We present a density-matrix functional within the recently introduced framework for tensor-product expansions of the two-particle density matrix. It performs well both for the homogeneous electron gas as well as atoms. For the homogeneous electron gas, it performs significantly better than all previous density-matrix functionals, becoming very accurate for high densities and outperforming the Hartree-Fock method at metallic valence electron densities. For isolated atoms and ions, it is on par with generalized-gradient approximations to the density-functional theory. We also present analytic results for the correlation energy in the low-density limit of the free-electron gas for a broad class of such functionals.

The free induction signals of dense Rb atoms are observed with an injection-seeded power laser diode. The decay rate of signals is found to depend on the number density of Rb atoms, the static magnetic field, the electron spin polarization, and the pulse area of the oscillating magnetic field. We note that the observed broadening of the magnetic resonance line, appearing at high polarization and large pulse area, is the key to understanding the spin dynamics of the precessing atoms which interact with each other. The feature of broadening is quantitatively interpreted by numerically calculating, in a wide range of parameters, the nonlinear Liouville equation that includes the spin-exchange interaction between Rb atoms.

Measurements of positronium formation cross sections for positrons in the energy range down to a few tenths of one electron volt scattered by Li and Na atoms are reported. The reasonable agreement of the measured cross sections for Li with theoretical predictions is in striking contrast to the case for Na where there is a pronounced divergence between calculated and measured values below 1 eV.

It is demonstrated that by taking into account many-electron correlations within the framework of the generalized random-phase approximation with exchange, it becomes possible to describe within the experimental error the recently obtained data [Kjeldson et al. Phys. Rev. A 62, 020702(R) (2000)] on the photoionization of iodine ions ${\mathrm{I}}^{+}$ and ${\mathrm{I}}^{2+}$ near and above the ${4d}^{10}$-subshell threshold. Results are also presented for the single photoionization cross sections of the ${\mathrm{I}}^{+}$ and ${\mathrm{I}}^{2+}$ ions.

Results are presented for $e^{+}$ scattering by ${\mathrm{H}}^{-}$ in the impact energy range $0<~E_0<~10\hspace{0.5em}\mathrm{eV}.$ These include integrated cross sections for Ps formation in the $1s,\hspace{0.5em}2s,$ and $2p$ states, as well as in an aggregate of states with $n>~3,$ and for direct ionization. Differential cross sections for Ps formation in the $1s,\hspace{0.5em}2s,$ and $2p$ states are also exhibited. The calculations are based on a coupled pseudostate approach employing 19 Ps pseudostates centered on the $e^{+}.$ It is found that Ps formation in the $2p$ state dominates that in the $1s$ or $2s$ states below 8 eV, that formation in states with $n>~3$ exceeds the sum of the $n=1\mathrm{}$ and $n=2\mathrm{}$ cross sections above 2.5 eV, and that direct ionization outstrips total Ps formation above 6.3 eV. The threshold law ${(E}_0\to 0)$ for exothermic Ps formation, which includes the cases $\mathrm{Ps}\mathrm{}\left(1s\right),\hspace{0.5em}\mathrm{Ps}\mathrm{}\left(2s\right),$ and $\mathrm{Ps}\mathrm{}\left(2p\right),$ is shown to be ${1/E}_0.$

We report the results of a fully ab initio study of resonant vibrational excitation of ${\mathrm{CO}}_2$ by electron impact via the 3.8 eV ${}^2{A}_1$ shape resonance. First, we solve the fixed-nuclei, electronic scattering problem using the complex Kohn variational method for a variety of symmetric-stretch geometries and for a range of bending angles. We then carry out a three-mode treatment of the nuclear dynamics using a complex local potential or “boomerang” model using resonance parameters derived from our calculated fixed-nuclei cross sections. The results show that a multidimensional treatment of the nuclear motion is essential for a proper description of the vibrational dynamics of ${\mathrm{CO}}_2,$ in particular for describing resonant excitation of the two components of the well-known lowest Fermi dyad.

