We report a calculation of the parity nonconserving (PNC) $E1\mathrm{}$ amplitude for the ${6p}_{1/2}\to {6p}_{3/2}$ transition in ${}^{205}\mathrm{Tl}.$ Our result for the reduced matrix element is ${\mathrm{}\left(E1\mathrm{}\right)\mathrm{}}_{\mathrm{PNC}}=-(66.7\mathrm{}\pm 1.7)\times \mathrm{i}{10}^{-11}(-Q_W/N)\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{}$ Comparison with the experiment of Vetter et al. [Phys. Rev. Lett. 74, 2658 (1995)] gives the following result for the weak charge of ${}^{205}\mathrm{Tl}:\hspace{0.5em}\hspace{0.5em}{Q}_W{/Q}_W^{\mathrm{SM}}=0.97(\pm {0.01)}_{\mathrm{expt}}(\pm {0.03)}_{\mathrm{theor}},$ where $Q_W^{\mathrm{SM}}=-116.7\pm 0.1$ is the standard-model prediction. This result confirms an earlier conclusion based on the analysis of a Cs experiment that atomic PNC experiments are in agreement with the standard model.

In this paper we develop a mathematical framework for the characterization of separability and entanglement of formation (EOF) of general bipartite states. These characterizations are variational in nature, meaning that separability and EOF are given in terms of a function that is to be minimized over the manifold of unitary matrices. A major benefit of such a characterization is that it directly leads to a numerical procedure for calculating EOF. We present an efficient minimization algorithm and apply it to the bound entangled $3\times 3$ Horodecki states; we show that their EOF is very low and that their distance to the set of separable states is also very small. Within the same variational framework we rephrase the results by Wootters [W. Wootters, Phys. Rev. Lett. 80, 2245 (1998)] on EOF for $2\times 2$ states and also present some progress in generalizing these results to higher-dimensional systems.

A photon source based on postelection from entangled photon pairs produced by parametric frequency down-conversion is suggested. Its ability to provide good approximations of single-photon states is examined. Application of this source in quantum cryptography for quantum key distribution is discussed. Advantages of the source compared to other currently used sources are clarified. Future prospects of the photon source are outlined.

A proposal is described to construct a quantum-information processor using ferroelectrically coupled Ge/Si quantum dots. The spin of single electrons form the fundamental qubits. Small-diameter (<10 nm) Ge quantum dots are optically excited to create spin-polarized electrons in Si. The static polarization of an epitaxial ferroelectric thin film confines electrons laterally in the semiconductor; spin interactions between nearest-neighbor electrons are mediated by the nonlinear process of optical rectification. Single-qubit operations are achieved through “g-factor engineering” in the Ge/Si structures; spin-spin interactions occur through Heisenberg exchange, controlled by ferroelectric gates. A method for reading out the final state, while required for quantum computing, is not described; approaches involving single-electron transistors may prove fruitful in satisfying this requirement.

We calculate the trade-off between the quality of estimating the quantum state of an ensemble of identically prepared qubits and the minimum level of disturbance that has to be introduced by this procedure in quantum mechanics. The trade-off is quantified using two mean fidelities: the operation fidelity, which characterizes the average resemblance of the final qubit state to the initial one, and the estimation fidelity, describing the quality of the obtained estimate. We analyze properties of quantum operations saturating the achievability bound for the operation fidelity versus the estimation fidelity, which allows us to reduce substantially the complexity of the problem of finding the trade-off curve. The reduced optimization problem has the form of an eigenvalue problem for a set of tridiagonal matrices, and it may be easily solved using standard numerical tools.

An entangled two-mode coherent state is studied within the framework of 2×2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.

