We present a self-calibrating method for measuring local multiphoton-ionization yields as a function of absolute intensity. In contrast to the method recently described by Walker et al. [Phys. Rev. A 57, R701 (1998)], our method does not require any assumption on the intensity distribution inside a laser focus, nor does it use any mathematical procedure such as deconvolution that would be based on such an assumption. In this sense, our method is self-calibrating. The proposed method immediately gives ion yields as a function of absolute intensity. Furthermore, it allows the intensity distribution inside the focal volume to be measured with a spatial resolution of a few μm. The proposed method uses a five-grid high-resolution reflecting time-of-flight ion spectrometer, in combination with an electron spectrometer. The advanced design of the ion spectrometer allows detection of ions originating exclusively from a well-defined source volume with μm-size dimensions, thus enabling absolute measurements of ionization probabilities and saturation intensities. By moving the source volume of the ion spectrometer through the focal region, we can quantitatively measure local ion densities inside the focus. The corresponding spatial absolute intensity distribution is measured by electron-ion coincidence measurements via the ponderomotive shifts in the electron spectrum of a suitable target gas, e.g., He. Both aspects of the proposed method (ion measurements from a confined volume and intensity measurements based on ponderomotive shifts) have been successfully applied in the past.

An estimate of the duration of the period of nonexponential decay is made for a recent experiment. It is based on a general definition of “jump time.”

We analyze the linewidth narrowing in the fluorescence spectrum of a two-level atom driven by a squeezed vacuum field of a finite bandwidth. It is found that the fluorescence spectrum in a low-intensity squeezed field can exhibit a $(\omega -{\omega }_0{)}^{-6}$ frequency dependence in the wings. We show that this fast fall-off behavior is intimately related to the properties of a narrow-bandwidth squeezed field and does not extend into the region of broadband excitation. We apply the linear response model and find that the narrowing results from a convolution of the atom response with the spectrum of the incident field. On the experimental side, we emphasize that the linewidth narrowing is not sensitive to the solid angle of the squeezed modes coupled to the atom. We also compare the fluorescence spectrum with the quadrature-noise spectrum and find that the fluorescence spectrum for an off-resonance excitation does not reveal the noise spectrum. We show that this difference arises from the competing three-photon scattering processes.

The stationary solution is obtained for the photorefractive subharmonic gratings excited in crystals of the sillenite family by a standing light interference pattern and an applied ac electric field. We show that the main subharmonic with doubled spatial period may become unstable against excitation of the subharmonic with quadrupled spatial period. The threshold condition for this bifurcation is found.

We report on a demonstration of a gain-length product greater than five for recombination-pumped Li-like soft-x-ray lasers, using a long plasma length of 3.3 cm. Slab aluminum targets are irradiated by a multipulse Nd:glass laser pump at an intensity of 1 ${\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ A time-integrated small-signal gain coefficient of 1.7 ${\mathrm{cm}}^{-1}$ and a gain-length product of 5.6 are observed for the 154.7 Å Li-like Al laser. Space-resolved observations reveal a gain region width of 200 $\mu$m full width at half maximum, which is found to be wide enough for saturated amplification experiments.

We discuss quantum conditional probability and its applications to deterministic hidden-variable models. We derive empirical tests corresponding to mathematical no-go proofs, providing rigorous statistical tests based on experimental outcomes. Evidently, it now possible to examine the statistical power of the empirical tests, and place confidence intervals on the parameters that precisely measure the departure of hidden-variable models from quantum experimental outcomes. Moreover, reinterpretation of well-known results in the light of quantum conditional probability provides other experimental demonstrations and no-go proofs: outcomes for the familiar Young double-slit experiment show that there are no deterministic hidden-variable models of the type considered by Kochen and Specker [J. Math. Mech. 17, 59 (1967)] or Bell [Rev. Mod. Phys. 38, 447 (1966)].

Using the ideas of supersymmetry and shape invariance we rederive the spectrum of the $A_{N-1}$ and ${\mathrm{BC}}_N$ Calogero-Sutherland model. We briefly discuss how to obtain the corresponding eigenfunctions. We also discuss the difficulties involved in extending this approach to the trigonometric models.

We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a decomposition. Separable states correspond to mixing from one to four pure product states. Inseparable states can be described as pseudomixtures of four or five pure product states, and can be made separable by mixing them with one or two pure product states.

We show that the quadratic short time behavior of transition probability is a natural consequence of the inner product of the Hilbert space of the quantum system. We provide a relation between the survival probability and the underlying geometric structure such as the Fubini-Study metric defined on the projective Hilbert space of the quantum system. This predicts the quantum Zeno effect even for systems described by nonlinear and nonunitary evolution equations, within the collapse mechanism of the wave function during measurement process.

