Starting from the Gross-Pitaevskii nonlinear Schrödinger equation, we derive a set of nonlinear coupled equations describing four-wave mixing with matter waves and solve them analytically without utilizing the undepleted pump approximation.

It was recently shown that nonseparable density operators on the Hilbert space ${\mathcal{H}}_1\otimes {\mathcal{H}}_2$ are trace norm dense if either factor space has infinite dimension. We show here that nonlocal states, i.e., states whose correlations cannot be reproduced by any local hidden variable model, are also dense. Our constructions distinguish between the case $\dim {\mathcal{H}}_1=\dim {\mathcal{H}}_2=\infty ,$ where we show that states violating the Clauser-Horne-Shimony-Holt (CHSH) inequality are dense, and the case $\dim {\mathcal{H}}_1<\dim {\mathcal{H}}_2=\infty ,$ where we identify open neighborhoods of nonseparable states that do not violate the CHSH inequality but show that states with a subtler form of nonlocality (often called “hidden” nonlocality) remain dense.

The problem of the experimental determination of the amount of entanglement of a bipartite pure state is addressed. We show that measuring a single observable does not suffice to determine the entanglement of a given unknown pure state of two particles. Possible minimal local measuring strategies are discussed, and a comparison is made on the basis of their best achievable precision.

We study the experimental realization of quantum teleportation as performed by Bouwmeester et al. [Nature (London) 390, 575 (1997)] and the adjustments to it suggested by Braunstein and Kimble [Nature (London) 394, 841 (1998)]. These suggestions include the employment of a detector cascade and a relative slow-down of one of the two down-converters. We show that coincidences between photon pairs from parametric down-conversion automatically probe the non-Poissonian structure of these sources. Furthermore, we find that detector cascading is of limited use, and that modifying the relative strengths of the down-conversion efficiencies will increase the time of the experiment to the order of weeks. Our analysis therefore points to the benefits of single-photon detectors in non post selected-type experiments, a technology currently requiring roughly 6 °K operating conditions.

The resonant photon emission following the excitation of a highly symmetric system to core-excited electronic states is discussed within a time-dependent formulation. Two types of vibrational modes—localizing modes and symmetry breaking but nonlocalizing modes—are considered, named according to their impact on dynamical symmetry breaking and localization accompanying the process. The decay rates are proportional to the population of a coherent superposition of the relevant core states vibronically coupled via the appropriate vibrational modes. This population is essentially a product of partial contributions of the two types of vibrational modes mentioned above. The general arguments are illustrated on the ${\mathrm{CO}}_2$ molecule. Here, the bending mode is the symmetry breaking but nonlocalizing mode and the asymmetric stretching mode is the localizing mode. The decay rates and total resonant photon emission intensities are calculated in the leading terms approximation of the potential matrix Hamiltonian. The impact of the asymmetric mode on localization and hence on the optical selection rules as a function of time is discussed in detail. It is shown that the vibronic coupling via the bending mode changes the polarization of the emitted light and exerts an impact on the effect of vibronic coupling via the asymmetric stretching mode.

We argue that quantum electrodynamics dictates resonance phenomena in multiphoton processes as the laser intensity varies. A perturbation theory is developed in which the coupling between an electron and the second quantized laser mode is treated nonperturbatively. As an example, we predict that the above-threshold ionization rate can exhibit resonance at intensities with integer ponderomotive parameter. Such quantum effects may be exploited to calibrate laser intensities.

The theory of an interferometric six-wave mixing quasiecho signal from a modeled molecular liquid using broadband (“noisy”) light is reported. The line-shaping function is treated by a standard mixture of a dynamic (homogeneous) dephasing process and a static (inhomogeneous) Bohr frequency distribution. Simulations are presented in either limit of the overall process to demonstrate the rephasing aspects of this nonlinear spectroscopy. The general aspects of the two-dimensional signal are inferred from factorized time correlator (FTC) diagrams. These diagrams pictorially represent the correlation functions of the random noise (associated with the broadband light) that arise upon stochastic averaging at the signal level. The entire set of FTC diagrams is seen to be isomorphic with those that describe a nonecho interferometric noisy light spectroscopy at fifth order, and the third-order electronically resonant four-wave mixing. Similarities between these three very different processes are discussed in terms of this one-to-one correspondence.