We discuss aspects of the theory and computation of resonance (autoionizing) states of polyelectronic atoms and their positive and negative ions, in the context of the state-specific approach, using as paradigms the ${\mathrm{He}}^{\mathrm{-}}{2s}^{2}2p{}^2{P}^o$ and ${2s2p}^2{}^{2}D$ triply excited states. The ${\mathrm{He}}^{\mathrm{-}}{}^{2}D$ resonance has been the subject of controversy about its nature and its very existence, with ramifications as to the physics of electron-He scattering measurements and as to the theory of resonance states in multiparticle systems in general. By carrying out a series of computations, we show how (quasi)localization of these resonances takes place. The results confirm the existence of the ${}^{2}D$ resonance just below the energy of the He $2s2p{}^3{P}^o$ resonance, with which it overlaps. The localization of the two ${\mathrm{He}}^{\mathrm{-}}$ resonances is achieved already at the single-configuration level, provided the orbitals are calculated by solving state-specific restricted Hartree-Fock (HF) equations. Accounting for orbital flexibility and relaxation due to the self-consistent interactions is essential to the achievement of a local energy minimum. The localized nature of the wavepacket is revealed even more definitely by solving appropriate multiconfigurational HF (MCHF) equations containing the information from the self-consistent interaction with closed channels as well as with the neighboring significant open ones. Reaching a reliable MCHF solution for a variety of polyelectronic multiply excited states may often be difficult, but once it is achieved it provides the overwhelmingly dominant characteristics of the state. It is then used as the reference wave function for computing variationally the remaining of the localized electron correlation in terms of optimized analytic orbitals representing very nearly the full space of the electron virtual excitations. The calculation of the localized part ${\Psi }_0$ and of $E_0=〈{\Psi }_0/H/{\Psi }_0〉,$ is done by nonorthonormal configuration interaction (NONCI) since parts of ${\Psi }_0$ are optimized separately in terms of their own basis sets. The final ${\Psi }_{0}s$ for the two resonances consisted of 683 symmetry-adapted configurations for the ${}^2{P}^o$ state and 778 ones for the ${}^{2}D$ state. Using these functions and final state scattering functions with continuum orbitals obtained numerically in term-dependent core potentials, without and with polarization, of a number of lower-lying open channels, we employed the independent channel approximation and computed partial and total energy shifts and widths, the latter from energy-dependent golden rule expressions. Critical comparison of our results for ${E=E}_0+\Delta ,$ where Δ is the shift induced by the interaction of ${\Psi }_0$ with the continuum, and for the width, Γ, with the existing few experimental and theoretical values, led us to the conclusion that the E and Γ lie in the following ranges: For the ${}^2{P}^o$ state: $E=57.204\mathrm{}\pm 0.005\mathrm{eV},$ $\Gamma =68\mathrm{}–74\mathrm{meV},$ and for the ${}^{2}D$ state: $E=58.295\mathrm{}\pm 0.010\mathrm{eV},$ $\Gamma =38\mathrm{}–55\mathrm{meV}.$ Of special theoretical and experimental interest is the determination of the partial and total widths of the three-electron ${\mathrm{He}}^{\mathrm{-}}{}^{2}D$ resonance, since it overlaps from below the two-electron threshold state He $2s2p{}^3{P}^o,$ whose position is at 58.312 eV with a width of 8 meV.

The candidate structures for the ground-state geometry of the ${\mathrm{Al}}_{13},$ ${\mathrm{Al}}_{12}\mathrm{M},$ and ${\mathrm{Al}}_{13}\mathrm{M}$ $(\mathrm{M}=\mathrm{Cu},$ Ag, and Au) clusters are obtained within the spin-polarized density-functional theory with a three-parameter hybrid functional to describe the exchange-correlation effects. Binding energy, vertical ionization potential, vertical electron affinity, and the energy gap between the highest-occupied molecular-orbital level and the lowest-unoccupied molecular-orbital level have been calculated to investigate the stability of these clusters. These results are compared with those of the alkali doped ${\mathrm{Al}}_{12}$ and ${\mathrm{Al}}_{13}$ clusters. The adatom energies (defined as the energy gained upon adding the atom to the host ${\mathrm{Al}}_{13}$ clusters) are found to be substantially larger for the coinage metal atom than those for alkali and Al atoms. The natural population analysis was carried out to get a qualitative picture of the bonding in these clusters.

We present theoretical calculations that show a systematic increase of the spectral widths of the successive above-threshold-ionization (ATI) peaks using Fourier-limited pulses. The increase of the width is attributed to the effective Fourier width corresponding to the higher-order processes. Based on that interpretation, we propose a simple model of calculating the width of a $N\mathrm{th}$-order ATI peak. We compare the results obtained from this model to the results obtained through the direct propagation of the time-dependent Schrödinger equation. For this, we have selected the negative hydrogen ion that represents the simplest possible system to study this feature due to the absence of resonances, that may obscure the results. Considering that Fourier-limited laser pulses with duration of the order of few tens of fs and wavelengths around the optical regime are nowadays readily available, we address the question about the nature of the photoelectron energy spectrum when the atoms are exposed in such fields.

We study the quantum description of parametric heating in harmonic potentials both nonperturbatively and perturbatively, having in mind applications to atom traps. The first approach establishes an explicit connection between classical and quantum descriptions; it also gives analytic expressions for properties such as the width of fractional frequency parametric resonances. The second approach gives an alternative insight into the problem and can be directly extended to take into account nonlinear effects. This is especially important for shallow traps.

