We study the spatial correlations of quantum fluctuations that can be observed in multimode parametric down-conversion in the regime of high gain. We investigate both a type-I and a type-II phase-matching configuration: in the latter case spatial correlations at the quantum level are shown to exist both in the near-field and in the far-field zones of the down-converted light. In the stationary and plane-wave approximation we treat the problem analytically. A stochastic model is solved numerically to obtain quantitative results beyond this approximation. The finite transverse size and pulse duration of the pump beam and other features of the system, such as spatial walk-off and diffraction are taken into account, and we show that correlations beyond the standard quantum limit exist for values of parameters consistent with realistic experiments.

Employing the general bilateral controlled-NOT operation and local state discrimination, the mixed state of the form ${\rho }_d^{\mathrm{}\left(k\right)\mathrm{}}{=(1/d}^2\left){\sum }_{m,n=0\mathrm{}}^{d-1}\right(|{\phi }_{\mathrm{mn}}〉〈{\phi }_{\mathrm{mn}}|{)}^{\otimes k}$ is proved to be quasipure, where $\{|{\phi }_{\mathrm{mn}}〉\}$ is the canonical set of mutually orthogonal maximally entangled states in $d\times d.\mathrm{}$ Therefore irreversibility does not occur in the process of distillation for this family of states. Also, the distillable entanglement is calculated explicitly.

Auger resonances of dissociating atoms in randomly oriented molecules experience large electronic Doppler shifts. We predict that when fixed-in-space molecules are considered there will appear extra Doppler resonances resulting from the diffractional scattering of the Auger electrons by the surrounding atoms. These resonances show sharp maxima in bond directions, something that makes them very promising as probes for local molecular structure using current energy- and angular-resolved electron-ion coincidence experiments.

A combined experimental and theoretical study of transition matrix elements of the $6p{}^2{P}_j\to 8s{}^2{S}_{1/2}$ transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an $\approx 200{\mathrm{cm}}^{-1}$ range on the low-frequency side of the $6s{}^2{S}_{1/2}\to 6p{}^2{P}_{3/2}$ resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance $6s{}^2{S}_{1/2}\to \mathrm{np}{}^2{P}_j\to 8s{}^2{S}_{1/2}$ transitions. In addition, as the measured quantities are ratios of polarization-dependent intensities at a single-excitation frequency, they are quite insensitive to a variety of common-mode systematic effects; matrix-element ratios may then be determined to high accuracy. In the past, the matrix-element dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the $6p{}^2{P}_j\to 8s{}^2{S}_{1/2}\mathrm{}(j=1/2,3/2\mathrm{})\mathrm{}$ transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).

We investigate the effects of a strong electric field on the rovibrational spectra of diatomic heteronuclear molecules in a ${}^1{\Sigma }^{+}$ electronic ground state. Using a hybrid computational technique combining discretization and basis set methods, the full rovibrational equation of motion is solved. As a specific example, the rovibrational spectrum and properties of the carbon monoxide molecule are analyzed for experimentally accessible field strengths. Results for energy levels, expectation values, and rovibrational spectral transitions are presented. They indicate that, while low-lying states are not significantly affected by the field, for highly excited states strong orientation and hybridization are achieved. We propose an effective rotor Hamiltonian, including the main properties of each vibrational state, to describe the influence of an electric field on the rovibrational spectra of a molecular system with a small coupling between its rotational and vibrational motions. The validity of this approach is illustrated by comparison with the results obtained with the fully coupled rovibrational Schrödinger equation. We thereby demonstrate that it is possible to create state-dependent hybridization of a molecular system, which is of importance for vibrational state-selective chemical reactions. This state dependence is individually different for each molecular system and represents therefore a characteristic feature of the species.

