We show that the continuous-variable analogues to the multipartite entangled Greenberger-Horne-Zeilinger states of qubits violate Bell-type inequalities imposed by local realistic theories. Our results suggest that the degree of nonlocality of these nonmaximally entangled continuous-variable states, represented by the maximum violation, grows with increasing number of parties. This growth does not appear to be exponentially large as for the maximally entangled qubit states, but rather decreases for larger numbers of parties.

A simple and straightforward WKB approach to calculating the lifetime of quasistationary states in spherically symmetric potential wells is suggested. Using this approach, a general formula for the imaginary part of the energy for potentials of the form $V\left(x\right)=P\left(x\right)\mathrm{}-\mu Q\left(x\right)\mathrm{}\mathrm{—}\mathrm{where}$ $P\left(x\right)\mathrm{}$ is the radial part of the potential for a spherically symmetric harmonic oscillator and $Q\left(x\right)\mathrm{}$ is an even polynomial—is derived. Using this formula, the usual tedious procedure of the explicit asymptotic matching of the WKB and perturbative wave functions is avoided, and calculations are substantially simplified. The leading term and a few corrections of the series for the imaginary part of the energy and the related lifetime are analytically calculated.

I investigate the decoherence of two-mode squeezed vacuum states by analyzing the relative entropy of entanglement. I consider two sources of decoherence: (i) the phase damping and (ii) the amplitude damping due to the coupling to the thermal environment. In particular, I give the exact value of the relative entropy of entanglement for the phase damping model. For the amplitude damping model, I give an upper bound for the relative entropy of entanglement, which turns out to be a good approximation for the entanglement measure in the usual experimental situations.

Single-photon photodetachment of mass-selected $W_n^{-}$ clusters has been studied by photoelectron imaging spectroscopy. Velocity map imaging allows us to measure simultaneously the kinetic-energy spectrum and the angular distribution of photoelectrons. This provides a clear distinction between the two major decay mechanisms: isotropic thermionic emission and anisotropic direct photoemission. A careful study of threshold electrons shows that the thermal distribution cannot be described by a bulklike formula or a simple exponentially decreasing Boltzmann function. On the contrary, our results are in excellent agreement with more refined theoretical models taking into account the spherical symmetry of the cluster. The kinetic-energy distribution of thermal electrons corresponding to thermionic emission is found to vary as $p\left(\epsilon \right)\propto {\epsilon }^{1/2}\exp \left(-\epsilon {/k}_{B}T\right).\mathrm{}$ Our results indicate that a transition toward a bulklike statistical behavior of the internal-energy redistribution occurs in very small systems owing to the high density of states in metal clusters. Moreover, the angular distribution of direct photoelectrons is obtained and the evolution as a function of size is discussed. The asymmetry parameter β of the most intense band observed in direct photoemission for each cluster decreases monotonically with size: the direct photoemission of smaller systems is strongly anisotropic, becoming isotropic as the size of the system increases. This probably indicates the loss of coherence induced by electron-electron collisions occurring in large systems.

We present a combined theoretical and experimental study of the effects of laser polarization on optical coherences produced in two-color, resonant four-wave mixing (TC-RFWM). A time-dependent model incorporating diagrammatic perturbation theory and spherical tensor formalism is used to interpret observations of quantum beats due to molecular hyperfine structure in time-resolved TC-RFWM in nitric oxide. Good agreement is found between the model and the observed time-resolved signals for two distinct excitation schemes and a variety of polarization configurations including both polarization and population gratings. Measured hyperfine energy intervals are reported for the $X{}^2{\Pi }_{1/2},$ $v=0\mathrm{}$ ground state and the $A{}^2{\Sigma }^{+},$ $v=0\mathrm{}$ excited state of NO. The experimental results demonstrate that TC-RFWM can be used to perform state-selective, quantum beat spectroscopy in three-level systems by suitably designing three experimental features: the excitation scheme for the matter-field interaction, the time ordering of the laser pulses, and the polarization of the incident laser beams.

Excited-state angular-momentum alignment–orientation conversion for atoms with hyperfine structure in the presence of an external magnetic field is investigated. Transversal orientation in these conditions is reported. This phenomenon occurs under Paschen Back conditions at intermediate magnetic-field strength. Weak radiation from a linearly polarized diode laser is used to excite Rb atoms in a cell. The laser beam is polarized at an angle of $\pi /4\mathrm{}$ with respect to the external magnetic-field direction. Ground-state hyperfine levels of the ${5S}_{1/2}$ state are resolved using laser-induced fluorescence spectroscopy under conditions for which all excited ${5P}_{3/2}$ state hyperfine components are excited simultaneously. Circularly polarized fluorescence is observed to be emitted in the direction perpendicular to both to the direction of the magnetic field $\mathbf{B}$ and direction of the light polarization $\mathbf{E}.$ The obtained circularity is shown to be in quantitative agreement with theoretical predictions.