For some time, the theoretical result for the transition temperature of a dilute three-dimensional Bose gas in an arbitrarily wide harmonic trap has been known to first order in the interaction strength. We extend that result to second order. The first-order result for a gas trapped in a harmonic potential can be computed in mean-field theory (in contrast to the first-order result for a uniform gas, which cannot). We show that, at second order, perturbation theory suffices for relating the transition temperature to the chemical potential at the transition, but the chemical potential is nonperturbative at the desired order. The necessary information about the chemical potential can be extracted, however, from recent lattice simulations of uniform Bose gases.

We provide evidence for the zero-temperatuture damping of condensate radial oscillations in the elongated cylindrical trap. The origin of this damping is a parametric resonance leading to an energy transfer from the coherent oscillations of condensate to longitudinal sound waves in certain frequency interval.

We study in detail the structure of the ground state of elongated rotating Bose-Einstein condensates. This ground state is composed of one or more vortex lines which bend even in completely symmetric setups. This symmetry breaking allows the condensate to smoothly adapt to rotation and to produce tightly packed arrays of vortex lines. The dependence of vortex bending on the relevant parameters is studied.

We show how the application of a coupling field connecting the two lower metastable states of a $\Lambda$ system can produce a variety of effects on the propagation of a weak electromagnetic pulse. In principle the light propagation can be changed from subluminal to superluminal. The negative group index results from regions of anomalous dispersion and gain in susceptibility.

Time-dependent Born-series calculations are carried out for various short and long range three-body scattering systems. The long range system is a standard s-wave model for electron-atom scattering developed by Temkin [Phys. Rev. 126, 130 (1962)] and Poet [J. Phys. B 11, 3081 (1978)]. A direct solution of the time-dependent Schrödinger equation yields exact excitation and ionization cross sections for all the scattering systems. For short range forces the time-dependent Born-series calculations are found to converge more rapidly for weak binding potentials and high incident electron energies. For long range forces the time-dependent Born-series calculations do not converge, although the first-order excitation and ionization cross sections are quite reasonable.

We calculated, within the Gross-Pitaevskii formalism, the critical number of atoms for Bose-Einstein condensates with two-body attractive interactions in cylindrical traps with different frequency ratios. In particular, by using the trap geometries considered by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)], we show that the theoretical maximum critical numbers are given approximately by $N_c{=0.55(l}_0/|a|).\mathrm{}$ Our results also show that, by exchanging the frequencies ${\omega }_z$ and ${\omega }_{\rho },$ the geometry with ${\omega }_{\rho }<{\omega }_z$ favors the condensation of larger number of particles. We also simulate the time evolution of the condensate when changing the ground state from $a=0\mathrm{}$ to $a<\mathrm{}0\mathrm{}$ using a 200 ms ramp. A conjecture on higher-order nonlinear effects is also added in our analysis with an experimental proposal to determine its signal and strength.

We have observed clear Rabi oscillations of a weak probe in a strongly driven three-level $\Lambda$ system in laser-cooled rubidium. When the coupling field is nonadiabatically switched on using a Pockels cell, transient probe gain without population inversion is obtained in the presence of uncoupled absorptions. Our results are supported by three-state computations.

We demonstrate that any pure bipartite state of two qubits may be decomposed into a superposition of a maximally entangled state and an orthogonal factorizable one. Although there are many such decompositions, the weights of the two superposed states are, remarkably, unique. We propose a measure of entanglement based on this decomposition. We also demonstrate that this measure is connected to three measures of entanglement previously set forth: maximal violation of Bell’s inequality, concurrence, and two-particle visibility.

We show that the beating of a nanojoule femtosecond pulse with a Raman coherence adiabatically prepared by a pair of millijoule nanosecond pulses in solid hydrogen leads to an efficient generation of a triplet, doublet, or even singlet of subfemtosecond pulses. The energy conversion efficiency of the subfemtosecond pulse generation can be larger than unity due to the transfer of energy from the driving pulses.

We consider two barriers enclosing a well that possesses a bound state. In the presence of an oscillating field, this bound state is transformed into a resonance with a width reflecting the escape process by absorption of quanta from the field. We show that a particle incident on this device with an energy just one quantum above the bound-state energy has a transmissivity approaching unity as the amplitude of the field is reduced. The conditions for efficient transmission at this energy are examined.