and ${}_{}{}^{1,3}{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{}{}_{}{}^{}$ excited states. This computational method gives the best wave functions to date for the GK(3 ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{}{}_{}{}^{}$) and e(2 ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{}{}_{}{}^{}$) excited states at an internuclear distance R=1.5 a.u., without using explicitly correlated basis functions, i.e., James-Coolidge or Hylleraas-type basis functions. Using these excited-state wave functions, accurate generalized oscillator strengths for excitation to a few of the lower excited states at R=1.4 a.u. are calaculated and given for comparison with other calculations reported elsewhere. It is found that the effect of the ground-state electron correlation is important for excitation to the lowest excited states, but it becomes less significant for excitation to still higher excited states. It is concluded that the CI method and the computation technique presented here is the most practical and accurate one for studying the inelastic scattering by ${\mathrm{H}}_2$ of fast, charged particles or the electron-impact spectroscopy of ${\mathrm{H}}_2$.

We report an experimental and theoretical study of the hyperfine structure (hfs) in various metastable levels in ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ ii. Hyperfine structures in 11 levels arising from the 4${\mathit{d}}^3$ and 4${\mathit{d}}^2$5s configurations were measured using the laser-rf double-resonance method in a collinear laser–ion-beam geometry. The hfs A and B constants were measured to a precision of 4 and 11 kHz, respectively. Less precise values for hfs constants for nine upper levels in the 4${\mathit{d}}^2$5p configuration were derived from optical spectra. Theoretically, the A and B constants for the metastable levels having J=0.5 and 1.5 were calculated using a relativistic configuration-interaction (RCI) approach. The final many-body wave function produced energy gaps between the five J=0.5 levels which differ from experiment by an average of 0.050 eV, whereas the corresponding value for the ten J=1.5 levels is 0.087 eV. For the two J=0.5 levels measured and calculated, the average error in A is 31.8%. For the three J=1.5 levels, the situation is better, with the average error in A being 9.2%. For comparison, the average errors in A using independent-particle Dirac-Fock (DF) wave functions were 88% and 136% for J=0.5 and 1.5, respectively. In all cases, the many-body (RCI) result represents a vast improvement from the DF result for the A values. The value for the electric-quadrupole moment of ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ obtained from a comparison of the experimental B values and theoretical matrix elements is 0.257(0.013) b. In addition, the calculations confirm a previous report that the level at 17 614.00 ${\mathrm{cm}}^{\mathrm{-}1}$ reported in Moore’s Atomic Energy Levels, Vol. II (U.S. Government Printing Office, Washington, D.C., 1971) is spurious.

Our relativistic configuration-interaction (RCI) methodology has been extended to multireference cases, and improved to permit the construction of angular-momentum functions of arbitrary size, and to minimize the number of vectors needed with each configuration. We report RCI calculations on the fine (fs) and hyperfine (hfs) structure for the (d+s${)}^3$ J=0.5 and 1.5 levels of Zr ii. The average fs error is 0.075 eV, and 17% for hfs, when compared to available experiment. These results indicate that it is possible to correctly position all levels of (d+s${)}^{\mathit{n}}$ configurations in the transition-metal atoms.

We generalize a recently developed perturbation approach [F. M. Fernández and E. A. Castro, Phys. Rev. A 46, 7288 (1992)], extending its applicability to a wider variety of separable quantum-mechanical problems. As an illustrative example, we consider a particle in a one-dimensional box with a finite potential wall perturbed by a linear potential and obtain the perturbation corrections to the wave function and energy of an arbitrary state in terms of the corresponding unperturbed quantities.

Positronium is the quasistable bound system consisting of an electron and its antiparticle, the positron. Its energy levels can be explained to a high degree of accuracy by the electromagnetic interaction, affording an ideal test of the quantum electrodynamic (QED) theory of bound systems. We have measured the 1 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$–2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ interval in positronium by Doppler-free two-photon spectroscopy to be 1 233 607 216.4±3.2 MHz. We employ continous-wave (cw) excitation to eliminate the problems inherent with pulsed laser measurements of nonlinear transitions. Positronium (Ps) atoms generated in vacuum are excited to the 2S state using cw laser light built up to 2.5 kW circulating power in a resonant Fabry-Pérot cavity. The excited-state atoms are photoionized using a pulsed laser at 532 nm, and the liberated positrons counted as the cw laser is tuned relative to a reference line in tellurium (${\mathrm{Te}}_2$) molecular vapor. The fit of a detailed theoretical model to the measured line shape determines the Ps resonance frequency relative to the ${\mathrm{Te}}_2$ reference line. The Monte Carlo model includes details of the excitation and detection geometry, the Ps velocity distribution, and the dynamic Stark shift, and gives excellent agreement with the measured line shapes. The quoted 2.6 parts per billion (ppb) uncertainty is dominated by the measurement of the Ps line center relative to the ${\mathrm{Te}}_2$ reference line, with a 1.0-ppb contribution from a recent calibration of our ${\mathrm{Te}}_2$ cell relative to the hydrogen 1S-2S transition frequency. The measurement is in excellent agreement with theory and sufficiently accurate to provide a test of the as-yet-uncalculated ${\mathrm{\alpha }}^4$${\mathit{R}}_{\mathrm{\infty }}$ QED correction. Our measurement tests the ${\mathrm{\alpha }}^2$${\mathit{R}}_{\mathrm{\infty }}$ QED contributions to the energy of the 1 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ and 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ states to 3.5 parts in ${10}^5$.

The generalized variational method is used to compute energies for the Yukawa and Hulthén potentials for states with n≤6. This straightforward approach is based on forming trial wave functions from a linear combination of independent functions. The estimates for the energies produced by this method are considerably more accurate than previous results for a wide range of values for the screening parameter.

In this paper, we discuss the normalization of nonrelativistic continuum wave functions by using an iterated WKB method and suggest a numerical procedure of evaluating the phase shifts of the continuum wave functions. To illustrate the efficiency and accuracy of the procedure, we calculate the phase shifts of a free electron in the ‘‘polarization’’ Yukawa potential. The results are in very good agreement with other exact values. The hybrid grid mesh ρ=αr+β ln(Zr), which is appropriate to the computation of continuum wave functions, is used in the calculation.