We present a general, semi-classical theory describing the interaction of an atom with an internal state consisting of a number of degenerate energy levels with static and oscillating magnetic fields. This general theory is applied to the ${}^3{P}_2$ metastable energy level of neon to determine the dynamics of the populations and coherences that are formed due to the interaction. Through these calculations we demonstrate how the interaction may be used for the internal state preparation of an atom.

Exact non-Born-Oppenheimer numerical solutions of the time-dependent Schrödinger equation for the one-dimensional ${\mathrm{H}}_2^{+}$ molecule in an intense, two-color $(\omega +2\mathrm{}\omega )$ laser field, with relative phase $\phi ,$ have been obtained. Both electron and proton kinetic energy spectra show spatial, correlated, asymmetric distributions. The calculated spectra exhibit the same unusual correlations as seen in experiments, in which both positively charged nuclear fragments and negatively charged photoelectrons are preferentially emitted in the same direction. It is found that, for the most asymmetric combined electric field $(\phi =0),$ the electron is ionized in a “counterintuitive” direction: i.e., more electrons follow the direction of the maximum electric field. This unexpected behavior of electrons is not specific to molecules: we show that the same effect occurs in atoms. The above asymmetries of photoemission of electrons are interpreted in the framework of a quasistatic tunneling model and it is shown that for $\phi =0\mathrm{}$ the electron asymmetry is induced by the Coulomb attraction from the parent ion. Proton asymmetries found in the dissociation $\mathrm{H}+p$ channel depend strongly on the initialization: proton asymmetry for low vibrational state initialization is opposite that for high vibrational states. In the latter case, for $\phi =0,$ protons follow the direction of the maximum field. Coulomb explosion spectra are shown to arise from an enhanced ionization mechanism, which is phase dependent also.

We propose and analyze an all-optical atomic beam splitter based on a multistep adiabatic passage in a “tripod” atomic level configuration. The spatial interference patterns obtained may exhibit extremely fine structure due to splittings of many times the photon momentum. The visibility of the obtained interference pattern is also shown to exhibit collapses and revivals as the distance from the interaction region is varied.

We evaluate the frequencies of scissors modes for density and concentration fluctuations in a vapor of fermionic atoms placed in two hyperfine levels inside a spherical harmonic trap. Both the superfluid and normal states are considered, with inclusion of the interactions at the random-phase level. Two main results are obtained: (i) the transition to the superfluid state is signaled by the disappearance of soft transverse modes of the normal fluid in the collisionless regime; and (ii) the eigenfrequency of the density fluctuations in the superfluid coincides with that of the normal fluid in the collisional regime. The latter property is related to the opening of the gap in the single-pair spectrum.

We have investigated nonlinear atom optical effects which arise from atom-atom collisional interactions in a single-mode atomic Fabry-Perot cavity driven by a coherent cw atom laser beam. When the nonlinear interaction energy per single atom is small, the exact numerical solution of the master equation is well reproduced by a mean-field treatment in which quantum fluctuations are included linearizing the stochastic equations of the Positive-P representation. On the other hand, when the damping of the cavity mode is very weak and its wave-function is tightly confined in space, a regime of strong nonlinearity can be achieved. For the specific case of an incident atom laser frequency at resonance with the empty cavity, the numerical calculations predict a sort of atom blockade effect, which is a sort of atom optical analog of the well-known Coulomb blockade effect of electronic transport through microscopic structures: only one atom can occupy the cavity mode at a time and the statistical properties of the transmitted beam, being very similar to the resonance fluorescence from a single two-level system, show definitely nonclassical behaviors such as antibunching. Only at very large incident intensities, more than one atom can be simultaneously forced inside the cavity mode: in this regime, the results of the numerical calculations can be successfully interpreted using a dressed cavity model. From the formal analogy between atomic matter waves and optical light waves in nonlinear media, it follows that the same results hold for photonic systems.

The effect of partial coherence on four-wave mixing in photorefractive media is studied by taking into account the evolution and propagation of the mutual coherence via a theoretical model. This model is applied to four-wave mixing and two-wave mixing with fully or partially coherent waves. We studied the effect of partial coherence with the presence of all the gratings, and compared the results with those of the transmission grating approximation and of the reflection grating approximation, respectively.

We study the dynamics of an optical mode in a cavity with a movable mirror subject to quantum Brownian motion. We study the phase-noise power spectrum of the output light, and we describe the mirror Brownian motion, which is responsible for the thermal-noise contribution, using the quantum Langevin approach. We show that the standard quantum Langevin equations, supplemented with the appropriate non-Markovian correlation functions, provide an adequate description of Brownian motion.