We report a different type of optical Stern-Gerlach effect, where a magnetic-field gradient is replaced with a light-intensity gradient and a paramagnetic atom is deflected according to its magnetic quantum number. The laser light is detuned between the $D1\mathrm{}$ and $D2\mathrm{}$ frequencies, with the size of the detuning from the $D2\mathrm{}$ resonance being twice that from the $D1\mathrm{}$ resonance, and it is circularly polarized to produce an ac Stark shift that takes the form of a pure Zeeman shift. Slow rubidium atoms are extracted from a magneto-optical trap and then spin polarized. The atoms traversing the laser-intensity gradient on one side of the Gaussian beam profile show deflections that depend on the atomic spin state and the laser polarization. When the laser-beam axis is aligned with the slit that defines the atomic beam, we observe focusing and defocusing of the atomic beam.

We simulate collisions between two atoms, which move in an optical lattice under the dipole-dipole interaction. The model describes simultaneously the two basic dynamical processes, namely the Sisyphus cooling of single atoms, and the light-induced inelastic collisions between them. We consider the $J=1/\overrightarrow{2}J=3/2\mathrm{}$ laser cooling transition for Cs and Na. We find that the hotter atoms in a thermal sample are selectively lost or heated by the collisions, which modifies the steady-state distribution of atomic velocities, reminiscent of the evaporative cooling process.

We present a family of generalized unitary transformations that simplifies the Hamiltonian for a harmonically trapped two-level atom (or ion) interacting with a plane wave laser field. Near-resonant single as well as double vibrational phonon dynamical regimes are found. The validity condition of the often used motional rotating-wave approximation (MRWA) is examined both numerically and analytically. Large errors are found within typical regimes of the MRWA with respect to the motional degrees of freedom. The effects of the MRWA in trapped ion systems are shown to be opposite to that of the rotating-wave approximation in the usual Jaynes-Cummings model. Our study points to a more restrictive condition on the particle localization (Lamb-Dicke) parameter for the validity of the MRWA in the single phonon dynamical regime. It also sheds light on quantum information storage and processing with trapped atoms.

We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation the ground-state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to the density profile to second order in an expansion around the Thomas-Fermi limit. By summing the ladder diagrams, we obtain a modified equation that includes gradient corrections.

We show that, for a continuous-wave input, the error probability, of bit transmission along a third-order nonlinear line with high nonlinearity, might decrease even below its input value. Quantum fluctuations are handled by means of the Wigner function. The resulting evolution equation is exactly solved with the Green-function method, which permits to calculate the density-matrix elements.

We examine the absorption of a weak probe beam by a laser driven V-type atom with a pair of closely lying excited levels, where both the driving and probe lasers interact simultaneously with the two transitions. The effects of quantum interference among decay channels on the absorption spectra are also investigated. We introduce dipole moments in the dressed-state representation and the Hamiltonian in terms of the dressed states describing the interaction between the probe and the atom. In the degenerate case, features similar to that of a driven two-level atomic system are found due to some dark transitions in the spontaneous emission and the fact that the probe beam only detects certain transitions. In the nondegenerate case, the absorption spectrum is strongly influenced by the degree of quantum interference, resulting in different line shapes for emission peaks, absorption peaks, and dispersionlike profiles. The effect of probe polarization on the absorption spectrum is also investigated.

We present a general, semimicroscopic, self-consistent treatment of spontaneous emission for a two-level atom in a dielectric microcavity with arbitrary shape. Both lossless and absorbing media are considered. Our approach is based on linear-response theory and the coupled-dipole method. We illustrate our method on spherical and cubic cavities. We discuss the Purcell effect, the frequency shift, the local-field effect, and the dipole-dipole coupling experienced by a source placed in a microcavity.

We report a quantum eraser experiment which actually uses a Young double slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert, and Walther [Nature (London) 351, 111 (1991)]. One photon of an entangled pair is incident on a Young double slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the interference pattern. To recover interference, we measure the polarization of the other entangled photon. In addition, we perform the experiment under “delayed erasure” circumstances.

