The photodissociation cross section of $\mathrm{Na}\left(3d{}^2\mathrm{D}\right)+\mathrm{Na}\left(3s{}^2\mathrm{S}\right)$ atoms from the ${\mathrm{Na}}_2$ $3{}^3{\Pi }_{0\mathrm{g}}$ state was measured as a function of photoexcitation energy. The dissociation was identified as predissociation induced by the electronic coupling of the $3{}^3{\Pi }_{0\mathrm{g}}$ bound state with the $2{}^3{\Pi }_{0\mathrm{g}}$ continuum above its dissociation limit. Observed asymmetrical resonance line shapes in the cross section were analyzed by solving numerically two-channel coupled equations, and the calculated results were in good agreement with the observed results. The strength and shape of the resonance lines are determined by the magnitude and phase of vibrational wave functions of the discrete $3{}^3{\Pi }_{0\mathrm{g}}$ and continuum $2{}^3{\Pi }_{0\mathrm{g}}$ states. The resonance width is determined by the magnitude of the electronic coupling between the discrete and the continuum. The matrix element of the electronic coupling changes sign in the vicinity of the crossing of the potential-energy curves, and therefore the reversal of the asymmetrical line shape occurs in the vicinity of the crossing.

The inelastic contribution of target electrons to different electronic processes in the projectile is obtained by employing the local-density approximation as usually applied in the dielectric formalism. Projectile-electron-loss cross sections due to the electron-electron interaction are calculated and compared with those obtained by using atomic antiscreening theories. We also calculate ionization cross sections and stopping power for bare ions impinging on different gases. The good agreement with the experimental data and the simplicity of the local-density approximation make it an efficient method for describing inelastic processes of gaseous target electrons. It is expected to be useful for targets with large atomic number. In this case, the number of possible final states to be considered by the traditional atomic methods makes it a tough task to be tackled. On the contrary, the more electrons the target has, the better the local plasma approximation is expected to be.

We investigate the behavior of a system for generating “fast-light” pulses in which a bichromatic Raman pumping beam is used to generate optical gain at two frequencies and a region of anomalous dispersion between them. It is expected that increasing the gain will increase the pulse advancement. However, as the gain increases, the pumping field becomes increasingly distorted, effectively limiting the pulse advancement. We observe as much as 12% of the input pump power converted to orthogonal polarization, broadening of the initially bichromatic pump field (25 MHz initial frequency separation) to more than 2.5 GHz, and a temporal collapse of the pump beam into an erratic train of sub-500-ps pulses. The instability is attributed to the combined effects of the cross modulation instability and stimulated Raman scattering. Extreme distortion of an injected pulse that should (absent the instability) experience an advancement of 21% of its width is observed. We conclude that the fast-light pulse advancement is limited to just a few percent of the pulse width using this pulse advancement technique. The limitation imposed by the instability is important because careful study of the information velocity in fast-light pulses requires that pulse advancement be large enough to distinguish the velocities of different pulse features. Possible methods for achieving pulse advancement by avoiding the distortion caused by the instability are discussed.

We analyze the phase resolution limit of a Mach-Zehnder atom interferometer whose input consists of degenerate quantum gases of either bosons or fermions. For degenerate gases, the number of atoms within one de Broglie wavelength is larger than unity, so that atom-atom interactions and quantum statistics are no longer negligible. We show that for equal atom numbers, the phase resolution achievable with fermions is noticeably better than for interacting bosons.

Bloch oscillations of cold atoms in two-dimensional optical lattices are studied. The cases of separable and nonseparable potentials are compared by simulating the wave-packet dynamics. For these two classes of optical potential, the Bloch oscillations were found to be qualitatively the same in the case of a weak static field but fundamentally different in the case of a strong field. In addition, the dynamics of the atoms in a double-period potential (which can easily be realized in two dimensions) is studied for the regime of a weak static field.

The separable state closest to a given entangled state in the relative entropy measure is called the closest disentangled state. We provide an analytical formula connecting the entangled states and the closest disentangled state in two qubits. Using this formula, when any disentangled state $\sigma$ located at the entangle-disentangle boundary is given, entangled states to which $\sigma$ is closest can be obtained analytically. Further, this formula naturally defines the direction normal to the boundary surface. The direction is uniquely determined by $\sigma$ in almost all cases.

Schmidt numbers of bipartite mixed states [B. M. Torhal and P. Horodecki, Phys. Rev. A 61, R040301 (2001)] characterize the minimum Schmidt ranks of pure states that are needed to construct such mixed states. Schmidt number is the minimum number of entangled degrees of freedom of a bipartite mixed state. We give a lower bound for the Schmidt numbers of low-rank bipartite mixed states and conclude that generic low-rank mixed states have relatively high Schmidt numbers and thus entangled.

The so-called local plasma approximation is generalized to deal with projectiles colliding with surfaces of amorphous solids and with a specific crystalline structure (plannar channeling). Energy loss of protons grazingly colliding with aluminum, SnTe alloy, and LiF surfaces is investigated. The calculations agree quite well with previous theoretical results and explain the experimental findings of energy loss for aluminum and SnTe alloy, but they fall short to explain the data for LiF surfaces.

