For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parametrization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parametrization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few-qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight into the possible origin of entanglement for such densities.

We extend previous calculations of many-electron processes in ion-atom collisions to the case of state-selective electron capture by protons from the $K,L,M$ shells in argon at 1–200 keV/amu collision energies. The results are based on a time-dependent density functional theory framework and the basis generator method for the propagation of atomic orbitals. Impact-parameter-dependent probabilities are obtained from a statistical analysis. The results for capture to the $\mathrm{H}\mathrm{}(K,L,M)\mathrm{}$ shells are compared with experiments, and are found to agree with them much better than previous calculations. This serves as an indication that both a proper account of atomic structure and flexibility in the propagation of atomic orbitals are important.

We theoretically investigate collisions between electrostatically trapped cold polar molecules and compare boson and fermion isotopes. Evaporative cooling seems possible for fermion molecules as the ratio of the collision loss cross section to the elastic collision cross section (R) gets smaller as the molecular temperature T lowers. With boson molecules, R gets larger as T lowers, which makes evaporative cooling difficult. The elastic collision cross section between fermion molecules can be larger than that for boson molecules with certain conditions.

We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\Lambda$ shaped and driven at two-photon resonance by a pair of lasers, which cool the center-of-mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb-Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second-order perturbation theory. We find that the spectrum of resonance fluorescence is composed of two narrow sidebands—the Stokes and anti-Stokes components of the scattered light—while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow-type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behavior of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two levels.

The multiphoton strong-field phenomenon of high-energy above-threshold ionization (or high-order ATI) of an isolated atomic system exposed to an intense monochromatic linearly polarized laser field is considered analytically and studied numerically within the framework of an alternative nonrelativistic strong-field approach developed earlier for theoretical treatment of high-order harmonic generation process. The related proposed alternative strong-field ATI model is fully quantum mechanical and mainly based on the Keldysh approximation combined with making use of the essential states method (along with the pole approximation). Applying together these two methods allows for representation of the total ATI amplitude in a closed and compact analytical (the so-called factorized) form quite transparent for interpretation and available for direct numerical calculations. To demonstrate the model applicability, a number of certain photoelectron spectra produced by various atomic species (mostly noble gas atoms and negative ions) have been calculated numerically and shown to reproduce the well-known conventional semiclassical rule for the extent of high-energy plateau and position of its cutoff energy. All the calculated photoelectron spectra as well as the specific details of respective angular distributions (viz., their sidelobes or so-called rings) corresponding to a certain photoelectron peak within a high-energy plateau region (formed primarily by rescattered photoelectrons) demonstrate a very credible behavior within a broad and most interesting region of the problem parameters. Moreover, they all are also in an excellent or fairly good accordance with typical ones measured in standard ATI experiments or calculated by other authors within different (analytically more sophisticated or computationally very demanding) approaches and methods developed earlier.

The autoresonance phenomenon allows excitation of a classical, oscillatory nonlinear system to high energies by using a weak, chirped frequency forcing. Ladder climbing is its counterpart in quantum mechanics. Here, for the first time to our knowledge, conditions for the transition from the quantum to the classical regimes are outlined. The similarities and differences between the two approaches are presented.

Here, I discuss the interaction of two matched ultrashort pulses with a Λ-like system in which the upper intermediate state is replaced by a manifold of discrete states. Many of these states are simultaneously accessed by the broad bandwidth of the two excitation pulses. The equations of motion for the probability amplitudes of the levels involved in the excitation process are solved analytically in the quasi-impulsive regime. In this regime, the excitation pulses are made shorter than the characteristic time of the excited manifold; population is then transferred to the manifold without Rabi cycling. Under the appropriate conditions, this “multi-Λ” system can exhibit coherence effects such as coherent population trapping and electromagnetically induced transparency of one of the excitation pulses.

Two electron interference experiments which are far from each other are considered. They are irradiated with correlated nonclassical electromagnetic fields, produced by the same source. The phase factors are in this case operators, and their expectation values with respect to the density matrix of the electromagnetic field quantify the observed electron fringes. The correlated photons create correlations between the observed electron intensities. Both cases of classically correlated (separable) and quantum mechanically correlated (entangled) electromagnetic fields are considered. It is shown that the induced correlation between the distant electron interferences is sensitive to the nature of the correlation between the irradiating photons.

It has been shown that there exist two inequivalent classes of three-qubit entangled states, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the W class. In this paper, we propose conditional schemes to generate GHZ states and W states of three distant atoms, which are trapped separately in three leaky cavities. More generally, the schemes can be modified to generate any superposition of the Dicke states of three distant atoms. The proposed schemes require linear optical elements and a multifold coincidence detection and are insensitive to the quantum noise. It is briefly pointed out that these schemes can be extended to generate GHZ states and W states of N distant atoms.

