Based on a recent definition of a measure for entanglement [Plenio and Vedral, Contemp. Phys. 39, 431 (1998)], examples of maximum entangled states are presented. The construction of such states, which have symmetry SU(1,1) and SU(2), follows the guidance of thermofield dynamics formalism.

Multiple scale techniques are well known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution of the Heisenberg equations of motion and the Hamiltonian spectrum.

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity system, have exactly one ebit of entanglement, but are not maximally entangled. We demonstrate this by showing that they violate, but, in general, not maximally, Bell’s inequality due to Clauser, Horne, Shimony, and Holt [Phys. Rev. Lett. 23, 880 (1969)]. These states are interesting in that they exhibit the entanglement between two distinct degrees of freedom (one is discrete and another is continuous). We then demonstrate these entangled states as a valuable resource in quantum-information processing including quantum teleportation, entanglement swapping and quantum computation with “parity qubits.” Our work establishes an interesting link between quantum-information protocols of discrete and continuous variables.

We introduce a procedure for qubit rotation, alternative to the commonly used method of Rabi oscillations of controlled pulse area. It is based on the technique of stimulated Raman adiabatic passage and, therefore, it is robust against fluctuations of experimental parameters. Furthermore, our work shows that it is, in principle, possible to perform quantum logic operations via stimulated Raman adiabatic passage. This opens up the search for a completely new class of schemes to implement logic gates.

We study the Levinson theorem in (1+1) dimensions for a Dirac particle coupled to a background pseudoscalar field, which is allowed to evolve into a soliton with arbitrary topological charge. We demonstrate the difficulty with defining the phase shifts when solitons are present, and then present a prescription for defining the phase shifts when the background field has arbitrary boundary values. We find that a modified form of the Levinson theorem holds, in which half the total number of threshold bound states at zero strength of the potential needs to be subtracted from the total number of bound states. We then present the Levinson theorem in a form that is universal to both relativistic and nonrelativistic quantum mechanics, which also includes all the exceptional cases. We also find generalizations to the Levinson theorem by finding relations between the bound states and the values of the phase shifts at each boundary of the continua separately. We relate the values of the phase shifts at the boundaries of a given continuum to the spectral deficiency in that continuum. We also relate the values of phase shifts at infinite energies to the topological charge of the solitons and their adiabatic contribution to the vacuum polarization that they induce.

Electron-impact-ionization cross sections for Na-like ${\mathrm{Cr}}^{13+}$ have been calculated using semirelativistic distorted-wave Born-exchange approximation. We have included direct ionization, excitation autoionization, and resonant-excitation double-autoionization (REDA) processes in our calculation. The overall agreement between experimental data and our theoretical values is very good. Strong resonant peaks from REDA processes are found, and the REDA processes contribute about 50% and 25% to the average total ionization cross section between 570 and 650 eV and between 650 and 860 eV, respectively. A detailed investigation about the effects of radiative damping and loss channels on the REDA cross section has been carried out. The ionization-rate coefficients of ${\mathrm{Cr}}^{13+}$ are also presented. Besides, we have compared our calculated results of ${\mathrm{Fe}}^{15+}$ to experimental data and other theoretical values for examining the reliability of our calculations.

We reexamine the problem of calculating the positions and widths of the lowest-lying resonances in the $\mathrm{Ps}+\mathrm{H}$ scattering system that consists of two electrons, one positron and one proton. The first of these resonances, for $L=0,$ was found by the methods of complex rotation and stabilization, and later described as a Feshbach resonance lying close to a bound state in the closed-channel $e^{+}+{\mathrm{H}}^{-}$ system. Recently, results for the $L=1\mathrm{}$ and 2 scattering states were published, and it was found, surprisingly, that there is a large shift in the positions of these resonances. In this paper we repeat the analysis for $L=1\mathrm{}$ and find an unexpected explanation for the shift.

The Sturmian theory of ion-atom collisions is constructed for arbitrary (nonzero) impact parameters. The approach is essentially nonperturbative, and has a wide range of applicability: from low velocities, provided that quantum motion of heavy particles can be neglected, to high velocities, as long as the relativistic effects are not important. The theory is applied to calculation of electron spectra at low and high collision velocities. For slow collisions we describe Fermi oscillations in the spectra of ejected electrons. At higher velocities our theory confirms the possibility of cusp formation even when the heavy particles are neutral in the final state.

We present results of integral-excitation and total-ionization cross section calculations from the $6s6p{}^1{P}_1,$ $6s5d{}^1{D}_2,$ $6s6p{}^3{P}_{0,1,2},$ and $6s5d{}^3{D}_{1,2,3}$ states of Ba. The unitarized first-order many-body theory and the close-coupling method were used to obtain the integrated cross sections, while the Born approximation was used to estimate the ionization cross sections. A comparison is given with the semiempirical estimates of excitation cross sections obtained from small-angle differential cross-section measurements.