We establish the minimum time it takes for an initial state of mean energy E and energy spread $\Delta E$ to move from its initial configuration by a predetermined amount. Distances in Hilbert space are estimated by the fidelity between the initial and final states. In this context, we study the role of entanglement among subsystems in speeding up the dynamics of a composite system.

The matrix element of a bound electron interacting with the nucleus through exchange of a Z boson is studied for the gauge-invariant case of ${2s}_{1/2}-{2p}_{1/2}$ transitions in hydrogenic ions. The QED radiative correction to the matrix element, which is $-\alpha /2\mathrm{}\pi$ in lowest order, is calculated to all orders in $Z\alpha$ using exact propagators. Previous calculations of the first-order binding correction are confirmed both analytically and by fitting the exact function at low Z. Consequences for the interpretation of parity nonconservation in cesium are discussed.

Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple quantum “coins” (or more generally, coins of higher dimension) in order to diminish the effects of interference between paths. We find solutions to this system in terms of the single-coin random walk, and compare the asymptotic limit of these solutions to numerical simulations. We find exact analytical expressions for the time dependence of the first two moments, and show that in the long-time limit the “quantum-mechanical” behavior of the one-coin walk persists, even if each coin is flipped only twice. We further show that this is generic for a very broad class of possible walks, and that this behavior disappears only in the limit of a new coin for every step of the walk.

We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an $\mathcal{ABAB}$ linear array of group-V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state $S=3/2.\mathrm{}$ Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automaton is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum-cellular-automata quantum computing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automaton operation and obtain a rough figure of merit for the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantum computer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes toward meeting the fifth criterion: qubit readout.

We investigate direct positron annihilation during a collision in a gas; this is physically separable from indirect annihilation, i.e., via formation of positronium (Ps) and its decay. The cross section of direct annihilation is calculated from the evolution of a wave packet with a time width much shorter than the Ps lifetime, where the direct contribution is extracted through the time dependence of the survival probability. The cross section obtained for a hydrogen atom is found to be enhanced in energies around 10 eV well above the Ps formation threshold. This enhancement is shown to be due to temporal positron capture with electronic excitation in the atom.

Thin luminescent foils covered upstream with layers of Formvar or gold of various thicknesses were bombarded with ${\mathrm{C}}_8$ clusters with energies between 5 and 10 MeV. The ${\mathrm{C}}_8$ induced relative luminescence yield ${\Phi }_8$ increases with growing layer thickness and approaches smoothly the value $8{\Phi }_1,$ i.e., the luminescence yield induced by eight well-separated ${\mathrm{C}}_1$ cluster constituents. This is a clear demonstration of the gradual separation between the cluster constituents during the passage of the cluster through the layers. The layer thickness necessary to separate cluster constituents far enough to act as independent atomic ions with respect to the luminescence process was calculated. The result is that Formvar layers with a thickness of about 1150 nm or $\approx 250-\mathrm{nm}$-thick gold layers are necessary to establish this mutual independence of the cluster constituents. Both calculated values agree roughly with the layer thickness obtained from an extrapolation of the experimental data.

We present an extension of the well-known Bogoliubov theory to treat low-dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretization in cells of size l. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two, and three dimensions with no ultraviolet or infrared divergence. Furthermore, this approach exactly matches Bogoliubov’s approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, and the first order and second order correlation functions of the field. Explicit calculations are done for homogeneous systems.

A vortex in a Bose-Einstein condensate generates the optical analog of the Aharonov-Bohm effect when illuminated with slow light. In contrast to the original Aharonov-Bohm effect the vortex will exchange forces with the light that leads to a measurable motion of the vortex.

We show that it is possible to improve the efficiency of a classical Otto-cycle heat engine by adding a high-Q microwave cavity and a laser system that can extract coherent laser energy from thermally excited “exhaust” atoms. This improvement does not violate the second law of thermodynamics, i.e., we show that a combined high-Q microwave cavity and a laser system does not improve the efficiency of a classical Carnot-cycle heat engine.

The robustness of entanglement results of Vidal and Tarrach [Phys. Rev. A 59, 141 (1999)] considered the problem whereby an entangled state is mixed with a separable state so that the overall state becomes nonentangled. In general, it is known that there are also cases when entangled states are mixed with other entangled states and where the sum is separable. In this paper, we treat a more general case where entangled states can be mixed with any states so that the resulting mixture is unentangled. It is found that entangled pure states for this generalized case have the same robustness as the restricted case of Vidal and Tarrach.

We present a phase-space representation of the hydrogen atom using the Kirkwood-Rikaczek distribution function. This distribution allows us to obtain analytical results, which is unique because an exact analytical form of the Wigner functions corresponding to the atom states is not known. We show how the Kirkwood-Rihaczek distribution reflects the properties of the hydrogen atom wave functions in the position and momentum representations.

A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented [Phys. Rev. A 63, 052111 (2001)]. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional Morse, Pöschl-Teller, and square well potentials. We show how the method can deal with potentials having several bound states, and for the square well case we present a comparison of the discretized and exact continuum wave functions.