We study a set of L spatial bosonic modes localized on a graph $\Gamma .$ The particles are allowed to tunnel from vertex to vertex by hopping along the edges of $\Gamma .$ We analyze how, in the exact many-body eigenstates of the system, i.e., Bose-Einstein condensates over single-particle eigenfunctions, the bipartite quantum entanglement of a graph vertex with respect to the rest of the graph depends on the topology of $\Gamma .$

We have recalculated the photodissociation cross section of NaH as a function of photon wavelength for the $X{}^1\overrightarrow{\sum }B{}^1\Pi$ transition using the time-independent Fermi golden rule. We have made an attempt to clarify the discrepancy between a recent calculation where the time-dependent autocorrelation function was employed and an earlier one where the Fermi golden rule was used.

State engineering in nonlinear quantum dynamics sometimes may demand driving the system through a sequence of dynamically unstable intermediate states. This very general scenario is especially relevant to the dilute Bose-Einstein condensates, for which ambitious control schemes have been based on the powerful Gross-Pitaevskii mean-field theory. Since this theory breaks down on logarithmically short time scales in the presence of dynamical instabilities, an interval of instabilities introduces quantum corrections, which may possibly derail a control scheme. To provide a widely applicable theory for such quantum corrections, this paper solves a general problem of time-dependent quantum-mechanical dynamical instability, by modeling it as a second-quantized analog of a Landau-Zener avoided crossing: a “twisted crossing.”

Entanglement sharing among sites of one-particle states is considered using the measure of concurrence. These are the simplest in a hierarchy of number-specific states of many qubits and correspond to “one-magnon” states of spins. We study the effects of onsite potentials that are both integrable and nonintegrable. In the integrable case, we point to a metal-insulator transition that reflects on the way entanglement is shared. In the nonintegrable case, the average entanglement content increases and saturates along with a transition to classical chaos. Such quantum chaotic states are shown to have universal concurrence distributions that are modified Bessel functions derivable within random matrix theory. Time-reversal breaking and time-evolving states are shown to possess significantly higher entanglement sharing capacity than eigenstates of time-reversal symmetric systems. We use the ordinary Harper and the kicked Harper Hamiltonians as model systems.

Recent numerical work indicates that the classical motion of positronium in a constant magnetic field does not exhibit chaotic behavior if the system is confined to two dimensions. One would therefore expect this system to possess a second constant of the motion in addition to the total energy. In this paper we construct a generalization of the Laplace-Runge-Lenz vector and show that a component of this vector is a constant of the motion.

We develop further a new method for employing a set of real basis functions to represent the Green function at energies in the continuum, without regard for the asymptotic boundary conditions. The method is based on the analyticity of the Green function with respect to its underlying time scale. The diagonalization of large matrices is unnecessary. Although a large complex symmetric linear system of equations must be solved, this can be done with high stability and efficiency by using a generalization of the Cholesky decomposition of real positive definite symmetric matrices. We present results of test applications to ${}^1$S-wave electron scattering from a hydrogen atom and photodetachment of the negative hydrogen ion. The extension from two- to three-body collisions entails the use of projection operators to distinguish different groups of asymptotic channels.

Fundamental phase-shift detection properties of optical multimode interferometers are analyzed. Limits on perfectly distinguishable phase shifts are derived for general quantum states of a given average energy. These bounds are found to be independent of the number of interfering modes, and are consistent with the Heisenberg limit. A short discussion on the concept of well-defined relative phase is also included.

We describe an error-reconciliation protocol, which we call Winnow, based on the exchange of parity and Hamming’s “syndrome” for N-bit subunits of a large dataset. The Winnow protocol was developed in the context of quantum-key distribution and offers significant advantages and net higher efficiency compared to other widely used protocols within the quantum cryptography community. A detailed mathematical analysis of the Winnow protocol is presented in the context of practical implementations of quantum-key distribution; in particular, the information overhead required for secure implementation is one of the most important criteria in the evaluation of a particular error-reconciliation protocol. The increase in efficiency for the Winnow protocol is largely due to the reduction in authenticated public communication required for its implementation.