The highly accurate solution of the Schrödinger equation in the form of common Landau exponential factor multiplied by a power series in two variables, the sine of the cone angle and radial variable is completed by the first-order relativistic correction calculated within the framework of the relativistic direct perturbation theory (DPT). It is found that in contrast to behavior of relativistic corrections for the ground state and ${2p}_{-1}{(m}_s=-1/2)$ excited state, which change sign from negative to positive near $B\approx {10}^{11}\mathrm{G}$ and $B\approx {10}^{10}\mathrm{G},$ respectively [Z. Chen and S. P. Goldman, Phys. Rev A $45,$ 1722 (1992)], the relativistic corrections for ${2s}_0{(m}_s=-1/2)$ and ${2p}_0{(m}_s=-1/2)$ excited states are negative for the magnetic field varying in range $0<B<\mathrm{}{10}^{13}\mathrm{G}.$ If relativistic correction significantly mix nonrelativistic states the near-degenerate version of DPT is used. The avoided crossings of relativistic levels with $\mu =-1/2$ and $\pi =-1,$ evolving from field-free states with principal quantum numbers $n=2,3,4\mathrm{}$ are presented.

We discuss a method to create two-dimensional (2D) traps as well as atomic shell, or bubble, states for a Bose-Einstein condensate initially prepared in a conventional magnetic trap. The scheme relies on the use of time-dependent, radio-frequency-induced adiabatic potentials. These are shown to form a versatile and robust tool to generate interesting trapping potentials. Our shell states take the form of thin, highly stable matter-wave bubbles and can serve as stepping stones to prepare atoms in highly excited trap eigenstates or to study “collapse and revival phenomena.” Their creation requires gravitational effects to be compensated by applying additional optical dipole potentials. However, in our scheme gravitation can also be exploited to provide a route to two-dimensional atom trapping. We demonstrate the loading process for such a trap and examine experimental conditions under which a 2D condensate may be prepared.

Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic quantum computing, which accurately describes the evolution of the quantum state in a perturbative way, in which the adiabatic limit is the zeroth-order approximation. As an application of this formulation, nonadiabatic correction or error is estimated for several physical implementations of the adiabatic geometric gates. A quantum-computing process consisting of many adiabatic gate operations is considered, for which the total nonadiabatic error is found to be about the sum of those of all the gates. This is a useful constraint on the computational power. The formalism is also briefly applied to the adiabatic quantum algorithm.

The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts, and then measure the joint output state. This measurement could be an entangled one or it could be separable (e.g., measurements which can be implemented with local operations and classical communication or LOCC). A comparison is made between these possibilities and it is shown that by using nonseparable measurements one can improve the accuracy of the estimation by a factor of $2(d+1\mathrm{})/d$ where d is the dimension of the Hilbert space on which U acts.

Using the unique nature of the average output state of an optimal signalling ensemble, we prove that for a special class of qudit unital channels, the Holevo-Schumacher-Westmoreland channel capacity is $\mathcal{C}={\log }_2\mathrm{}\left(d\right)\mathrm{}-{\min }_{\rho }\mathcal{S}\left(\mathcal{E}\right(\rho \left)\right),$ where d is the dimension of the qudit. The result is extended to products of the same class of unital qudit channels. Thus, the connection between the minimum von Neumann entropy at the channel output and the transmission rate for classical information over quantum channels extends beyond the qubit domain.

We present an efficient generalization of the exterior complex scaling (ECS) method to extract discrete inelastic and ionization amplitudes for electron-impact scattering of atomic hydrogen. This fully quantal method is demonstrated over a range of energies for the collinear and Temkin-Poet models and near-threshold ionization is examined in detail for singlet and triplet scattering. Our numerical calculations for total ionization cross sections near threshold strongly support the classical threshold law of Wannier [Phys. Rev. 90, 817 (1953)] $\left(\sigma \propto E^{1.128\pm 0.004}\right)$ for the $L=0\mathrm{}$ singlet collinear model and the semiclassical threshold law of Peterkop [J. Phys. B 16, L587 (1983)] $\left(\sigma \propto E^{3.37\pm 0.02}\right)$ for the $L=0\mathrm{}$ triplet collinear model, and are consistent with the semiclassical threshold law of Macek and Ihra [Phys. Rev. A 55, 2024 (1997)] $\left(\sigma \propto \exp \right[(-6.87\pm {0.01)E}^{-1/6}])$ for the singlet Temkin-Poet model.

Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable ${}^4\mathrm{He}$ is discussed. We also present calculations for the damping of the analogous $m=0\mathrm{}$ monopole-quadrupole condensate mode in the superfluid phase.

