Effective range theory is applied to the description of annihilation processes in positron-atom scattering. It is found that the result $Z_{\mathrm{eff}}\mathrm{}\left(k\right)\mathrm{}\sim k^{2\mathcal{l}}\left[{a+o(k}^2\right)]$ is obeyed for the $\mathcal{l}\mathrm{th}$ partial wave irrespective of whether the scattering potential includes long-range polarization potentials or not.

Analytical local potentials for modeling the electron-electron interaction in an atom reduce significantly the computational effort in electronic structure calculations. The development of such potentials has a long history, but some promising ideas have not yet been taken into account for further improvements. We determine a local electron-electron interaction potential akin to those suggested by Green et al. [Phys. Rev. 184, 1 (1969)], which are widely used in atom-ion scattering calculations, electron-capture processes, and electronic structure calculations. Generalized Yukawa-type model potentials are introduced. This leads, however, to shell-dependent local potentials, because the origin behavior of such potentials is different for different shells as has been explicated analytically [J. Neugebauer, M. Reiher, and J. Hinze, Phys. Rev. A 65, 032518 (2002)]. It is found that the parameters that characterize these local potentials can be interpolated and extrapolated reliably for different nuclear charges and different numbers of electrons. The analytical behavior of the corresponding localized Hartree-Fock potentials at the origin and at long distances is utilized in order to reduce the number of fit parameters. It turns out that the shell-dependent form of Green’s potential, which we also derive, yields results of comparable accuracy using only one shell-dependent parameter.

Recombination of ${\mathrm{Bi}}^{80+}$ ions with electrons at low relative energies has been investigated employing the electron cooler at the experimental storage ring of the Gesellschaft für Schwerionenforschung in Darmstadt. Absolute recombination rate coefficients have been determined for relative energies $E_{\mathrm{rel}}$ between $1\times {10}^{-5}$ and 10 eV. Simulations of cooling-force effects were carried out to assure the validity of these energies. In the range 10 meV $\lesssim E_{\mathrm{rel}}\lesssim 10\mathrm{eV}$ the measured rate coefficients agree well with the theory for radiative recombination (RR). Towards lower relative energies ${(E}_{\mathrm{rel}}\lesssim 10\mathrm{meV})$ the measured rate coefficients increasingly exceed the prediction of the RR theory. At the lowest accessible relative energy the ratio of measured and calculated rates reaches a factor of 3.5. The enhancement is found insensitive to a variation of the electron density from $1.6\times {10}^6$ to $4.8\times {10}^6{\mathrm{cm}}^{-3}.$

Cold collisions involving highly rotationally excited diatomic molecules are investigated. As the translational energy is lowered, the total inelastic cross section decreases sharply for specific channels where quasiresonant transitions are no longer energetically allowed. Rate coefficients are given for collisional quenching of rotationally excited ${\mathrm{H}}_2,{\mathrm{D}}_2,{\mathrm{T}}_2,$ and ${\mathrm{O}}_2$ at zero temperature. The specific rotational states that are stable against collisional relaxation would be interesting prospects for cooling and trapping. The application of collisional cooling methods together with recently developed schemes for producing rotationally hot molecules may allow high densities of ultracold “super rotors” to be achieved.

Considering the Fermi gases of alkali-metal atoms that are trapped in a harmonic potential, we study theoretically the elastic and inelastic scattering of the electrons by the trapped Fermi atoms and present the corresponding differential cross sections. We also obtain the stopping power for the cases that the electronic state as well as the center-of-mass state are excited both separately and simultaneously. It is shown that the elastic scattering process is no longer coherent in contrast to the electron scattering by the atomic Bose-Einstein condensate (BEC). For the inelastic scattering process, on the other hand, the differential cross section is found to be proportional to the 2/3 power of the number of the trapped atoms. In particular, the trapped fermionic atoms display the effect of “Fermi surface,” that is, only the energy levels near the Fermi energy have dominant contributions to the scattering process. Moreover, it is found that the stopping power scales as the 7/6 power of the atomic number. These results are fundamentally different from those of the electron scattering by the atomic BEC, mainly due to the different statistics obeyed by the trapped atomic systems.

