We investigate the propagation dynamics of a two-mode probe field traveling with ultraslow group velocities. We show that a strong cross-beam coupling occurs between the two modes of the probe wave in the presence of a two-mode control laser field that maintains two-photon resonance excitations in a three-level system. In the adiabatic limit and under appropriate conditions, both modes can travel with matched temporal profiles, amplitudes, and greatly reduced group velocities, and one mode can grow and take on features of the other mode. When only one mode of probe field is injected, the generation and growth of the second mode has the characteristics of four-wave mixing, resulting in a tunable, ultraslow four-wave mixing field with nearly 100% photon flux conversion efficiency. We further show a type of induced transparency resulting from an efficient one- and three-photon destructive interference. This is to be contrasted with the conventional one-mode, three-level electromagnetically induced transparency where the interference involves two one-photon pathways.

We study four-wave mixing in a double-$\Lambda$ system, for cw laser beams whose transverse intensity profiles (TIP’s) are initially Gaussian, by solving the Maxwell-Bloch equations numerically. For systems where coherent population trapping (CPT) is initially absent, we show that efficient frequency conversion, without focusing or ring formation, can occur even at distances which are much shorter than those required to establish CPT. We also show, for certain configurations, that blue-detuned beams become focused on propagation so that very high frequency conversion, even exceeding 100% at the center of the profile, can occur. This focusing is, however, accompanied by ring formation. We show that focusing, without ring formation, can occur for identical blue-detuned beams when the initial relative phase is $\pi$ so that CPT cannot be established on propagation. The behavior of the TIP’s of the beams on propagation is explained by considering the effective linear and third-order contributions to the off-diagonal density-matrix elements.

We discuss the impact of a dielectric nanoparticle on the fluorescence light from an emitter embedded in the particle. Numerical and analytical calculations predict a slower radiative decay compared to a bulk dielectric due to electrostatic screening. We assess the relevance of the nanoparticle shape and size and the position and orientation of the molecule. The numerical results are obtained from a rigorous solution of the Maxwell equations, formulated as boundary integral equations.

We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multiparty entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multiparty entanglement, (D) the test whether states are multiparty entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree 3 or less. We then apply very recently established known methods from the theory of semidefinite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of efficiently decidable sufficient criteria for multiparticle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach.

A uniform ground-state three-dimensional Fermi gas with short-range repulsive pairwise interaction is under consideration. Its kinetic and interaction energies are calculated up to the second order of the expansion in the gas parameter. Similar to recent results for an interacting Bose gas, the quantities in question are found to depend on the pairwise interaction through two characteristic lengths: the former, $a$, is the $s$-wave scattering length, and the latter, $b$, is related to $a$ by $b=a-m(\partial a∕\partial m)$, where $m$ stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest “from scratch.” The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.

We use the relativistic Hartree-Fock method, many-body perturbation theory, and configuration-interaction method to calculate the dependence of atomic transition frequencies on the fine-structure constant $\alpha =e^2∕\hslash c$. The results of these calculations will be used in the search for variation of the fine-structure constant in quasar absorption spectra.

The time-dependent characteristic function for the vibrational quanta of two ions separately trapped in two cascaded optical cavities is obtained analytically beyond the bad cavity limit, in which the motional mode of the ion in the first cavity is coupled to the cavity field via an effective parametric interaction and that of the ion in the second cavity via a linear-mixing interaction as proposed by Peng and Parkins [Phys. Rev. A 65, 062323 (2002)]. It is found that the two ions develop in a two-mode mixed Gaussian entangled state if there exists a unidirectional coupling from the first cavity to the second one.

Using a complex model potential, we have calculated the total, integrated elastic, momentum transfer, absorption, and differential cross sections for positrons scattered from molecular hydrogen. The widely available software package GAUSSIAN is used to generate the radial electronic charge density of the molecule which is used to produce the interaction potentials. The quasifree absorption potential, previously developed and used for positron-atom scattering, is extended to positron scattering from molecular targets. It is shown that this model potential approach produces accurate results even into the low-energy regime.

The triple-differential cross section (TDCS) for the photo-double-ionization of Ne and He leading to the ${\mathrm{Ne}}^{2+}\left(2s^{-2}2p^6\right)$ and ${\mathrm{He}}^{2+}\left(1s^{-2}\right)$ states have been measured $20\mathrm{eV}$ above their respective thresholds in equal energy sharing conditions. The experimental results show that the Ne TDCS’s are qualitatively different from the He ones. A calculation using the convergent close coupling method with a He-like final state and different initial-state wave functions clearly shows that the observed differences can be ascribed to an initial-state effect.

Mass analyzed product ions have been detected in coincidence with the projectile following the ionization of water by proton impact. Measurement of the projectile charge state postcollision enables the different ionization processes to be identified: direct ionization, single electron capture, and double electron capture. A complete set of partial and total absolute cross sections is reported for the direct ionization and electron capture processes initiated by proton collisions at 20–150 keV. The cross sections for the direct ionization of ${\mathrm{H}}_2\mathrm{O}$ by proton impact are compared with previous electron impact results [Straub et al., J. Chem. Phys. 108, 109 (1998)].