The Auger cascade processes following the Kr ${3d}_{5/2}\to 5p$ and Xe ${4d}_{5/2}\to 6p$ excitations have been studied both theoretically and experimentally. Experimental spectra have been measured with high photon and electron energy resolutions and the results have been compared with theoretical predictions obtained by multiconfiguration Dirac-Fock (MCDF) method. The MCDF approach is able to reproduce well the cascade process of Kr, but strong discrepancies are observed in the case of Xe. Some possible reasons for that are discussed.

A time-domain atomic multiple-wave interferometer using laser-cooled and trapped sodium atoms has been developed under pulsed magnetic fields. Each atomic phase was shifted due to the scalar Aharonov-Bohm effect by applying spatially homogeneous pulsed magnetic fields between numerous Raman excitation laser pulses. Interference fringes with a finesse of 11 were demonstrated for 11 successive Raman pulses and ten magnetic-field pulses.

We demonstrate two ways of obtaining subnatural linewidth for probe absorption through room-temperature Rb vapor. Both techniques use a control laser that drives the transition from a different ground state. The coherent drive splits the excited state into two dressed states (Autler-Townes doublet), which have asymmetric linewidths when the control laser is detuned from resonance. In the first technique, the laser has a large detuning of 1.18 GHz to reduce the linewidth to 5.1 MHz from the Doppler width of 560 MHz. In the second technique, we use a counterpropagating pump beam to eliminate the first-order Doppler effect. The unperturbed probe linewidth is about 13 MHz, which is reduced below 3 MHz $\left(0.5\mathrm{}\Gamma \right)$ at a detuning of 11.5 MHz.

The loss of ultracold trapped atoms in the vicinity of a Feshbach resonance is treated as a two-stage reaction, using the Breit-Wigner theory. The first stage is the formation of a resonant diatomic molecule, and the second one is its deactivation by inelastic collisions with other atoms. This model is applied to the analysis of recent experiments on ${}^{87}\mathrm{Rb},$ leading to an estimated value of $7\times {10}^{-11}{\mathrm{cm}}^3/\mathrm{s}$ for the deactivation rate coefficient.

We propose a cavity-based laser-cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave that acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate traveling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high-frequency component, which is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering.

Through the control of laser energy and chirp, continuous wavelength tuning of high-order harmonics was achieved without sacrificing spectral sharpness. This process was implemented after the amplification stage in a chirped-pulse amplification Ti:sapphire laser, without changing laser spectrum. It opens a new pathway for the realization of a continuously tunable, coherent, femtosecond x-ray source, i.e., a tabletop synchrotron.

In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP), it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor [e-print quant-ph/0201008] showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. Assuming that the dimension of subsystems in the prior-entangled state is the same as the dimension of the input space, we study similar RSP protocols, but not necessarily oblivious to Bob. We show that in this case Bob’s quantum operation can be safely assumed to be a unitary transformation. We then derive an equation that is a necessary and sufficient condition for such a protocol to exist. By studying this equation, we show that one-qubit RSP requires two classical bits of communication, which is the same amount as in teleportation, even if the protocol is not assumed oblivious to Bob. For higher dimensions, it is still an open question whether the amount of classical communication can be reduced by abandoning oblivious conditions.

