Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an ensemble may be increased via a two-qubit unitary operation by twice the operation’s capacity for entanglement.

State-of-the-art ab initio techniques have been applied to compute the potential-energy curves for the ground $X{}^1{\Sigma }_g^{+}$ and excited ${}^1{\Pi }_g\mathrm{}\left(4s3d\right)\mathrm{}$ states of the calcium dimer in the Born-Oppenheimer approximation. The weakly bound ground state was calculated by symmetry-adapted perturbation theory, while the strongly bound excited state was computed using a combination of the linear-response theory within the coupled-cluster singles and doubles framework for the core-valence electronic correlation and of the full configuration interaction for the valence-valence correlation. The ground-state potential has been corrected by considering the relativistic terms resulting from the first-order many-electron Breit theory, and the retardation corrections. The magnetic electronic transition dipole moment governing the ${}^1{\Pi }_g{\leftarrow }^1{\Sigma }_g^{+}$ transitions has been obtained as the first residue of the polarization propagator computed with the coupled-cluster method restricted to single and double excitations. The computed energies and transition moments have been analytically fitted and used in the dynamical calculations of the rovibrational energy levels, ground-state scattering length, photoassociation intensities at ultralow temperatures, and spontaneous emission coefficients from the ${}^1{\Pi }_g\mathrm{}\left(4s3d\right)\mathrm{}$ to the $X{}^1{\Sigma }_g^{+}$ state. The spectroscopic constants of the theoretical ground-state potential are in a good agreement with the experimental values derived from the Fourier-transform spectra [O. Allard et al., Eur. Phys. J. D (to be published)]. The theoretical s-wave scattering length for the ground state is $a=44\mathrm{}\mathrm{bohrs},$ suggesting that it should be possible to obtain a stable Bose-Einstein condensate of calcium atoms. Finally, the computed photoassociation intensities and spontaneous emission coefficients suggest that it should be possible to obtain cold calcium molecules by photoassociation of cold atoms to the first ${}^1{\Pi }_g$ state followed by a spontaneous emission to the ground state.

We have measured the electron-impact excitation cross sections for argon into the ten levels of ${3p}^{5}5p$ configuration, as well as numerous levels of the ${3p}^{5}6p$ and ${3p}^{5}7p$ configurations. Fluorescence from the decay of the excited atoms to the levels of ${3p}^{5}4s$ configuration was used to determine the optical-emission cross sections. These results were combined with transition probabilities to find apparent cross sections into the ${3p}^{5}5p$ and ${3p}^{5}6p$ levels. These new cross sections of the $\mathrm{Ar}{(3p}^{5}np)$ levels along with the available $\mathrm{Ne}{(2p}^{5}3p),$ $\mathrm{Kr}{(4p}^{5}5p),$ and $\mathrm{Xe}{(5p}^{5}6p)$ data help provide a global view of the excitation behaviors of the ${\mathrm{np}}^5{n}^{\prime }p$ levels of the rare-gas series.

We analyze the adiabatic potential-energy surfaces relevant for neutralization of singly charged ions in slow vertical incidence onto a lithium fluoride surface. The surface is represented by a cluster of varying size augmented by point charges of alternating sign in order to include the proper Madelung potential of the ionic crystal. Our calculation proceeds on the multiconfiguration self-consistent-field and multireference configuration-interaction levels. Size-consistency corrections based on the Davidson correction and multireference averaged quadratic coupled cluster methods are included as well. We emphasize the importance of a proper treatment of electron correlation signifying the polarization of the surrounding cluster environment in ab initio calculations of charge transfer at surfaces. From the topology of the surfaces, in particular the existence or absence of avoided crossings (or, more generally, conical intersections), qualitative predictions for the neutralization process can be made. The comparative analysis of potential curves for ${\mathrm{H}}^{+},$ ${\mathrm{C}}^{+},$ ${\mathrm{S}}^{+},$ and ${\mathrm{Ne}}^{+}$ projectiles provides an explanation for the recently observed threshold behavior for potential sputtering.