We show that on exceeding a certain degree of mixedness (as quantified by the von Neumann entropy), entangled states become useless for teleportation. By increasing the dimension of the entangled systems, this entropy threshold can be made arbitrarily close to maximal. This entropy is found to exceed the entropy threshold sufficient to ensure the failure of dense coding.

We introduce the notion of a Schmidt number of a bipartite density matrix. We show that k-positive maps witness the Schmidt number, in the same way that positive maps witness entanglement. We determine the Schmidt number of the family of states that is made from mixing the completely mixed state and a maximally entangled state. We show that the Schmidt number does not necessarily increase when taking tensor copies of a density matrix $\rho ;$ we give an example of a density matrix for which the Schmidt numbers of $\rho$ and $\rho \otimes \rho$ are both $2.$

A fully nonadiabatic calculation gives $3.178303\times 4\pi {\epsilon }_0{a}_0^3$ for the electric dipole polarizability of the $v=0,$$N=1\mathrm{}$ vibration-rotation level of the ground electronic state of ${\mathrm{H}}_2^{+}.$ This is in agreement with the experimental value of Sturrus et al. [Phys. Rev. A 44, 3032 (1991)]. The importance of nonadiabatic effects is discussed.

Elastic and spin-changing inelastic collision cross sections between oxygen molecules and helium atoms are computed in the energy range 0.1–10 K. This study explores the recently demonstrated buffer-gas cooling process that produces magnetically trapped, translationally cold molecules. Conclusions are drawn about the favorable prospects of cooling oxygen molecules, and about the general feasibility of this cooling technique.

We present two procedures for the calculation of ionization rates of multielectron atoms. The validity of the procedures is established by comparison with exact field ionization rates of helium. Better than 85% accuracy at field strengths of up to 1 a.u. is obtained with a frozen core model, when the exact field-free ground state is included. A Hartree-Fock calculation gives above-barrier ionization rates that are accurate to 75% or better.

The application of coherent control to modify the real and imaginary parts of the refractive index n of a material is described. Parameters to control the refractive index, and to minimize absorption, are identified. An application to gaseous ${\mathrm{N}}_2$ shows that extensive control over n is possible.

We consider a more correct treatment of photon scattering from randomly oriented atoms, going beyond the level of description used in currently available results. We focus on cross sections which include an elastic scattering component. The most sophisticated results available to describe high-energy elastic scattering are relativistic coherent elastic S-matrix calculations within independent-particle approximation, which, however, perform an averaging over magnetic substates at the level of the amplitude (averaged-amplitude approach), exact only for fully filled subshells. The present S-matrix calculations also do not consider incoherent elastic scattering (in which an electron makes a transition to a different magnetic substate in the same subshell), which can occur when there are partially filled subshells. A more proper treatment of these situations involves an averaging over the cross sections for all possible orientations of the target. Here we consider the total elastic scattering (both coherent and incoherent), and we also include the unresolved contributions of inelastic (Raman and Compton) scattering. In particular we consider inelastic Raman scattering between relativistic subshells that are nearly energy degenerate, which may not be resolved, given finite experimental resolution, and which may be degenerate in nonrelativistic theory (e.g., Coulombic ${2p}_{1/2}$ and ${2p}_{3/2}$ subshells). Thus, for example, the nonrelativistic result for elastic scattering (coherent and incoherent) from excited hydrogen in the $2p$ state corresponds to the result obtained by summing relativistic elastic scattering (coherent and incoherent) together with the relativistic inelastic scattering for transitions between the ${2p}_{1/2}$ and ${2p}_{3/2}$ subshells. The averaged-amplitude approach does poorly in this case. However, results for scattering from ground-state boron indicate that the averaged-amplitude approach generally works well for many-electron ground-state atoms, due to the large coherent contribution from electrons in fully filled subshells.