We present a general discussion of the techniques of destabilizing dark states in laser-driven atoms with either a magnetic field or modulated laser polarization. We show that the photon-scattering rate is maximized at a particular evolution rate of the dark state. We also find that the atomic-resonance curve is significantly broadened when the evolution rate is far from this optimum value. These results are illustrated with detailed examples of destabilizing dark states in some commonly trapped ions and supported by insights derived from numerical calculations and simple theoretical models.

Rydberg atoms in a static electric field provide an experimental system with which many aspects of strong atom-field interactions can be tested. We report measurements of multiphoton transitions in Rydberg states of potassium driven by chirped pulses of rf radiation. Pulses of rf are produced with frequencies swept from 675 to 825 MHz at rates from 0.25 MHz/ns to 7.5 MHz/ns. We present measurements of population transfer in a two-level system as a function of rf field strength and sweep rate. The data is analyzed with a dynamical Floquet model using Landau-Zener transition probabilities; this model accurately describes these transitions.

Free expansion of attractive and repulsive Bose-Einstein condensed vortex states formed in an axially symmetric trap is investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation. In a repulsive condensate the vortex-core radius is much smaller than the radial root-mean-square (rms) radius, which makes the experimental observation of the vortex core difficult. The opposite is found to be true in an attractive condensate that makes it a better candidate for experimental observation. Also, in all cases the ratio of vortex-core radius to radial rms radius increases as the angular momentum of the vortex increases. This makes the vortex states with higher angular momenta more suitable for experimental confirmation.

We develop an exact sum rule that relates the spectral shift of a trapped gas undergoing cold collisions to measurable quantities of the system. The method demonstrates the dependence of the cold collision frequency shift on the quantum degeneracy of the gas and facilitates extracting scattering lengths from the data. To illustrate the method, we consider optical shift for the Thomas-Fermi model of Bose-Einstein condensate in a harmonic optical trap.

An experiment is proposed that permits the observation of the reduced de Broglie wavelengths of two- and four-photon wave packets using present technology. It is suggested to use a Mach-Zehnder setup and feed both input ports with light generated by a single nondegenerate down-conversion source. The strong quantum correlations of the light in conjunction with boson enhancement at the input beam splitter allow us to detect a two- and fourfold decrease in the observed de Broglie wavelength with perfect visibility. This allows a reduction of the observed de Broglie wavelength below the wavelength of the source.

We theoretically analyze the optical response from an ultrathin film built up of oriented molecular aggregates, the operating states of which are represented by Frenkel exciton states. A four-level model, involving transitions between the ground, one-exciton and two-exciton states, exciton-exciton annihilation from the two-exciton state as well as relaxation from the annihilation level back to the one-exciton and ground states, is used for describing the film optical response. It is proved that the exciton-exciton annihilation may act not as a destructive but, on the contrary, as a constructive factor tending towards the occurrence of bistability. In particular, the effect of inhomogeneous broadening of the exciton optical transition, preventing the bistable behavior, may be suppressed considerably due to a fast exciton-exciton annihilation.

Maximally entangled photonic states of a two-mode field have applications in Heisenberg-limit interferometry and in photolithography where they may be used to transfer images with resolutions exceeding the Rayleigh diffraction limit. In a recent paper by one of us [C. C. Gerry, Phys. Rev. A 61, 043811 (2000)] it was shown that a nonlinear four-wave mixer could produce the requisite states for input states containing only even photon numbers. For superpositions of even number states the output is just a superposition of maximally entangled even states. In the present paper we extend the earlier work to consider both even coherent states and squeezed vacuum states as inputs and study their applications to interferometry and lithography.

We investigate the orbital angular momentum correlation of a photon pair created in a spontaneous parametric down-conversion process. We show how the conservation of the orbital angular momentum in this process results from phase matching in the nonlinear crystal.

We consider what happens to a laser when all incoherent processes are reduced to the minimum needed to keep emission irreversible. Specifically, we investigate the case where the vacuum Rabi frequency is larger than any decay rate in the laser except for the atomic polarization decay rate. Using a fully quantum description, we show that this laser can be made to go continuously from a regime with a well-defined threshold to the ideal thresholdless regime, where the photon statistics is always Poissonian even for arbitrarily small pump powers. We suggest how a proof-of-principles experiment can be realized in the microwave domain.

Two geometries are chosen to make predictions and to test the Coulomb-Born approximation against the distorted-wave Born approximation and experiment, the symmetric coplanar constant ${\Theta }_{12}$ geometry for K-shell ionization of Ag and the asymmetric coplanar geometry for L-subshell ionization of U. Even for the heaviest target, good agreement is found as long as the two electrons emerge on opposite sides of the beam axis.