The dynamics of a three-level atom in a cascade (or ladder) configuration with both transitions coupled to a single structured reservoir of quantized electromagnetic field modes is treated using Laplace transform methods applied to the coupled amplitude equations. In this system two-photon excitation of the reservoir occurs, and both sequences for emitting the two photons are allowed and included in the theory. An integral equation is found to govern the complex amplitudes of interest. It is shown that the dynamics of the atomic system is completely determined in terms of reservoir structure functions, which are products of the mode density with the coupling constant squared. This dependence on reservoir structure functions rather than on the mode density or coupling constants alone, shows that it may be possible to extend pseudomode theory to treat multiphoton excitation of a structured reservoir—pseudomodes being introduced in one-one correspondence with the poles of reservoir structure functions in the complex frequency plane. A general numerical method for solving the integral equations based on discretizing frequency space, and applicable to different structured reservoirs such as high-$Q$ cavities and photonic band-gap systems, is presented. An application to a high-$Q$-cavity case with identical Lorentzian reservoir structure functions is made, and the non-Markovian decay of the excited state shown. A formal solution to the integral equations in terms of right and left eigenfunctions of a non-Hermitian kernel is also given. The dynamics of the cascade atom, with the two transitions coupled to two separate structured reservoirs of quantized electromagnetic field modes, is treated similarly to the single structured reservoir situation. Again the dynamics only depends on reservoir structure functions. As only one sequence of emitting the two photons now occurs, the integral equation for the amplitudes can be solved analytically. The non-Markovian decay of the excited state is shown for the same high-$Q$-cavity case of identical Lorentzian reservoir structure functions, and differs from that for the single reservoir situation.

Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.

We investigate the generation of nonlinear operators with single-photon sources, linear optical elements, and appropriate measurements of auxiliary modes. We provide a framework for the construction of useful single-mode and two-mode quantum gates necessary for all-optical quantum information processing. We focus our attention generally on using minimal physical resources while providing a transparent and algorithmic way of constructing these operators.

We examine the problem of verifying the implementation of a desired noiseless subsystem from a quantum error-correcting perspective. General conditions are identified, under which the verification of error-correcting behavior against a linear set of errors $\mathcal{E}$ suffices for the verification of noiseless subsystems of an error algebra $\mathcal{A}$ contained in $\mathcal{E}.$ From a practical standpoint, our results imply that the verification of a noiseless subsystem need not require the explicit verification of noiseless behavior for all possible initial states of the syndrome subsystem.

We have developed a theory of three-pulse coherent control of photochemical processes. It is based on adiabatic passage and quantum coherence and interference attributed to the lower-lying dissociation continuum and excited upper discrete states, which are otherwise not connected to the ground state by one-photon transitions. Opportunities offered by the proposed scheme are demonstrated through extensive numerical simulations with the aid of a model relevant to typical experiments. The opportunities for manipulating the distribution of the population among discrete and continuous states with any necessary ratio by the end of the pulses are demonstrated.

Using the method of quantum-defect theory, we calculate the ultra-long-range molecular vibrational states near the dissociation threshold of a diatomic molecular potential which asymptotically varies as $-{1/R}^3.$ The properties of these states are of considerable interest as they can be formed by photoassociation (PA) of two ground-state atoms. The Franck-Condon overlap integrals between the harmonically trapped atom-pair states and the ultra-long-range molecular vibrational states are estimated and compared with their values for a pair of untrapped free atoms in the low-energy scattering state. We find that the binding between a pair of ground-state atoms by a harmonic trap has significant effect on the Franck-Condon integrals and thus can be used to influence PA. Trap-induced binding between two ground-state atoms may facilitate coherent PA dynamics between the two atoms and the photoassociated diatomic molecule.

We study the quantum description of energy fluctuations induced by stochastic changes in the frequency of atom traps. Using the connection between classical and quantum descriptions of parametric oscillators, the classical cumulant expansion method is used to obtain quantum results beyond standard perturbation theory. Both the case of static and time-dependent traps are explicitly worked out.

It is always expected that the conversion efficiency is as high as possible for nonlinear interactions at any pump intensity. We present a method of controlling the conversion efficiency of sum-frequency generation in the periodic optical superlattices with different duty cycles, which is based on the controllable linear gratings induced by electro-optic effect here. The calculated results verify that this method is feasible and very efficient in attaining the complete transfer between the pump and sum-frequency waves at any given pump intensity. In addition, we demonstrate the electric-optic control is better than temperature control.

As a consequence of having a positive partial transpose, bound entangled states lack many of the properties otherwise associated with entanglement. It is therefore interesting to identify properties that distinguish bound entangled states from separable states. In this paper, it is shown that some bound entangled states violate a nonsymmetric class of local uncertainty relations [H. F. Hofmann and S. Takeuchi, Phys. Rev. A 68, 032103 (2003)]. This result indicates that the asymmetry of nonclassical correlations may be a characteristic feature of bound entanglement.