The change in the average value of the electric field and of the electric field squared following excitation of an atomic dipole is calculated using a density matrix approach in the Schrödinger picture. It is shown that field emission is perfectly causal provided non-energy-conserving terms are included. The Schrödinger picture approach offers some advantages over the conventional Heisenberg picture approach.

Interaction between system and reservoir is considered to be linear in the coordinates of heat bath but nonlinear in the system coordinate and velocity. The reduced partition function of the system is presented and the corresponding effective classical potential is calculated by using the path-integral Monte Carlo method. In the presence of the nonlinear coupling, a dissipative threshold is observed at finite temperatures, and the decay rate of a particle in a metastable potential can be hindered by inhomogeneous dissipation above twice the crossover temperature.

Cross sections for antiproton capture are calculated using the fermion molecular dynamics method for ions of current interest in experiments determining nuclear structure of the radioactive nuclei ${}^8\mathrm{He},$ ${}^{11}\mathrm{Li},$ ${}^{11}\mathrm{Be},$ and ${}^{21}\mathrm{Mg}.$ The cross sections for the corresponding neutral atoms are also calculated. It is found that, except for helium, the cross sections for the ion and neutral atom at usual capture energies are similar, i.e., neither the enhanced trajectory curvature nor the absence of the most weakly bound electron have great effect. The behavior of the cross sections is also analyzed at very low collision energies, where the ion cross sections go as $1/E$ and the neutral cross sections as $1/\sqrt{E}.$

State-specific dielectronic recombination (DR) rate coefficients from ground states of H- and He-like Al, Ti, Ni, Kr, and Mo ions have been calculated in the isolated resonance and intermediate coupling approximation. The data generated for these calculations consists of energies of singly and doubly excited states, radiative rates, autoionization rates, and dielectronic recombination branching ratios. A Hartree-Fock method that includes relativistic corrections was employed in order to carry out the calculations. Three parameter fits to the data were then made using the Al, Ti, and Kr data to obtain scaling relations that enable one to calculate similar data for other ions by interpolation in the range between Al and Kr and somewhat beyond by extrapolation. The scaling accuracy was verified by comparing the scaling relation predictions to detailed data obtained for Ni and Mo calculations. The results obtained also compared well with other published work in which total ground state to ground state dielectronic recombination rates were calculated. The DR rate coefficients that are calculated from the scaled DR data are generally most accurate for intermediate to high-temperature collisional plasmas. However, in low-temperature photoionized plasmas, significant DR contributions come from the $\Delta n=0\mathrm{}$ core excitations that are not present for K-shell recombination and thus one should expect the Z scaled DR rates to be accurate for any range of temperatures of interest.

The interactions of charged particles with carbon nanotubes are studied by means of the linearized hydrodynamic theory for electronic excitations on the nanotube surface. General expressions are derived for the induced potential, the self-energy, and the stopping power for a charged particle moving paraxially in a nanotube. Numerical results are obtained showing the influence of the damping factor, the nanotube radius, and the particle position on its self-energy and the stopping power. Results for stopping power in the linearized hydrodynamic model are compared with those obtained by means of the dielectric formalism in random-phase approximation, showing a close agreement between the two approaches for high speeds of charged particles.

We present a minimally destructive interferometric measurement of the column density of cold atoms with a passively stabilized separated beam path interferometer. We achieve a heating rate of 4 (photons/sec)/atom. The interferometer employed in these measurements utilizes a photodiode rather than a charge-coupled device camera and is suitable for the measurement of fast dynamics in Bose-Einstein condensates and real-time feedback with atom lasers. The technique is compatible with modulation techniques employing squeezed light as the probe beam for sub-shot-noise-limited measurements.

A time-dependent Kohn-Sham-like equation for N bosons in a trap is generalized for the case of inelastic collisions. We derive adiabatic equations which are used to calculate the nonlinear dynamics of the Bose-Einstein condensate and non-mean-field corrections due to the three-body recombination. We find that the calculated corrections are about 13 times larger for three-dimensional (3D) trapped dilute bose gases and about seven times larger for 1D trapped weakly interacting Bose gases when compared with the corresponding corrections for the ground-state energy and for the collective frequencies. The results are obtained at zero temperature.