Considering a general closed system with a discrete energy spectrum and a given mean energy, we derive the states that minimize the time it takes to evolve into an orthogonal state under free evolution. The implications on optical interferometry are discussed.

We construct a class of one-dimensional Lie-algebraic problems based on sl(2), where the spectrum in the algebraic sector has a dynamical symmetry $E\leftrightarrow -E.\mathrm{}$ All $2j+1$ eigenfunctions in the algebraic sector are paired and inside each pair are related to each other by a simple analytic continuation $\overrightarrow{x}ix,$ except the zero mode appearing if j is integer. At $\overrightarrow{j}\infty$ the energy of the highest level in the algebraic sector can be calculated by virtue of the quasiclassical expansion, while the energy of the ground state can be calculated as a weak-coupling expansion. Both series coincide identically.

We show, by explicit examples, that the Jaynes principle when applied to compound quantum systems may produce the entangled maximum entropy states compatible with data coming from nonentangled (separable) states. It means that the Jaynes statistical inference scheme may lead to a wrong conclusion about entanglement, which is a crucial parameter in quantum information theory. We suggest that in all the processes where entanglement is needed, the proper inference scheme should involve minimization of entanglement. Examples illustrating the proposed scheme are provided.

Although one can show formally that a time-of-arrival operator cannot exist, one can modify the low-momentum behavior of the operator slightly so that it is self-adjoint. We show that such a modification results in the difficulty that the eigenstates are drastically altered. In an eigenstate of the modified time-of-arrival operator, the particle, at the predicted time of arrival, is found far away from the point of arrival with probability $1/2.$

Long ago in quantum mechanics a discussion appeared about the problem of opening a completely absorbing shutter on which a stream of particles of definite velocity was impinged. The solution of the problem was obtained in a form entirely analogous to the optical one of diffraction by a straight edge. The argument of the Fresnel integrals was time dependent, and thus the first part in the title of this paper. In this paper we reformulate the problem in Wigner distributions and tomographical probabilities. In the former case the probability in phase space is very simple but, as it takes positive and negative values, the interpretation is ambiguous, though it gives a classical limit that agrees entirely with our intuition. In the latter case we can start with our initial conditions in a given reference frame, but obtain our final solution in an arbitrary frame of reference.

We show the feasibility of a tomographic reconstruction of “Schrödinger-cat states” generated according to the scheme proposed by S. Song, C.M. Caves, and B. Yurke [Phys. Rev. A $41,$ 5261 (1990)]. We present a technique that tolerates realistic values for quantum efficiency at photodetectors. The measurement can be achieved by a standard experimental setup.

The aim of this paper is to give explicit calculation of the classical capacity of quantum Gaussian channels, in particular, involving squeezed states. The calculation is based on a general formula for the entropy of a quantum Gaussian state, which is of independent interest, and on the recently proved coding theorem for quantum communication channels.

Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using Greenberger-Horne-Zeilinger (GHZ) states. In the quantum case the presence of an eavesdropper will introduce errors so that his presence can be detected. We also show how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.

We study the electron correlations in singly, doubly, and triply excited states of a three-electron atom. While electron correlation in general is weak for singly excited states, correlation plays major roles in determining the characteristics of doubly and triply excited states. Using the adiabatic approximation in hyperspherical coordinates, we show that the distinction between singly, doubly, and triply excited states is determined by the radial correlations, while finer distinctions within doubly or triply excited states lie in the angular correlations. Partial projections of the body-fixed frame wave functions are used to demonstrate the characteristic nodal surfaces which provide clues to the energy ordering of the states. We show that doubly excited states of a three-electron atom exhibit correlations that are similar to the doubly excited states of a two-electron atom. For the triply excited states, we show that the motion of the three electrons resemble approximately that of a symmetric top.

The sharp hydrogen $1S-2S$ two-photon transition is a promising candidate for the realization of a frequency standard based on an atomic transition in the optical region. In recent work we have used this transition to precisely determine the Rydberg constant, the $1S$ Lamb shift and the hydrogen-deuterium isotope shift. In this paper we focus on substantially improved spectroscopic methods leading to a much higher spectral resolution of the $1S-2S$ transition in hydrogen and deuterium. We have successfully applied a time-delayed measurement scheme, which allowed us to reduce the linewidth to 1 kHz at 243 nm corresponding to a spectral resolution of $\Delta \nu /\nu =8\mathrm{}\times {10}^{-13}.$ A theoretical line-shape model based on a solution of the Master equation allows us to determine the unperturbed hydrogen $1S-2S$ two-photon transition frequency from our spectra to a level of $1.5\times {10}^{-14}.$

The bound states of a Morse potential are described in terms of a basis of states that are characterized for being eigenstates of the Morse variable. These states are strongly localized in configuration space; thus they are called configuration localized Morse (CLM) wave functions. These are shown to provide a powerful tool to calculate analytically, to a good approximation, matrix elements of arbitrary functions of the interatomic separation between vibrational states of anharmonic diatomic molecules. Applications of CLM wave functions to the calculation of vibrational transitions in HF and DF diatomic molecules are presented.