We study expansion of quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) after switching off the confining harmonic potential. Exact solution of dynamical equations is obtained in the framework of the hydrodynamic approximation and it is compared with the direct numerical simulation of the full problem, showing excellent agreement at realistic values of physical parameters. We analyze the maximum of the current density and estimate the velocity of expansion. The results of the 1D analysis provides also qualitative understanding of some properties of BEC expansion observed in experiments.

A method to prepare molecules in nonequilibrium nuclear configurations is proposed. By using strong laser fields it is possible to stabilize the dissociative continuum of an electronic potential. Depending on the parameters of the laser the dissociative potential can be shaped to continuously change the equilibrium position over a broad range of values. In order to transfer the molecular wave packet from the ground electronic state to the stabilized dissociative potential, a novel adiabatic passage method is exploited that uses nonresonant time-delayed chirped pulses, so that the wave packet is moved to the desired place without distortion. The principles of the method are tested numerically in a diatomic molecule modeled by three analytic potential curves.

Recently, it was found that Mermin’s inequalities may not always be optimal for the refutation of a local realistic description [Phys. Rev. Lett. 88, 210402 (2002)]. To complete this work, we derive an inequality for the Greenberger-Horne-Zeilinger-type pure state for a system with N spin-$\frac{1}{2}$ particles and the violation of the inequality can be shown for all the non product pure states. Mermin’s inequality for a system of N spin-$\frac{1}{2}$ particles and Gisin’s theorem for a system of two spin-$\frac{1}{2}$ particles are both included in our inequality.

Following our previous study on ${\mathrm{H}\mathrm{e}-\mathrm{N}}_2,$ we present close-coupling calculations of the vibrational quenching cross sections and rate constants for the ${\mathrm{F}}_2(\nu =1,j=0)$ molecule colliding with ${}^3\mathrm{He}$ atoms. High-level ab initio molecular electronic-structure calculations are carried out for the ${\mathrm{H}\mathrm{e}-\mathrm{F}}_2$ van der Waals complex at the BCCD(T) level. A potential energy surface is obtained by fitting the ab initio points using the reproducing kernel Hilbert space method. This surface exhibits two minima, the linear minimum being deeper than the T-shaped one. Close-coupling calculations are performed in the collision energy ${10}^{-6}$ to $2000-{\mathrm{cm}}^{-1}$ interval. A comparison is made with the previous investigations of the vibrational relaxation of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$ molecules with ${}^3\mathrm{He}$ atoms at very low energies. We find that these three systems exhibit the same general behavior due to scattering resonances. We also analyze the very low energy limit, using a recent semiclassical approach due to Dashevskaya and Nikitin [Phys. Rev. A 63, 012711 (2000)]. We find that the simple algebraic formulas they proposed provide good estimates of the relative quenching rates at ultra-low temperatures.

We present an experimentally viable approach for suppressing the spontaneous emission in several atomic and molecular systems. We have shown [E. Frishman and M. Shapiro, Phys. Rev. Lett. 87, 253001 (2001)] that a coherent excitation of overlapping resonances followed by the application of infrequent interruptions can result in complete suppression of spontaneous emission. In the present work, the overlapping resonances result from splitting a single resonance with an external (spectator) field. An optimized superposition of the two components is formed by a shaped pulse excitation from the ground state.

Laser ablation of solid lithium, sodium, potassium, and lithium-sodium alloy was performed using a 308-nm excimer laser at fluences close to $1\mathrm{J}{\mathrm{cm}}^{-2}.$ Frequency and time resolved $A-X$ and $B-X$ electronic transitions of ${}^{6,7}{\mathrm{Li}}_2,$ ${\mathrm{Na}}_2,$ LiNa and ${\mathrm{K}}_2$ respectively, were observed. Lithium atom, dimer velocities, and influence of the background gas on dimer content of the plume have been measured. The origin of dimers at high densities, with subthermal internal energy, is discussed.

It was recently shown [A. Bulgac, Phys. Rev. Lett. 89, 050402 (2002)] that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons, fermions, and their mixtures by controlling their interaction properties by means of a Feshbach resonance. Since the quantum fluctuations in this regime could, in principle, destabilize these objects, we extend the previous mean-field analysis of these quantum liquids by computing the lowest-order quantum corrections to the ground-state energy and the depletion of the Bose-Einstein condensate and by estimating the higher-order corrections as well. We show that the quantum corrections are relatively small, do not lead to the destabilization of the droplets and are controlled by the diluteness parameter $\sqrt{n|a{|}^3}\ll 1,$ even though strictly speaking in this case there is no low density expansion.