The first three dynamic multipole polarizabilities for the ground state of hydrogen, helium, hydride ion, and positronium hydride PsH have been computed using the variational Monte Carlo (VMC) method and explicitly correlated wave functions. Results for the static dipole polarizability by means of the diffusion Monte Carlo method and the finite field approach show the VMC results to be quite accurate. From these dynamic polarizabilities van der Waals dispersion coefficients for the interaction of PsH with ordinary electronic systems can be computed, allowing one to predict the dispersion energy for the interaction between PsH and less exotic atoms and molecules.

The process of single ionization has been studied in ${\mathrm{C}}^{6+}-\mathrm{He}$ collisions at the collision velocities of 1.17, 1.36, and 1.63 a.u. Ejected electrons were detected in coincidence with the recoil ions. Two components of the electron-momentum and the full-momentum vector of the recoil ion were measured. From these, two-dimensional momentum-space distributions of the continuum electrons were deduced, projected parallel or perpendicular to the collision plane, and for several values of the recoil transverse momentum. The distributions do not show the molecular-orbital-like patterns seen in similar collisions with singly and doubly charged projectiles. They do tend to lie preferentially along a ridge joining the target and projectile velocities, and show an increasing tendency to go in the direction of the projectile, both longitudinally and transversely, as the collision velocity is raised and the impact parameter lowered. The results are in agreement with classical trajectory Monte Carlo predictions for similar systems.

The proof of Bell’s theorem without inequalities by Greenberger, Horne, and Zeilinger (GHZ) is extended to multiparticle multilevel systems. The proposed procedure generalizes previous partial results and provides an operational characterization of the so-called GHZ states for multiparticle multilevel systems.

We derive a well-behaved nonlinear extension of the nonrelativistic Liouville–von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure-state limit reduces to the usual Schrödinger evolution, while mixtures evolve toward maximum entropy equilibrium states with canonical-like probability distributions on energy eigenstates. The linear, near-equilibrium limit is found to amount to an essentially exponential relaxation to thermal equilibrium; a few elementary examples are given. In addition, the modified dynamics is invariant under the time-independent symmetry group of the Hamiltonian, and also invariant under the special Galilei group provided the conservation of total momentum is accounted for as well. Similar extensions can be generated for, e.g., nonextensive systems better described by a Tsallis q entropy.

The premise of nuclear magnetic resonance (NMR) quantum computing is that pseudopure quantum states, for which the populations of all energy levels but one are equal, can be used instead of pure quantum states. However, for systems with a large number of quantum bits (qubits), it would require elaborate pulse sequences with many steps to prepare these pseudopure states. To overcome this problem, a method using pairs of pseudopure states (POPS) instead of individual pseudopure states as the basis for NMR quantum computing is introduced here. The POPS approach has a significant advantage over the existing methods that, regardless of the number of qubits, only a single step is needed to prepare each pair of pseudopure states. A detailed analysis of a 16-level spin system is given, and the results of applying a $c^2$-NOT quantum logic gate (a controlled-NOT gate conditional upon the state of two other qubits) to all the POPS in the system are presented.

The time-dependent approach to electron-atom scattering is emerging as an alternative to more conventional methods of treating atomic collisions. Solving the time-dependent Schrödinger equation directly has several very attractive features including a completely nonperturbative solution, dense representation of the nonphysical positive energy states, circumvention of the need to explicitly impose boundary conditions for ionization, and the convenience of being able to “watch” the electronic probability density evolve though the collision. Two principal approaches have so far been applied to treat electron-atom scattering, namely, the time-dependent close couping (TDCC) method and what we refer to as the time-dependent Hylleraas (TDH) method. The TDCC method solves coupled equations with two variables within a truncated infinite sum over individual angular momenta for each total angular momentum L of the system. In contrast, the TDH method avoids an infinite summation over the angular momenta of the individual electrons at the expense of solving a coupled equation with three variables for each L. The TDH method has previously been used for $L=0\mathrm{}$ only. An important question, therefore, concerns whether the TDH method would represent a numerical advantage over the TDCC method for higher L values. This issue is investigated in this paper.

Cross sections for nonradiative charge transfer in ${\mathrm{H}}^{+}+\mathrm{N}\mathrm{a}\mathrm{}\left(3s\right)\mathrm{}$ collisions at energies less than or equal to 40 eV have been calculated using a fully quantum-mechanical approach. The calculated cross sections agree well with the experimental data in the entire energy range, but do not agree with other calculations at low energies. We discuss possible causes of this difference. Using the calculated cross sections, the rate coefficients at temperatures below 20 000 K have been calculated, and compared with those of other theoretical calculations.