Atomic ground-state properties are evaluated by means of a modified semiclassical approach with a quantum-mechanical treatment of the near-nuclear region. The results for the energy and lowest-order radial expectation values are close to Hartree-Fock results, improving the Thomas-Fermi-Dirac-Weizsäcker estimates.

Hot ${\mathrm{CH}}_2^{+}$ molecular ion ensembles were prepared, accelerated, and stored for radiative cooling to room temperature. The structure of the species was measured by the Coulomb explosion imaging method at different stages of cooling. The bending angle distributions were extracted and compared with recent theories as well as a previous Coulomb explosion imaging measurement. The comparison reveals an apparent large nonadiabatic contribution to the low-lying ${\mathrm{CH}}_2^{+}$ wave functions.

We have measured the ground-state hyperfine splitting between the ${3S}_{1/2}\hspace{0.5em}F=2,m=0\mathrm{}$ and ${3S}_{1/2}\hspace{0.5em}F=1,m=0\mathrm{}$ levels of ${}^{21}\mathrm{Na}.$ The measurement was performed with microwave spectroscopy on 40 000 radioactive ${}^{21}\mathrm{Na}$ atoms ${(t}_{1/2}=22\mathrm{}\hspace{0.5em}\sec )$ collected in a magneto-optical trap on-line at the 88-in cyclotron at LBNL. The transition was excited with microwaves directed at the atoms and detected with resonant probe fluorescence light. The splitting ${\nu }_{\mathrm{HFS}}$ in a zero magnetic field was determined to be 1 906 471 870±200 Hz.

Wavelengths of the fine structure transitions $2s{}^2{S}_{1/2}-2p{}^2{P}_{3/2}$ and $2s{}^2{S}_{1/2}-2p{}^2{P}_{1/2}$ in lithiumlike ${\mathrm{Ag}}^{44+}$ have been measured using beam-foil excitation and grazing incidence spectroscopy. The respective transition wavelengths of 40.829±0.004 Å and of 124.685±0.009 Å were not measured before for this ion. The achieved precision of 70 ppm for the 1/2-1/2 transition allows for a 0.2% QED test which sets a new benchmark in the medium Z range. Our experimental uncertainty is smaller than calculated two-photon exchange contributions to the transition energy. A summary of all published experimental data along the isoelectronic sequence for $Z>~$24, including our recent results for ${\mathrm{Ni}}^{25+}$ and ${\mathrm{Zn}}^{27+},$ is presented and compared with the best available calculations.

An ion storage technique, based on the capture of metastable multiply charged ions from an external ion source into a Kingdon ion trap, has been used to measure the lifetimes of eight metastable levels of Mn ions with ${3s}^2{3p}^k$ configurations, $k=1\mathrm{}–4.$ Although several lifetime calculations exist, some of the transition wavelengths have not been previously observed in any source. The lifetimes range from 1.5–35 ms. A measurement precision as good as 0.9% was obtained in favorable cases. The measured lifetimes are $\tau (\mathrm{Mn}\mathrm{}X,\hspace{0.5em}{3s}^2{3p}^4{}^1{S}_0)=2.1\mathrm{}\pm 0.3,$ $\tau (\mathrm{Mn}\mathrm{}X,\hspace{0.5em}{3s}^2{3p}^4{}^1{D}_2)=18.02\mathrm{}\pm 0.16,$ $\tau (\mathrm{Mn}\mathrm{}\mathrm{XI},\hspace{0.5em}{3s}^2{3p}^3{}^2{P}_{3/2})=3.0\mathrm{}\pm 0.2,$ $\tau (\mathrm{Mn}\mathrm{}\mathrm{XI},\hspace{0.5em}{3s}^2{3p}^3{}^2{P}_{1/2})=6.17\mathrm{}\pm 0.29,$ $\tau (\mathrm{Mn}\mathrm{}\mathrm{XI},\hspace{0.5em}{3s}^2{3p}^3{}^2{D}_{3/2})=35.1\mathrm{}\pm 1.43,$ $\tau (\mathrm{Mn}\mathrm{}\mathrm{XII},\hspace{0.5em}{3s}^2{3p}^2{}^1{S}_0)=1.5\mathrm{}\pm 0.2,$ $\tau (\mathrm{Mn}\mathrm{}\mathrm{XII},\hspace{0.5em}{3s}^2{3p}^2{}^1{D}_2)=11.16\mathrm{}\pm 0.10,$ and $\tau (\mathrm{Mn}\mathrm{}\mathrm{XIII},{3s}^{2}3p{}^2{P}_{3/2})=31.32\mathrm{}\pm 1.82\mathrm{ms}.$ These results are compared with the existing theoretical calculations, which have estimated uncertainties no better than 25%.

