It is known that a partially entangled state gives improved sensitivity in generalized Ramsey spectroscopy in the presence of decoherence, whereas a maximally entangled state does not. However, it has been an open question whether the known decoherence limit in the improvement is achievable. We show that every spin-squeezed state possesses pairwise entanglement, thereby improving the spectroscopic sensitivity, and that even suboptimal entanglement in its easiest implementation suffices to asymptotically reach the decoherence limit without any measurement optimization.

We derive a necessary and sufficient condition for the separability of tripartite three-mode Gaussian states that is easy to check for any such state. We give a classification of the separability properties of those systems and show how to determine for any state to which class it belongs. We show that there exist genuinely tripartite bound entangled states and point out how to construct and prepare such states.

Photodetachment microscopy has been used in a double-pass, field-collinear scheme in order to measure the electron affinity of atomic oxygen. As an illustration of the sensitivity of the method, electron images could be recorded even from the rarest ${}^{17}{\mathrm{O}}^{-}$ ion. Analysis of photodetachment images recorded with this odd isotope, however, requires that one knows the unresolved hyperfine structures of the ground states of both the neutral atom ${}^{17}\mathrm{O}$ and the negative ion. Calculation of the hyperfine structure of ${}^{17}{\mathrm{O}}^{-}$ was achieved, which permitted to add the electron affinity of ${}^{17}\mathrm{O}$ to the series of the measured electron affinities of oxygen isotopes. The anomalous isotope shift of these electron affinities is finally compared with ab initio calculations.

This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive-$P$ representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The model includes all interactions between the particles, background gas losses, two-body losses, and the numerical simulations are performed in three dimensions. It is found that it is possible to differentiate the quantum and semiclassical behavior when the particle density is sufficiently low and the coupling is sufficiently strong.

The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in $\alpha Z$ and to first order in $m/M$ is formulated. The complete $\alpha Z$-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order $(\alpha {Z)}^{2}m/M$ for an arbitrary state of a hydrogenlike atom.

We analyze the angular correlation of the 64 intrashell ${3l3l}^{\prime }{3l}^{″}$ states of a model atom with the three electrons confined on the surface of a sphere. Each wave function is examined in the body-fixed frame of the atom to search for the basic normal modes of the collective motion of the three electrons. Contour surfaces are used to display the interelectronic density distributions and nodal surfaces. It is shown that the calculated energy levels can be grouped into rotational patterns similar to those of a symmetric top. Three different basic normal modes of the joint motion of the three electrons are identified. For the higher states excitations of these three basic modes have also been discovered. Based on these normal modes we have classified all the 64 ${3l3l}^{\prime }{3l}^{″}$ states into manifolds of truncated rotational states of a symmetric top. The classification scheme is then used to group the ${3l3l}^{\prime }{3l}^{″}$ states of ${\mathrm{N}}^{4+}$ and the ${1s}^2{3l3l}^{\prime }{3l}^{″}$ states of ${\mathrm{N}}^{2+}$ calculated by Vaeck and Hansen [J. Phys. B 25, 883 (1992)], to show that their rotational level structures are similar to those of the model atom with very few modifications.

Extensive complex-rotation calculations are carried out for eight ${\mathrm{He}}^{-}$ ${3l3l}^{\prime }{3l}^{″}$ states in order to understand the resonance structure of ${\mathrm{He}}^{-}$ below the He ${3s3p}^1{P}^o$ threshold. It is found that the spectrum is very different from that of the ${\mathrm{He}}^{-}$ ${2l2l}^{\prime }{2l}^{″}$ states. A $3s-3p$ energy inversion is uncovered. Our result suggests that unlike the resonance structures below the $n=2\mathrm{}$ region, ${3s3p}^2{}^{2}S$ and ${3s3p}^2{}^{2}P$ do form closed-channel resonances below the $3s3p{}^3{P}^o$ threshold. The results of this study are used to understand the scattering experiment of Roy [Phys. Rev. Lett. 38, 1062 (1977)].

Absolute cross sections as a function of interaction energy were measured for ${\mathrm{H}}^{+}$ formation in electron-impact dissociation of ${\mathrm{C}}_2{\mathrm{H}}^{+}$ and ${\mathrm{C}}_2{\mathrm{H}}_2^{+}$ in the energy range from threshold up to 50 eV. The crossed beams technique was used, and light fragment ions emerging from a heavy target were detected. A common feature of the studied targets was almost the same $\left[\right(1.3\mathrm{}–1.7)\times {10}^{-16}\hspace{0.5em}{\mathrm{cm}}^2]$ cross section for ${\mathrm{H}}^{+}$ production from 25 to 50 eV. The results were compared with our previous results for ${\mathrm{CD}}_n^{+},$ and the observed propensity rules were found to apply in this case also.

Electron-impact excitation of the ${4p}^{5}5s$ and ${4p}^{5}5p$ levels of Kr I has been investigated in detail by calculating cross sections using distorted-wave and close-coupling approaches. The results are presented from the excitation thresholds up to 50 eV incident energy. They are contrasted among the different calculations and compared with other theoretical predictions and experimental data. Significant disagreement is found with many of the recent experimental data of Chilton et al. [Phys. Rev. A 62, 032714 (2000)].