A full quantum analysis of $100\%$ efficient interaction-free measurements is presented. It is shown that it is possible to describe consistently the phenomenon in terms of an effective interaction between object and apparatus that disturbs measurable quantities of the observed system.

In a recent paper Grot, Rovelli, and Tate (GRT) [Phys. Rev. A 54, 4676 (1996)] derived an expression for the probability distribution $\pi \mathrm{}(T;X)\mathrm{}$ of intrinsic arrival times $T\left(X\right)\mathrm{}$ at position $x=X$ for a quantum particle with initial wave function $\psi \mathrm{}(x,t=0\mathrm{})\mathrm{}$ freely evolving in one dimension. This was done by quantizing the classical expression for the time of arrival of a free particle at $X,$ assuming a particular choice of operator ordering, and then regulating the resulting time of arrival operator. For the special case of a minimum-uncertainty-product wave packet at $t=0\mathrm{}$ with average wave number $〈k〉$ and variance $\Delta k$ they showed that their analytical expression for $\pi \mathrm{}(T;X)\mathrm{}$ agreed with the probability current density $J(x=X,t=T)\mathrm{}$ only to terms of order $\Delta k/〈k〉.$ They dismissed the probability current density as a viable candidate for the exact arrival time distribution on the grounds that it can sometimes be negative. This fact is not a problem within Bohmian mechanics where the arrival time distribution for a particle, either free or in the presence of a potential, is rigorously given by $|J(X,T)\mathrm{}|$ (suitably normalized) [W. R. McKinnon and C. R. Leavens, Phys. Rev. A 51, 2748 (1995); C. R. Leavens, Phys. Lett. A 178, 27 (1993); M. Daumer et al., in On Three Levels: The Mathematical Physics of Micro-, Meso-, and Macro-Approaches to Physics, edited by M. Fannes et al. (Plenum, New York, 1994); M. Daumer, in Bohmian Mechanics and Quantum Theory: An Appraisal, edited by J. T. Cushing et al. (Kluwer Academic, Dordrecht, 1996)]. The two theories are compared in this paper and a case presented for which the results could not differ more: According to GRT’s theory, every particle in the ensemble reaches a point $x=X,$ where $\psi \mathrm{}(x,t)\mathrm{}$ and $J(x,t)\mathrm{}$ are both zero for all $t,$ while no particle ever reaches $X$ according to the theory based on Bohmian mechanics. Some possible implications are discussed.

Weyl functions are shown to be an important tool in quantum phase-space studies. Their properties are studied and relations with other quantities are derived. The use of Weyl functions for the understanding of quantum interference phenomena is discussed. The general theory is applied to superpositions of $m$ coherent states uniformly distributed on a circle (generalized Schrödinger cats). The properties of these states are explored and their interference behavior is discussed, using Weyl functions.

Generalized WKB connection formulas are used to derive the transmission amplitude describing tunneling through a potential barrier via two isolated classical turning points. The resulting formulas correctly reproduce the behavior in the vicinity of the base of the barrier where the tunneling probability vanishes exactly, and where formulas available to date fail.

It is shown that the Runge-Lenz vector of a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of the radial Schrödinger equation. A similar situation exists for an isotropic harmonic oscillator. It is seen that there exists an intimate relation between the conserved quantities responsible for the closeness of classical orbits on the one side and the quantum-mechanical raising and lowering operators on the other side, which is physically connected with the dynamical symmetry of the system considered. Some discussions are made about the factorization of a one-dimensional system.

The Bures distance between two displaced thermal states and the corresponding geometric quantities (statistical metric, volume element, scalar curvature) are computed. Under nonunitary (dissipative) dynamics, the statistical distance shows the same general features previously reported in the literature by Braunstein and Milburn for two-state systems. The scalar curvature turns out to have new interesting properties when compared to the curvature associated with squeezed thermal states.

The method used by Garrison and Wright for the calculation of complex geometrical phases in quantal dissipative systems is extended to all time periodic linear systems, including classical linear systems with nonunitary time evolution. Each eigenvector $|x_i\mathrm{}\left(t\right)\mathrm{}〉$ of the period map modified by a complex scaling exponent ${\theta }_i\mathrm{}\left(t\right)\mathrm{}$ has an associated complex geometrical phase, which admits a solid angle interpretation in two-dimensional systems. Pairs of the $|x_i\mathrm{}\left(t\right)\mathrm{}〉$ commonly determine quadratic periodic invariants corresponding to topologically distinct surfaces of the invariant torus, and a connection between the scaling exponents and classical angle variables is established. The method is illustrated by the calculation of explicit expressions for the classical and quantal nonadiabatic phases associated with angular momentum precession. A second application to a general quadratic Hamiltonian extends existing adiabatic results to the classical and quantal nonadiabatic phases of both elliptic and hyberbolic systems. The relevance of torus ensemble averaging in a classical angle-action formulation is discussed.