We discuss the theory and computation of the lowest three, $n=3\mathrm{}$ intrashell triply excited resonance states of ${\mathrm{He}}^{-}$ of Li, and of positive ions of the sequence, up to ${\mathrm{N}}^{4+}.$ These are the ${3s}^{2}3p{}^2{P}^o,$ ${3s3p}^2{}^{4}P,$ and ${3s3p}^2{}^{2}D$ states, for which wave function characteristics, energies, and widths are reported. Contrary to recently published results for ${\mathrm{He}}^{-}$ and to earlier ones for ${\mathrm{N}}^{4+},$ we found that electron correlation and orthogonality to lower states are such that they make the ${}^2{P}^o$ state the lowest $n=3\mathrm{}$ triply excited state (TES), as is the case with the $n=2\mathrm{}$ shell. Our predictions for these states of ${\mathrm{He}}^{-}$ are in harmony with the measurements of Roy [Phys. Rev. Lett. 38, 1062 (1977)], which were interpreted only recently [C. A. Nicolaides and N. A. Piangos, J. Phys. B 34, 99 (2001)]. In addition, our value for the position of the Li ${3s}^{2}3p{}^2{P}^o$ TES, 175.15 eV, agrees with the measurement $(175.165\mathrm{}\pm 0.050\mathrm{eV})$ of Diehl et al. [Phys. Rev. A 56, R1071 (1997)]. Apart from specifics, the paper discusses or points to certain basic aspects of computational quantum mechanics of such multiply excited states. For example, it refers to the utility of open-channel-like configurations toward proper convergence to a local energy minimum in the continuous spectrum, where quasibound and unbound states of the same symmetry lie below, and for which the normal eigenvalue properties of the discrete spectrum do not apply. Also, we discuss the possibility that is given by the state-specific theory for carrying out economic and physically transparent calculations and for deducing semiquantitative conclusions about the interplay between electronic structure, interference, and autoionization widths.

By using a magneto-optical trap we have measured the Rb $ns-(n+1\mathrm{})s$ and ${\mathrm{nd}}_j{-(n+1\mathrm{})d}_j$ two-photon millimeter-wave transitions for $32<~n<~37,$ observing 100-kHz-wide resonances, in spite of the trap’s 10 G/cm magnetic-field gradient, in which one might expect to observe resonances 5 MHz wide. This resolution is possible because of the similarity of the $g_j$ factors in the initial and final states. Under the same conditions, the single-photon ns-np resonances are ∼5 MHz wide. To make useful measurements of these intervals, we turned off the trap field and used the 300-K atoms of the background Rb vapor. Together these measurements improve the accuracy of the s, p, and d quantum defects by an order of magnitude.

We have measured the absolute energy-averaged cross section for electron-impact excitation of ${\mathrm{Si}}^{2+}(3s3p{}^3{P}^o\to 3s3p{}^1{P}^o)$ from energies below threshold to the turn-on of the $3s3p{}^3{P}^o\to {3p}^2{}^{3}P$ transition. A beams modulation technique with inclined electron and ion beams was used. Radiation at 120.65 nm from the decay of the excited ions to the ${3s}^2{}^{1}S$ ground state was detected using an absolutely calibrated optical system. The fractional population of metastable ${\mathrm{Si}}^{2+}\left(3s3p{}^3{P}^o\right)$ in the incident ion beam was determined to be $0.256\pm 0.035(1.65\sigma ).\mathrm{}$ The experimental energy spread ranged from 0.85 eV (full width at half maximum) at the lowest energies to 0.56 eV at the highest. Resonance features consistent with 12-state close-coupling R-matrix calculations are seen.

We report on energy loss measurements and charge state distributions for 60 keV ${\mathrm{N}}^{6+}$ and 75 keV ${\mathrm{N}}^{5+}$ ions scattered off a $\mathrm{Pt}\mathrm{}\left(110\right)(1\mathrm{}\times 2)$ single crystal surface. In particular, the influence of surface steps on the energy loss and the outgoing charge states is discussed. The scattering angle and the angle of incidence are varied. We use grazing incidence conditions, i.e., the momentum perpendicular to the surface is low enough to prevent penetration through the first atomic layer. Image charge effects are observed leading to an additional projectile acceleration towards the surface. Outgoing charge states are detected from $1+$ up to $3+.$ Axial channeling conditions are defined by scattering along the azimuthal [001] direction, i.e., the projectiles are guided along the [001]-atomic rows. The energy loss for axial channeling is found to be somewhat larger and the energy distribution to be broadened in comparison with the spectra for planar channeling conditions. The broadening is attributed to the interaction of the projectiles with the side wall potentials of the surface channels. We find a strong increase in the energy loss with increasing scattering angle, which exceeds the calculated contribution of the elastic energy transfer by orders of magnitudes. These increased energy losses are attributed to the interaction of the ions with the surface steps.