The continuity conditions for the wave function of a particle with a position-dependent mass and interacting with an oscillating field are derived. One-dimensional motion is assumed and the potential is represented as a series of constant steps. The method introduces discontinuities in the potential and the mass and the matching conditions need to be reformulated to take into account the presence of the field. An application is made to the calculation of the transmissivity of an electron with a sector-dependent effective mass in a nanostructure. The use in each sector of the wave equation without the $A^2$ term is necessary to ensure convergence with respect to the number of channels.

We have measured the above-threshold ionization (ATI) electron spectrum from nonsequential double ionization of Ar, and compare our results to the single-ionization ATI spectrum. A variation on the coincidence-tagging technique enables the subtraction of contamination associated with single ionization, revealing an excess of higher energy electrons with measured kinetic energies up to approximately ${2U}_p.$ We also find an excess of very low energy photoelectrons, not previously observed. Implications for the rescattering model are discussed.

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, the quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the sites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems. We show that the localization length can be used as an indicator of the effective temperature of the trapped ion, which can be experimentally measured.

We consider a case of two Bose-Einstein condensates corresponding to different hyperfine states of the same atomic species. Both hyperfine states are coupled to the same excited state via distinct modes of a microwave cavity. If one of the condensates contains a sufficiently large number of atoms such that it may be treated as an undepleted pump field, then it is possible to adiabatically transfer the quantum state of the other condensate into one of the cavity modes that is initially in a vacuum state.

We have carried out a neutron reflectivity measurement of silicon as a prelude to a search for the neutron electric dipole moment (EDM). Our technique uses multiple Bragg reflections for neutrons near 1.92 Å as they travel down slots cut along the (440) planes of a perfect silicon crystal. For neutrons within the Darwin peak width, a previous measurement places a lower limit on the reflectivity of $R>\mathrm{}\mathrm{0.9978.}\mathrm{}$ Our measurement has been performed at the University of Missouri Research Reactor and has resulted in a value of $R=0.999\mathrm{}976\pm 0.000075,$ which yields a value of $R>\mathrm{}0.9999\mathrm{}$ at the 90% confidence level. This is in agreement with the calculated reflectivity of $R=0.999\mathrm{}952$ and indicates that as many as 21 000 multiple Bragg reflections are possible before there is a significant loss of neutron intensity. By coupling the EDM to the atomic electric fields on each reflection, we estimate this technique will allow a measurement of the EDM with a sensitivity on the order of ${10}^{-27}e\mathrm{cm}.$

Using an explicit Euler substitution, a system of differential equations was obtained, which can be used to find the solution of the time-dependent one-dimensional Schrödinger equation for a general form of the time-dependent potential.

We demonstrate that the superpositions of macroscopically distinct coherent states are maximally entangled states. Among other possible applications of this result, in this paper we show that the experimental arrangements generating superpositions of macroscopically distinct coherent states may be adapted for precision phase-shift detection reaching the maximum sensitivity allowed by quantum physics (Heisenberg limit).

We consider three generic types of coupling between two quantum bits (qubits), which are typically found in solid-state qubits proposed in the literature. We show that proper choice of non-local Bell states can simplify significantly the implementation of quantum teleportation and quantum dense coding.

The equation of motion of the quantum characteristic function for the linear-algebraic dynamical system is derived from the von Neumann equation and reduced to a Schrödinger-like equation in a differential adjoint representation. The exact analytical solution to the von Neumann equation of the quantum characteristic function of the two-level Jaynes-Cummings model is obtained.

The Heisenberg inequality $\Delta X\Delta P>~ħ/2\mathrm{}$ can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wave functions. The statistics of complementary observables are thus connected by an “exact” uncertainty relation. Results may be generalized to angular momentum and phase, photon number and phase, time and frequency, and to states described by density operators. Connections to energy bounds, entanglement, Wigner functions, and optimal estimation of an observable from the measurement of a second observable are also given.

Measurements of electron impact ionization of neutral Al, Ga, and In show large cross sections compared to other elements in the same rows of the periodic table. Semiempirical and classical calculations of direct ionization cross sections are all substantially smaller. Calculations by McGuire [Phys. Rev. A 26, 125 (1982)] for aluminum that include excitations to autoionizing ${3s3p}^2$ doublet levels are 2.5 times higher than experiment at the peak. We report the direct ionization cross sections based on the binary-encounter-Bethe model of Kim and Rudd [Phys. Rev. A 50, 3954 (1994)], which is an ab initio theory. We add the autoionization contribution using scaled plane-wave Born cross sections as recently developed by Kim [Phys. Rev. A 64, 032713 (2001)] for excitations to the first set of autoionizing levels. Dirac-Fock wave functions are used for the atomic structure. Our results are in excellent agreement with experimental values and support substantial contributions from excitation-autoionization to the total ionization cross sections for these elements. We also compare the total ionization cross section of boron to available theories, though no experimental data are available.