We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters, and photodetectors. Our model enables us to simulate a quantum random walk using of the wave nature of classical light fields. Furthermore, the proposed setup allows the analysis of the effects of decoherence. The transition from a pure mean-photon-number distribution to a classical one is studied varying the decoherence parameters.

Angular distribution of the Xe $5p$ photoelectrons was measured in the 100–200-eV photon energy range using linearly polarized synchrotron radiation. The experiment was done out of so-called dipole plane in order to obtain information also about nondipole angular distribution parameters $\gamma$ and $\delta .$ The experimentally determined angular distribution parameters were compared with theoretical values obtained from the recent calculations based on the relativistic random-phase approximation. Experiment shows that both the dipole and nondipole parameters describing the angular distribution vary in accordance with calculations which account for the interchannel coupling. In addition, relativistic effects are visible in angular distribution of the Xe $5p$ spin-orbit components.

Presently available laser sources can yield powers for which the ponderomotive energy $U_p$ of an electron can be equal to or even larger than the rest energy ${\mathrm{mc}}^2$ of an electron. Therefore it has become of interest to consider fundamental radiation-induced or assisted processes in such powerful laser fields. In the present work we consider laser-assisted electron-electron scattering in such a field, assuming that the laser beam has linear polarization. We investigate in detail the angular and polarization dependence of the differential cross sections of the laser-assisted nonlinear processes as a function of the order N of absorbed or emitted laser photons $\omega .$ The present work is a continuation of our previous analysis of Compton scattering and of Mott scattering in a linearly polarized laser field [Phys. Rev. A 65, 022712 (2002); 65, 033408 (2002)].

The entropy-temperature curves are calculated for noninteracting bosons in a three-dimensional (3D) optical lattice and a 2D lattice with transverse harmonic confinement for ranges of depths and filling factors relevant to current experiments. We demonstrate regimes where the atomic sample can be significantly heated or cooled by adiabatically changing the lattice depth. We indicate the critical points for condensation in the presence of a lattice and show that the system can be reversibly condensed by changing the lattice depth. We discuss the effects of interactions on our results and consider nonadiabatic processes.

The dynamical instabilities and ensuing dynamics of singly and doubly quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full three-dimensional numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of Leanhardt et al. [Phys. Rev. Lett. 89, 190403 (2002)].

Beams that experience third-harmonic generation (THG) also experience Kerr effects. With Kerr effects, beams do not take simple Gaussian shapes, but exhibit nonlinear dynamics. These nonlinear dynamics have an effect on the THG accumulated by focusing and then diverging beams. We formulate a self-consistent and complete set of nonlinear Schrödinger equations for a pair of coupled beams—a fundamental and its third-harmonic. Numerical simulations show that the Kerr nonlinearities allow some third harmonic to propagate to the far-field even for zero or negative phase mismatch. This is because the nonlinear dynamics break the beams’ reflection symmetry about the focal plane and therefore increases far-field THG by changing some of the interference from destructive to constructive. THG conversion efficiencies are computed as functions of several beam parameters.

It is shown that any real and even function of the phase (time) operator has a self-adjoint extension and its relation to the general phase operator problem is analyzed.

We propose a scheme for preparing arbitrary two-photons polarization-entangled mixed states via controlled location decoherence. The scheme uses only linear optical devices and single-mode optical fibers, and may be feasible in experiment within current optical technology.

We prove that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory. For a subset of such channels we explicitly identify the optimal signal states. We show analytically that for such a class of channels entangled states are indeed optimal above a given memory threshold.

We propose a class of quantum cryptography protocols that are robust against photon-number-splitting attacks (PNS) in a weak coherent-pulse implementation. We give a quite exhaustive analysis of several eavesdropping attacks on these schemes. The honest parties (Alice and Bob) use present-day technology, in particular an attenuated laser as an approximation of a single-photon source. The idea of the protocols is to exploit the nonorthogonality of quantum states to decrease the information accessible to Eve due to the multiphoton pulses produced by the imperfect source. The distance at which the key distribution becomes insecure due to the PNS attack is significantly increased compared to the existing schemes. We also show that strong-pulse implementations, where a strong pulse is included as a reference, allow for key distribution robust against photon-number-splitting attacks.

We present the general theory of the collinear and noncollinear description for the magnetic effects within the full relativistic density-functional method. As examples for the implementation in a molecular code with numerical basis functions we present results with an even number of electrons $\left({\mathrm{Pt}}_2\right)$ and with an odd number of active electrons (NiAu). The results are promising.