We report strong J=0–1, 3p-3s lasing in Ne-like scandium, calcium, potassium, and chlorine at wavelengths ranging from 35.3 nm in scandium to 52.9 nm in chlorine. The experiments were carried out with the ASTERIX IV iodine laser using a 15% prepulse 5.2 ns before the main pulse. These results extend the range of laser plasma x-ray lasers into the extreme ultraviolet region. Gain lengths between 7 and 11 were measured for the different lines. The 38.3-nm laser in calcium lased at an intensity as low as 5×${10}^{12}$ W/${\mathrm{cm}}^{\mathrm{-}2}$.

We show that, contrary to common wisdom, the maximum gain mode of semiconductor lasers subject to optical feedback is always stable. The minimum linewidth mode is shown to be subject to a Hopf bifurcation associated with destabilizing the relaxation oscillations. This explains the experimental observation of narrow-linewidth, single-mode diode lasers operating with high optical feedback.

We study the one-dimensional propagation of a laser pulse through an atomic vapor of finite length L. Both the temporal and the time-dependent spectral profiles of the exiting laser pulse are calculated. It is shown that, when the pulse duration is comparable with or shorter than the effective relaxation time of the atomic density matrix, the spectrum of the final pulse exhibits frequency sidebands located in the vicinity of the time-varying generalized Rabi frequency, which can contain up to a few percent of the total laser power. The possible connection between this result and cone emission in the pulsed regime is addressed.

We consider the collision behavior of self-trapped optical beams in media with a quadratic nonlinearity. It is found that the solitary waves behave similarly to true solitons above a critical velocity. Below this velocity they merge and form oscillating states.

Hardy’s formulation of the Einstein-Podolsky-Roser paradox and the usual formulation based on Bell-type inequalities are compared. The role of the supplementary assumptions in an experimental test based on Hardy’s approach is discussed. It is proved that even in Hardy’s approach the supplementary assumptions play a fundamental role in refusing Einstein locality on the basis of the experimental results. The lowest value of quantum efficiency for a loophole-free experiment based on Hardy’s approach is deduced.

We explore further the suggestion to describe a pre- and postselected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically recast the basics of quantum mechanics—dynamics, observables, and measurement theory—in terms of two-states as the elementary quantities. We find a simple and suggestive formulation that "unifies" two complementary observables: probabilistic observables and nonprobabilistic "weak" observables. Probabilities are relevant for measurements in the "strong-coupling regime." They are given by the absolute square of a two-amplitude (a projection of a two-state). Nonprobabilistic observables are observed in sufficiently weak measurements and are given by linear combinations of the two-amplitude. As a subclass they include the "weak values" of Hermitian operators. We show that in the intermediate regime, one may observe a mixing of probabilities and weak values. A consequence of the suggested formalism and measurement theory is that the problems of nonlocality and Lorentz noncovariance, of the usual prescription with a "reduction," may be eliminated. We exemplify this point for the Einstein-Podolsky-Rosen experiment and for a system under successive observations.

Photon pairs produced by type-I and type-II parametric down-conversion are passed through a Michelson interferometer. Two quarter-wave plates in one arm of the interferometer allow variation of the polarization state of the photons. We investigate experimentally the geometric phase or Pancharatnam phase acquired by single photons and photon pairs dependent on the solid angle that is subtended by the circuit that represents the varying state of polarization on the Poincaré sphere. It is found that the geometric phase acquired by the pair depends on the initial polarization state of the two photons. If both photons are in equal states of linear polarization, we observe a doubling of the geometric phase compared to single photons; in the case of orthogonal states of linear polarization, the geometric phase is completely canceled. Our results show the role of Pancharatnam’s phase in nonclassical two-photon interference phenomena and the interplay between the geometric phase and the dynamical phase in these phenomena.

The stability of systems consisting of a negative charge $-q_1$ and two positive charges $q_2$ and $q_3$ is discussed as a function of the values of the charges $q_i$ and of the constituent masses $m_i$. We give general results and list some open questions of interest, which hopefully will stimulate further investigations.