For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived by Aftalion and Riviere [Phys. Rev. A 64, 043611 (2001)] in order to determine the shape of the vortex line according to the rotational velocity and the elongation of the condensate. The energy reflects the competition between the length of the vortex, which needs to be minimized taking into account the anisotropy of the trap, and the rotation term, which pushes the vortex along the z axis. We prove that if the condensate has the shape of a pancake, the vortex stays straight along the z axis, while in the case of a cigar, the vortex is bent. We study the local stability of the straight vortex and find an estimate for the critical angular speed at which bent vortices are nucleated. When vortices are nucleated, we prove that they must have some finite length.

We formulate a model that includes the thermal dynamics in the time evolution of a semiconductor multiple quantum-well microresonator, driven by a coherent holding beam. This model is analyzed in the case in which the active layer is electrically pumped, in such a way that the device behaves like an amplifier, but, in absence of the external beam, does not lase. The inclusion of thermal effects introduces a Hopf instability, which, in certain regions of the parameter space, dominates the behavior of the system. In this case our numerical simulations in one transverse dimension, both with periodic boundary conditions and with a spatially confined current, show that spatial patterns and cavity solitons perform a drift motion in the transverse direction. This motion develops over the slow time scale which characterizes thermal effects. We show that, by applying an appropriate phase modulation one can neutralize this effect and stabilize a cavity soliton around an equilibrium position. For larger values of the driving field intensity one meets the phenomenon of spontaneous formation of cavity solitons by thermal activation, without use of a writing beam, in accord with experimental observations.

Atomic ensembles have shown to be a promising candidate for implementations of quantum information processing by many recently discovered schemes. All these schemes are based on the interaction between optical beams and atomic ensembles. For description of these interactions, one assumed either a cavity-QED model or a one-dimensional light propagation model, which is still inadequate for a full prediction and understanding of most of the current experimental efforts that are actually taken in the three-dimensional free space. Here, we propose a perturbative theory to describe the three-dimensional effects in interaction between atomic ensembles and free-space light with a level configuration important for several applications. The calculations reveal some significant effects that were not known before from the other approaches, such as the inherent mode-mismatching noise and the optimal mode-matching conditions. The three-dimensional theory confirms the collective enhancement of the signal-to-noise ratio which is believed to be one of the main advantages of the ensemble-based quantum information processing schemes, however, it also shows that this enhancement needs to be understood in a more subtle way with an appropriate mode-matching method.

We investigate the utility of nonclassical states of simple harmonic oscillators, particularly a superposition of coherent states, for sensitive force detection. We find that like squeezed states, a superposition of coherent states allows displacement measurements at the Heisenberg limit. Entangling many superpositions of coherent states offers a significant advantage over a single-mode superposition state with the same mean photon number.

We report the experimental realization of a recently discovered quantum-information protocol by Peres implying an apparent nonlocal quantum mechanical retrodiction effect. The demonstration is carried out by a quantum optical method by which each singlet entangled state is physically implemented by a two-dimensional subspace of Fock states of a mode of the electromagnetic field, specifically the space spanned by the vacuum and the one-photon state, along lines suggested recently by E. Knill et al. [Nature (London) 409, 46 (2001)] and by M. Duan et al. [ibid. 414, 413 (2001)].

In a recent work [J. P. Hansen et al., Phys. Rev. A 64, 033418 (2001)], we demonstrated that classical methods provide a fair description of excitation and ionization dynamics of $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ in few-cycle pulses of frequency comparable to the binding energy of the atom and with intensities well below one atomic unit. Here, we extend our studies of classical and quantum dynamics to higher frequencies but similar intensities. For single-cycle pulses with a period smaller than the period of oscillation in the ground state, we observe large differences between quantum and classical physics even in the over-the-barrier regime. As a consequence, care should be exercised when applying classical concepts to the interpretation and understanding of the dynamics of atoms interacting with short pulsed intense lasers in the high-frequency regime.

We have previously reported experimental results on the trap-loss rate for a mixed species magneto-optical trap involving a pair of Na and Rb atoms [Phys. Rev. A 59, R23 (1999)]. The predicted dependence for the heteronuclear trap-loss rate as a function of laser detuning assuming a colliding pair of ground-state–excited-state atoms fails to explain the experimental results. Further investigation has shown that our observations are consistent if one assumes a loss channel involving an excited state–excited-state colliding pair of atoms. Here we present the model and discuss the physical interpretation applied to our previous experimental results. The present interpretation opens up other ways to understand the trap-loss mechanisms.

