The theory for temporally multidimensional, electronically resonant four-wave-mixing (FWM) spectroscopy based on broadband light interferometry is developed. Both homodyne and heterodyne detection are considered. Upon spectrally resolving the signal, the electronic Bohr frequency is seen to be extremely down-converted, even to zero frequency, but only with homodyne detection. These very low frequency fringes, referred to as radiation difference oscillations, are well known in the interferometric coherent Raman broadband light spectroscopies. Such low frequency fringes permit interferometry in the optical region using Nyquist criteria corresponding to far infrared sampling rates. Possible applications are illustrated by simulations of the two-dimensional third order signals from an electronic two-level system in a variety of “baths.” It is seen how homogeneous and inhomogeneous line-shaping mechanisms manifest themselves differently and revealingly in the free induction decay, the photon echo decay and their cross term components of the FWM signal.

In 1981, Agarwal proposed a Wigner quasiprobability distribution function on the group SU(2) that serves to analyze two-particle spin states on a sphere. Recent work by our group has included the definition of an apparently distinct Wigner function on generic Lie groups whose natural range has the dimension of the group and serves for all square-integrable representations; for the SO(3) case this entails a three-dimensional “meta-phase” space. Both have the fundamental properties covariance and completeness. Here we show how the former is obtained as a restriction of the latter.

Teleportation may be interpreted as sending and extracting quantum information through quantum channels. In this report, it is shown that to get the maximal probability of exact teleportation through a partially entangled quantum channel, the sender (Alice) need only operate a measurement that satisfies an “entanglement matching” to this channel. An optimal strategy is also provided for the receiver (Bob) to extract the quantum information by adopting a general evolution.

Valence shell relativistic configuration interaction calculations yield 15 bound states for ${\mathrm{Ce}}^{-}.$ These include eight $6p$ attachments calculated with respect to the ${4f5d6s}^2\hspace{0.5em}J=4\mathrm{}$ ground state with the following electron affinities (in meV with corresponding J in parentheses): 349 (9/2), 215 (7/2), 203 (5/2), 153 (7/2), 135 (3/2), 117 (11/2), 104 (9/2), and 53 (7/2). The remaining seven bound states are $5d$ attachments, treated as $6s$ attachments with respect to the excited ${4f5d}^{2}6sJ=8$ threshold, with the following electron affinities: 428 (7/2), 327 (9/2), 281 (9/2), 193 (11/2), 182 (7/2), 167 (9/2), and 149 (11/2). Core-valence effects were found to be minimal, and improvements with respect to our earlier work [K. Dinov, D. R. Beck, and D. Datta, Phys. Rev. A 50, 1144 (1994)] have been ascribed to better treatment of second order effects (in the case of the $6p$ attachments) and a more appropriate choice of neutral threshold (in the case of the $5d$ attachments).

The binary-encounter dipole (BED) model for electron-impact ionization is applied to helium using the continuum dipole oscillator strength calculated from the relativistic random-phase approximation. The resulting total ionization cross section agrees with available experimental data well within the quoted experimental uncertainties. The singly differential $(=\mathrm{energy}$ distribution of ejected electrons) cross section agrees well in shape with available experiments. Because of the remarkable agreement with experiment at all incident and ejected electron energies and the compact analytic form of the cross sections, we propose that the BED cross sections for helium serve as a normalization standard with an accuracy of ±5% from the threshold to 1 keV in the primary electron energy.

Using a high-efficiency, transmission grating spectrometer the ${3s}^2{3p}^6{3d}^4$ $J=2\mathrm{}–3$ ground-state transition was measured in Ti-like ${\mathrm{W}}^{52+}.$ The measurement has achieved 20 times better precision than the only previously reported high-$Z$ measurement. As such, it tests recent structure calculations for complex highly charged ions. Discrepancies of around $100\hspace{0.5em}\AA$ are found. This is true even for semi-empirical calculations. The measurement, however, validates a very recent calculation with which agreement is within $2\hspace{0.5em}\AA .$

The triple-photoionization cross section of atomic Li was measured near its threshold. Our results can be described by a threshold power law up to $\approx 5\hspace{0.5em}\mathrm{eV}$ with an exponent of 2.05(25) which is consistent with a previous experiment and theoretical predictions. At higher energies, we find that the cross section is well described by the threshold law for double ionization. The present analysis is based on the notion that for sufficient excess energy, triple photoionization of Li is reasonably well described by a double ionization of the inner electrons followed by a shakeoff of the outer electron.