The dynamics of an exact two-photon Hamiltonian is used to study the time evolution of an initially disentangled pure state of the atom-field system as it goes through cycles of entanglement separated by instances of disentanglement. For specific initial states of the electromagnetic field, the output state is a pure quantum superposition of a squeezed vacuum state and an orthogonal, odd-photon-number state. The odd-photon-number state, which is not a squeezed state, exhibits both nonclassical sub-Poissonian and classical super-Poissonian photon statistics. In the latter case the quantum superposition resembles a macroscopic superposition state. Conditions are obtained on the atom-cavity interaction time for such states to represent the steady states in the injection in a high-$Q$ cavity of a monoenergetic, low-density beam of three-level atoms in a coherent state.

A general consideration of the phase rotations in a quantum searching algorithm is undertaken in this work. As four phase rotations on the initial state, the marked state, and the states orthogonal to them are taken into account, we deduce a phase-matching condition for a successful search. The optimal options for these phases are then obtained.

Using numerical solutions of the three-dimensional time-dependent Schrödinger equation (TDSE) for the hydrogen atom in an intense, ultrashort, i.e., few-cycle, linearly polarized laser pulse, we demonstrate that ionization yields measured in the forward direction $(0<\theta <15\mathrm{}°)$ depend strongly (by a factor of 2) on the carrier phase, leading to considerable directional (forward or backward) photoelectron asymmetries along the laser polarization vector. This effect vanishes for pulses comprising more than 15 cycles. The phase dependence of photoelectron asymmetry is intensity-dependent: the strongest asymmetry is found in the intermediate multiphoton-tunneling regime, where asymmetry originates from the Coulomb attraction after tunneling. The character of asymmetry drastically changes when an electron ionizes in the barrier-suppression regime. A measurement method of the absolute phase and width, based on this directional effect, is proposed for linearly polarized ultrashort laser pulses pulses.

We report the demonstration of phase coherence and control for the recently developed “light-storage” technique. Specifically, we employ a dynamic form of electromagnetically induced transparency to bring the group velocity of a light pulse to zero, thereby mapping the photonic information into an ensemble spin coherence in warm Rb vapor. We then apply a pulsed magnetic field to vary the phase of the atomic spin excitations and map the altered information back into light. We detect the resultant phase shift in an optical interferometric measurement, thus confirming that the storage process preserves phase coherence.

Weak values as introduced by Aharonov, Albert, and Vaidman (AAV) are ensemble-average values for the results of weak measurements. They are interesting when the ensemble is preselected on a particular initial state and postselected on a particular final measurement result. It is shown that weak values arise naturally in quantum optics, as weak measurements occur whenever an open system is monitored (as by a photodetector). The quantum-trajectory theory is used to derive a generalization of AAV’s formula to include (a) mixed initial conditions, (b) nonunitary evolution, (c) a generalized (nonprojective) final measurement, and (d) a non-back-action-evading weak measurement. This theory is applied to the recent cavity-QED experiment demonstrating wave particle duality [G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000)]. It is shown that the “fractional-order” correlation function measured in that experiment can be recast as a weak value in a form as simple as that introduced by AAV.

All mixed states of two qubits can be brought into normal form by the action of local operations and classical communication operations of the kind ${\rho }^{\prime }=(A\otimes B)\rho (A\otimes {B)}^{†}.$ These normal forms can be obtained by considering a Lorentz singular-value decomposition on a real parametrization of the density matrix. We show that the Lorentz singular values are variationally defined and give rise to entanglement monotones, with as a special case the concurrence. Next a necessary and sufficient criterion is conjectured for a mixed state to be convertible into another specific one with a nonzero probability. Finally the formalism of the Lorentz singular-value decomposition is applied to tripartite pure states of qubits. New proofs are given for the existence of the Greenberger-Horne-Zeilinger (GHZ) class and W class of states, and a rigorous proof for the optimal distillation of a GHZ state is derived.