An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling and strong-coupling limits. This solution is shown to be more accurate than the optimized Gaussian approximation as well as the Thomas-Fermi approximation. The derivation of the solution is based on the self-similar approximation theory. The possibility of obtaining interpolation formulas in the case of nonspherical traps is discussed.

We have succeeded in simultaneously trapping a fermion and boson isotope pair of ytterbium (Yb) in a far off-resonant trap (FORT). We have found evidence of elastic cross collisions between fermions and bosons, and performed a successful sympathetic cooling of the fermions. We could also enhance the loading of the fermions ${}^{171}\mathrm{Yb}$ in the crossing region in a crossed FORT via cross collisions between the fermions ${}^{171}\mathrm{Yb}$ and the bosons ${}^{174}\mathrm{Yb}.$

We demonstrated the energy scaling of high-order harmonics using a self-guided beam under the phase-matched condition. By adjusting the argon gas density and pump laser focusing condition, a total output harmonic energy as high as $0.7\hspace{0.5em}\mu \mathrm{J}$ was obtained in the spectral region of 34.8 to 25.8 nm (the corresponding order of the 23rd to 31st harmonic), while the 27th-order harmonic (29.6 nm) energy attained was as high as $0.3\hspace{0.5em}\mu \mathrm{J}.$

We investigate the evolution of a single qubit subject to a continuous unitary “free” dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at certain times. The interrupting influence is represented by an operation, which is assumed to equivalently describe a nonselective weak measurement. It may be decomposed into the action of a positive operator, which in the case of a measurement represents the pure measurement part, followed by a unitary backaction depending on the result of the measurement (feedback). Equations of motion for the state evolution are derived in the form of difference equations. In the lowest order, the stochastic feedbacks cause a modification of the “free” Hamiltonian by an additional appropriately averaged Hamiltonian. The positive operator specifies a decoherence rate and results in a decoherence term. Two higher-order terms are discussed. One shows decoherence induced by the stochastic feedbacks and the other represents generalized friction. The selective evolution is investigated. In order to bridge the gap between sequential and continuous measurements, the continuum limit to a master equation is performed. Additional correcting higher-order terms are worked out in the Appendixes.

We construct an optimal quantum universal variable-length code that achieves the admissible minimum rate, i.e., our code is used for any probability distribution of quantum states. Its probability of exceeding the admissible minimum rate exponentially goes to 0. Our code is optimal in the sense of its exponent. In addition, its average error asymptotically tends to 0.

Binary collisions between ions and electrons in an external magnetic field are treated in second-order perturbation theory, starting from the unperturbed helical motion of the electrons. For the transfer of relative velocity in a collision, three kinematical regimes are identified, depending on the relative size of the cyclotron radius, the pitch of the helices, and the distance of the closest approach. The magnetic field suppresses the velocity transfer in the transverse direction, but it enhances the longitudinal velocity transfer, provided that the ion velocity itself has a transverse component. In order to relate the velocity transfer to the energy loss of the ions, particular attention must be paid to the nonconservation of the center-of-mass motion in a magnetic field. Hard collisions are accounted for by regularizing the energy transfer at small distances. For ions interacting with monochromatic beams closed expressions for the energy loss can be derived, which are averaged with respect to the velocity distribution of the electrons. The magnetic field reduces the energy loss for ion motion parallel to the magnetic field while it enhances the energy loss for transverse ion motion.

Seventeen-state close-coupling calculations are performed on the photoionization near the $1s-2p$ resonance region from the terms belonging to the configurations ${1s}^2{2s}^2,$ ${1s}^{2}2s2p,$ and ${1s}^2{2p}^2,$ of Be-like neon ions, Ne VII. The calculations include the total and partial photoionization cross sections and the contributions of the main ionization channels to the partial cross sections. The resonance energies, widths, and branching ratios of the $1s-2p$ core-excited states are determined from these cross sections. The resonance oscillator strengths of the corresponding $1s-2p$ transitions from Ne VII low-lying states are also obtained by integrating the photoionization cross sections. Our theoretical resonance energies, widths, and branching ratios are compared with existing experiments on the Auger spectra and other theoretical results. The calculated resonance energies are in rather good agreement with the latest experiment on the Auger spectra. For the autoionization width, good agreement is also found with recent theoretical results wherever available obtained using a saddle-point complex-rotation method.