Highly regular spatiotemporal or multidimensional patterns in the quantum mechanical probability or classical field intensity distributions can appear due to pair interference between individual eigenmodes of the system, thus forming the so-called intermode traces. These patterns are strongly pronounced in any anharmonic potential, provided that the traces are multidegenerate; they may occur in many areas of wave physics.

We propose an experiment where quantum interference between two different paths is modulated by means of a quantum nondemolition (QND) measurement on one or both the arms of an interferometer. The QND measurement is achieved in a Kerr cell. We illustrate a scheme for the realization of this experiment, and discuss some further developments.

A compact derivation is given for propagators of a wide class of time-dependent Hamiltonians that describe coupled spin (“qubit”) pairs. As many as eight of the 16 operators in the system, each with its own time-dependent coefficient, can be handled with no more difficulty than a single spin in a magnetic field. A single first-order (in time), quadratically nonlinear differential equation for a classical function is the only nontrivial ingredient in constructing the full quantum propagator for a wide variety of magnetic coherences and qubit interactions.

We show that the recently proposed scheme of teleportation of continuous variables [S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)] can be improved by a conditional measurement of the entangled state shared by the sender and the recipient. The conditional measurement subtracts photons from the original entangled two-mode squeezed vacuum, by transmitting each mode through a low-reflectivity beam splitter and performing a joint photon-number measurement on the reflected beams. In this way the degree of entanglement of the shared state is increased and so is the fidelity of the teleported state.

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d},$ where d is the dimension of the search space, whereas any classical algorithm necessarily scales as $O\left(d\right).$ It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting one quantum search within another. The average number of iterations required to find the solution of a typical hard instance of a constraint satisfaction problem is found to scale as $\sqrt{d^{\alpha }},$ with the constant $\alpha <1\mathrm{}$ depending on the nesting depth and the type of problem considered. This corresponds to a square-root speedup over a classical nested search algorithm, of which our algorithm is the quantum counterpart. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, $\alpha$ is estimated to be around 0.62.

We present a way of using numerical quadrature in momentum space for solving the three-dimensional Lippmann-Schwinger equation. The integration is performed in spherical coordinates. Test calculations show that the quadrature is well suited for the electron-molecule scattering problems. Sample results of elastic scattering of electrons are presented for the empirical Yukawa potential and ab initio Hartree-Fock potential of the hydrogen and methane molecules.

We show that for a superposition of Yukawa potentials, the exact left-hand cut discontinuity in the complex-energy plane of the (S-wave) scattering amplitude is given, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. With the discontinuity on the left-hand axis elucidated, we can construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The DR is numerically verified for the exponential potential at zero scattering energy. Generalization to higher partial waves, and extension of these ideas to field theory are discussed.

Electron capture cross sections for ${\mathrm{B}}^{4+}+\mathrm{H}$ collisions are calculated using a two-center atomic orbital close coupling expansion method. Total electron capture cross sections are shown to compare well with the recent experimental data of Pieksma et al. [Phys. Rev. A 57, 1892 (1998)] and with the molecular expansion calculation of Shimakura et al. [Phys. Rev. A 47, 3930 (1993)], but not with the molecular calculation of Fraija et al. [Phys. Rev. A 49, 272 (1994)]. Subshell electron capture cross sections are also compared.

Although perturbation theory applied to the optical response of a molecule or material system is only strictly valid far from resonances, it is often applied to “near-resonance” conditions by means of complex energies incorporating damping. Inconsistent signs of the damping in optical response tensors have appeared in the recent literature, as have errors in the treatment of the perturbation by a static field. The “equal-sign” convention used in a recent publication yields an unphysical material response, and Koroteev’s intimation that linear electro-optical circular dichroism may exist in an optically active liquid under resonance conditions is also flawed. We show that the isotropic part of the Pockels tensor vanishes.

We have computed the ground-state energies of the lithium and beryllium atoms using the Feynman-Kac path-integral method and high-quality trial wave functions. Our results are in excellent agreement with the best nonrelativistic values for these systems.

We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by direct numerical solution of the Gross-Pitaevskii-equation.

We present experimental results that show how the height of the turn-on peak of a class-B laser can be controlled by an appropriate modulation of the shape of the turn-on pulse. At the same time, the turn-on delay is reduced and continues to decrease even after a minimum peak height has been reached and starts to grow again. A physical interpretation is offered on the basis of an approximate analysis of turn-on in a class-B laser, and of numerical simulations, which very clearly illustrate the mechanisms that play a crucial role in the laser transient.

We introduce a family of bound-entangled quantum states in $3\times 3$ dimensions. Their density matrix $\rho$ depends on seven independent parameters and has four different nonvanishing eigenvalues.