The dark soliton solution of the Gross-Pitaevskii equation in one dimension has two parameters that do not change the energy of the solution: the global phase of the condensate wave function and the position of the soliton. These degeneracies appear in the Bogoliubov theory as Bogoliubov modes with zero frequencies and zero norms. These “zero modes” cannot be quantized as the usual Bogoliubov quasiparticle harmonic oscillators. They must be treated in a nonperturbative way. In this paper I develop a nonperturbative theory of zero modes. This theory provides a nonperturbative description of quantum phase diffusion and quantum diffusion of soliton position. An initially well localized wave packet for soliton position is predicted to disperse beyond the width of the soliton.

Excitation of an atomic-gas Bose-Einstein condensate (BEC) in the zeroth-order ground-state channel is studied with the hyperspherical adiabatic method of Bohn et al. [Bohn et al., Phys. Rev. A 58, 584 (1998)] suitably generalized to accommodate the anisotropic trapping potential. The method exploits the system’s size as an adiabatic parameter so that the explicit size dependence is immediately conducive to the virial theorem. The oscillation frequencies associated with the monopole (breathing) and quadrupole modes thus emerge naturally and converge to the well-known Thomas-Fermi limits. Analysis of the single-particle density and the projected excitation wave function shows that the excitation in the single hyperspherical ground-state channel merely represents a progressive increase in occupancy of the first excited single-particle state. The work paves the way for applying the adiabatic picture to other BEC phenomena.

The “ghost” interference experiment is analyzed when the source of entangled photons is a multimode optical parametric amplifier (OPA) whose weak limit is the two-photon spontaneous parametric down-conversion beam. The visibility of the double-slit pattern is calculated, taking the finite coincidence time window of the photon counting detectors into account. It is found that the coincidence window and the bandwidth of light reaching the detectors play a crucial role in the loss of visibility on coincidence detection, not only in the ghost interference experiment but in all experiments involving coincidence detection. The differences between the loss of visibility with two-mode and multimode OPA sources are also discussed.

We investigate an efficient scheme for generating ultraviolet single-photons $(\sim 300\mathrm{nm})$. The scheme combines the highly efficient single-photon four-wave mixing scheme and fast developing quantum dot single-photons on demand source technology. We show that near maximum, entanglement between two well matched ultraslowly propagating single-photon wave packets can be achieved. This study may lead to research and development opportunities in highly efficient entanglement schemes using photons of very large frequency difference, quantum information processing, and single-photon metrology and single-photon counting sensors in the uv spectra region.

The theory of a compound, large-angle atom beam splitter [A. Zh. Muradyan, A. A. Poghosyan, and P. R. Berman, Phys. Rev. A 68, 033604 (2003)] is generalized to allow for initial-state deflection. Atoms are prepared in an initial state by an off-resonant standing-wave field and then subject to two-standing-wave fields that couple the initial state to a final state. By a proper choice of parameters, atoms in the initial state can be deflected or split as a result of the interactions with the fields. The role of relaxation is considered.

We consider the problem of the validity of a statistical mechanical description of two-site entanglement in an infinite spin chain described by the $XY$ model Hamiltonian. We show that the two-site entanglement of the state, evolved from the initial equilibrium state, after a change of the magnetic field, does not approach its equilibrium value. This suggests that two-site entanglement, like (single-site) magnetization, is a nonergodic quantity in this model. Moreover, we show that these two nonergodic quantities behave in a complementary way.

A classical and a fully quantum mechanical formalism are introduced for the calculation of the torque experienced by a macro- and a microdipole immersed in an anisotropic homogeneous medium. This is done by obtaining first the frequency shift, and thereby evaluating the change in the energy of the dipoles. It is shown that the shift in energy depends on the orientation of the dipoles and thus introduces a vacuum torque. Although the classical and quantum approaches are different, we attempt to cast the final expressions into a unified form by making the use of a classical Green tensor.

We provide an exact solution of finding the optimum measurement strategy for distinguishing three mixed quantum states with mirror symmetry. The signal states reside in two-dimensional Hilbert space. By mirror symmetry, two of the three states have the same prior probabilities and transform into each other under the mirror symmetry. We find that the optimum measurement strategy may consist of three, two, or a single nonzero probability operator measure elements depending upon the prior probabilities of the quantum signals.

By splitting the Coulomb interaction into long-range and short-range components, we decompose the energy of a quantum electronic system into long-range and short-range contributions. We show that the long-range part of the energy can be efficiently calculated by traditional wave function methods, while the short-range part can be handled by a density functional. The analysis of this functional with respect to the range of the associated interaction reveals that, in the limit of a very short-range interaction, the short-range exchange-correlation energy can be expressed as a simple local functional of the on-top pair density and its first derivatives. This provides an explanation for the accuracy of the local density approximation (LDA) for the short-range functional. Moreover, this analysis leads also to new simple approximations for the short-range exchange and correlation energies improving the LDA.