A procedure is described by which the response of a two-center system to a perturbation can be expressed in terms of single-center wave functions. We use the formulation to evaluate the asymptotic long-range part of the Pauli-Dirac relativistic interaction between two ground-state hydrogen atoms and compare with the results of ab initio calculations.

We investigate the coupled dynamics of N two-level atoms in the field of a weakly pumped multimode high-Q cavity. While the field mode amplitudes are coupled by the atoms depending on their positions, the motion of the atoms is influenced by the radiation pressure and dipole force induced by the total intracavity field. In the strong coupling regime, where the atom field coupling g dominates the atomic and cavity decay rates (Γ, κ) strong correlations between the atoms themselves and between the atoms and the light field build up. For suitable operating conditions an efficient motional cooling of the atoms occurs. At the example of two atoms coupled to two counterpropagating modes in a ring cavity, we show that this can lead to a strong binding force between atoms trapped at a large distance at different antinodes of the cavity field.

The ground-state properties of interacting Bose gases in external potentials, as considered in recent experiments, are usually described by means of the Gross-Pitaevskii energy functional. We present here a rigorous proof of the asymptotic exactness of this approximation for the ground-state energy and particle density of a dilute Bose gas with a positive interaction.

A scheme to achieve dense quantum coding for the quadrature amplitudes of the electromagnetic field is presented. The protocol utilizes shared entanglement provided by nondegenerate parametric down-conversion in the limit of large gain to attain high efficiency. For a constraint in the mean number of photons $\mathrm{n̄}$ associated with modulation in the signal channel, the channel capacity for dense coding is found to be $\ln (1+\mathrm{n̄}+n^2),$ which always beats coherent-state communication and surpasses squeezed-state communication for $\mathrm{n̄}>1.\mathrm{}$ For $\mathrm{n̄}\gg 1,$ the dense coding capacity approaches twice that of either scheme.

Photoionization of hydrogen by periodic but strongly modulated anharmonic laser fields is investigated. Above-threshold ionization spectra are calculated by numerically solving the time-dependent Schrödinger equation in the Kramers-Henneberger frame by the split-operator method. Effects of amplitude and phase modulations of the laser field are examined by comparing the energy spectra of harmonic and anharmonic laser fields at the same cycle-averaged laser intensity. It is found that amplitude modulations with high peak intensities yield enhanced electron energies, and show substructures of the spectra due to atomic excitations. The energy spectra are found to be relatively insensitive to phase modulations at harmonic frequencies, but show an additional peak sequence for subharmonic modulations at half of the laser frequency. Possible applications to experiments with attosecond laser pulses are indicated.

We have studied in detail the spatial coherence of the far field of the 13th harmonic from a Ti:sapphire laser generated in xenon, as a function of the generation parameters. Experimentally, we use Fresnel mirrors to produce two-dimensional interferograms. This technique allows us to probe the coherence at different scales $d=1\mathrm{}–3\mathrm{mm}$ between the interfering rays, i.e., throughout the full section of the incident beam. A high uniform degree of mutual coherence ${\gamma }_d,$ larger than 0.5 in most cases, is measured as a function of the position of the jet relative to the focus, and pressure in the jet. It confirms the high intrinsic spatial coherence already reported for the extreme-ultraviolet harmonics, which is much larger than the one produced from x-ray lasers. Spatial coherence decreases when the laser focus is moved toward the jet, and when the pressure is increased: the onset of ionization, as well as the intensity-dependent phase of the nonlinear polarization, are rapidly varying factors in time and space which degrade the correlation between the fields at two different points. Simulation of the coherence degree emphasizes the role of the intensity-dependent phase in the evolution of the coherence degree.