In this paper, using quantum groups, noncommutative geometry, and the $q$-sequence theory, a complete algebraization scheme of quantum mechanics in view of Bohm's implicate order idea is given. It is pointed out that, in fact, there is some $q$-implicate order, and concrete expressions are given.

We show that the vacuum can induce a torque between two uniaxial birefringent dielectric plates. We discuss the differences and analogies between this torque and the Casimir force in the same configuration. We show that the torque can be interpreted as arising from angular-momentum transfer from the vacuum to the plates, as well as from the orientation dependence of the zero-point energy.

The geometric phase is defined for any arbitrary quantum evolution using a ‘‘reference section’’ of the bundle covering the curve in the projective Hilbert space. A canonical one-form is defined whose line integral gives the desired geometric phase. It is manifestly gauge, phase, and reparametrization invariant for all quantum evolutions. A simple proof of the vanishing nature of the geometric phase along the geodesic is given. Also, an elementary proof of the nonadditive nature of the geometric phase is given. In the limit of cyclic evolution of a pure quantum state, this phase reduces to the Aharonov and Anandan phase, precisely. It is observed that in addition to the geometric phase, other geometric structures exist, such as the ‘‘length’’ and ‘‘distance’’ during any arbitrary quantum evolution. The relations among all of these geometric quantities are pointed out. Finally, two simple examples are studied to illustrate the ideas introduced in this paper.

A so far most generalized Jaynes-Cummings (JC) model, which includes not only various ordinary JC models but also a special model describing spin-orbit interaction, is investigated from an algebraic point of view. We find that an alternative representation of su(2) algebra arises naturally from the system. This structure plays an essential role in the generalized system. As one result, the system behaves like a spin-1/2 system moving in a magnetic field. So it is rather easy to obtain the energy levels, eigenstates, and the time evolution operator, or any other quantities of physical interest. Two special cases are considered. Finally, a possible generalization to the three-level system is discussed.

It has been shown in experiments on induced coherence without induced emission using two coherently pumped nonlinear crystals that (a) no second-order interference occurs as long as it is possible, even if only in principle, to determine which of the two crystals emitted the photon pair; (b) second-order interference does occur whenever it is intrinsically impossible to determine which of the two crystals emitted the photon pair. The present paper discusses a variant of the previous experiments in which, apparently, (c) each photon of the pair is emitted by a different crystal. It is also shown that interference is not necessarily reduced when there is no intrinsic indistinguishability. The experiment provides a proof of Bell’s theorem for two particles without using an inequality and, at least in principle, could be used to test local realism against quantum mechanics. However, as in the case of the other experiments so far performed, some additional assumption would have to be introduced. It is then shown that the introduction of a reasonable assumption reduces the detectors’s efficiencies needed to test local realism, even if nonenhancement is not assumed.

It is shown that when the wave packet of a photon passes through a region where more than one path mode can be chosen, the interference between these modes of the probability waves of the photon causes a reshaping process of the wave packet. In some conditions this reshaping gives rise to an apparent superluminal traveling, as observed by Steinberg, Kwiat, and Chiao [Phys. Rev. Lett. 71, 708 (1993)]. The present model also leads to some predictions that can be tested experimentally.

Arguments of the Jaynes maximum entropy sort have proved to be surprisingly successful in providing one with approximate descriptions of pure states in a variety of scenarios, entirely bypassing any consideration of Schrödinger's equation. Thus far, however, the algorithm has been unable to incorporate input information concerning expectation values of complementary observables. We discuss here how to overcome this difficulty by recourse to diagonal hypervirial theorems.