The Stark widths of the Ne VII $2s3s-2s3p$ singlet and triplet lines are calculated in the impact approximation using quantum-mechanical convergent close-coupling and Coulomb-Born-exchange approximations. It is shown that the contribution from inelastic collisions to the linewidths exceeds the elastic width contribution by about an order of magnitude. Comparison with the linewidths measured in a hot dense plasma of a gas-liner pinch indicates a significant difference which may be naturally explained by nonthermal Doppler effects from persistent implosion velocities or turbulence developed during the pinch implosion. Contributions to the linewidth from different partial waves and types of interactions are discussed as well.

Relativistic configuration interaction (RCI) calculations predict that the ${4d}^7{5s}^{2}2J=9,$ 7, 5 and 3 ${}^{4}F$ levels of ${\mathrm{Ru}}^{-}$ are all bound with binding energies 1.076, 0.905, 0.795, and 0.725 eV, respectively. Using laser photodetachment threshold spectroscopy, the binding energies of the $2J=9$ and $2J=7$ levels are measured to be 1.04638(25) and 0.8653(10) eV, respectively, in good agreement with the calculated values. Hyperfine structure constants for all levels and magnetic dipole decay rates have also been calculated, and a systematic study of the important role of quadruple excitations is presented.

We have recorded angle-resolved He I photoelectron spectra of the three outermost valence states in ${\mathrm{N}}_2^{+},$ with high enough resolution to observe rotational line profiles. For the two $\Sigma$ states, the $X{}^2{\Sigma }_g^{+}$ and the $B{}^2{\Sigma }_u^{+},$ we found that the rotational branches corresponding to different changes in rotational quantum number can differ dramatically in $\beta$ value. The well-known difference in $\beta$ value for the $\nu =0\mathrm{}$ and ν=1 vibrations of the $X{}^2{\Sigma }_g^{+}$ state was found to be due to different rotational branching ratios and also different $\beta$ values of the rotational branches. For the $\nu =0\mathrm{}–2$ vibrations of the $A{}^2{\Pi }_u$ state, the $\beta$ value difference between rotational branches is much less pronounced than in the X and B states. We have also recorded synchrotron-radiation-excited photoelectron spectra of the $\nu =0\mathrm{}$ vibrational peaks of the $X{}^2{\Sigma }_g^{+}$ and $B{}^2{\Sigma }_u^{+}$ states where rotational line profiles are resolved. The intensities of the rotational branches were studied as function of photon energy, the X state between 23 and 65 eV, and the B state between 23 and 45 eV. The results for the X state have recently been presented in a Letter [G. Öhrwall, P. Baltzer, and J. Bozek, Phys. Rev. Lett. 81, 546, 1998]. The rotational branching ratios of the two states have very different behaviors as functions of photon energy. The relative intensities of the rotational branches in the X state change significantly over the studied energy range. The $3{\sigma }_g\to k{\sigma }_u$ shape resonance apparently gives rise to a non-Franck-Condon-like behavior for the rotational branching ratio of the X state. In the B state, the rotational branching ratios remain essentially constant over the studied energy range.

Post and prior forms of the multichannel Schwinger’s principle for rearrangement collisions are presented using discrete basis sets. An application is made to positronium formation in positron-hydrogen collisions at low energies in the range 6.8–30.0 eV. A total number of eight terms of a type of correlated basis functions involving inverse powers of half-odd integers is required to predict accurate results in conformity with the available variational and nonvariational values in the literature. Our findings indicate that destructive interference between partial-wave contributions to the scattering amplitude is responsible for the appearance of critical angles in positronium formation. Surface plots of the differential cross section display immensely rich structure. The total positronium formation cross sections agree nicely with the observed data of Zhou et al. [Phys. Rev. A 55, 361 (1997)] in the entire energy range.