Mass-selected, double-resonance, field-ionization spectroscopy is used to determine the first ionization potential of the three abundant isotopes of platinum. By fitting up to 38 member of s and d Rydberg series of ionization potentials of ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$, ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$, and ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}$ are determined to be 72 256.6±0.9 ${\mathrm{cm}}^{\mathrm{-}1}$ (8.958 68±0.000 11 eV). This yields a revised value of 27 580±320 ${\mathrm{cm}}^{\mathrm{-}1}$ (3.42±0.04 eV) for the bond strength of platinum dimercation ${\mathrm{Pt}}_2^{+}$.

We study the effects of finite proton mass on the energy levels of hydrogen atoms moving transverse to a superstrong magnetic field B with generalized pseudomomentum ${\mathit{K}}_{\mathrm{\perp }}$. Field strengths of order B∼${10}^{12}$ G are typically found on the surfaces of neutron stars, but we also study the regime B≳${\mathit{B}}_{\mathit{crit}}$=4.23×${10}^{13}$ G, where the Landau excitation energy of the proton is large. We adopt two different approaches to the two-body problem in strong magnetic fields and obtain an approximate but complete solution of the atomic energy as a function of B and ${\mathit{K}}_{\mathrm{\perp }}$. We show that, for B≫${\mathit{B}}_{\mathit{crit}}$, there is an orthogonal set of bound states that do not have any Landau excitation contribution in their energies. The states with very large ${\mathit{K}}_{\mathrm{\perp }}$ have small binding energies and small transverse velocities, but are nevertheless distinct from the fully ionized states. The final results for the excitation energies are given in the form of analytical fitting formulas. The generalized Saha equation for the ionization-recombination equilibrium of hydrogen gas in the presence of a superstrong magnetic field is then derived. Although the maximum transverse velocity of a bound atom decreases as B increases, the statistical weight due to transverse motion is actually increased by the strong magnetic field. For the astrophysically interesting case of relatively low density and temperature, we obtain analytic approximations for the partition functions. The highly excited bound states have a smaller statistical weight than the fully ionized component.

Two local-mode model Hamiltonians containing stretch-stretch couplings have been utilized to obtain the vibrational energy levels of the HCN molecule for the purpose of studying them statistically. The effect of the kinetic coupling has been clearly obtained from the statistical analysis which includes nearest-neighbor level-spacing distributions (NNLSD) and the ${\mathrm{\Delta }}_3$ statistics of Dyson and Mehta. For NNLSD, a pronounced tendency towards the Wigner distribution has been found. The role of isotopic masses in the statistical properties of the vibrational spectra has also been elucidated. Comparison has been made between the results obtained from the two models. Correlation has been found between a transition to chaos (utilizing Poincaré sections and Lyapunov exponents) through classical mechanics and the above statistical behavior of the spectra.

Valence-shell relativistic configuration-interaction calculations predict one ${\mathrm{U}}^{\mathrm{-}}$ bound state, viz., 5${\mathit{f}}^3$6d7${\mathit{s}}^2$7p J=13/2, with an electron affinity of 0.175 eV. We found no other J’s for this configuration to be bound, nor are any 5${\mathit{f}}^3$6${\mathit{d}}^2$7${\mathit{s}}^2$ levels expected to be bound. Attachment of a 5f electron is even more unlikely. The hyperfine structure (hfs) constants for the ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}_{}^{\mathrm{-}}{}_{}{}^{}$ state, in MHz, are, respectively, A,B=-72.4,2644. Although core polarization effects are absent, the valence hfs results for ${}_{}{}^{235}{}_{}{}^{}\mathrm{i}$ are in generally good agreement with experiment and represent a modest improvement compared to existing semiempirical values. An LS analysis is provided for the bound state.

The effect of the positive-energy continuum orbitals to the photoionization and bound-bound transitions in He and Mg-like divalent ${\mathrm{Al}}^{+}$ ion is estimated quantitatively in a B-spline-based configuration-interaction calculation. Our calculation has also shown that the theoretical uncertainty in radiative lifetimes measured in terms of the difference between the length and velocity results, due to the use of a parametrized long-range dipole core-polarization potential, is approximately 1–3 % for the Mg-like divalent ${\mathrm{Al}}^{+}$ ion.