The existence of the molecular ion ${\mathrm{H}}_3^{2+}$ in a magnetic field in a triangular configuration is revised. A variational method with an optimization of the form of the vector potential (gauge fixing) is used. It is shown that in the range of magnetic fields ${10}^8<B<\mathrm{}{10}^{11}\mathrm{G}$ the system $\mathrm{}\left(\mathrm{pppe}\right),$ with the protons forming an equilateral triangle perpendicular to the magnetic line, has a well-pronounced minimum in the total energy. This configuration is unstable under the decays $\left(\mathrm{H}\mathrm{atom}\right)+p+p$ and ${\mathrm{H}}_2^{+}+p.\mathrm{}$ The triangular configuration of ${\mathrm{H}}_3^{2+}$ complements ${\mathrm{H}}_3^{2+}$ in the linear configuration that exists for $B\gtrsim {10}^{10}\mathrm{G}.$

We present a two-dimensional (2D) magneto-optical trap (MOT) setup for the production of a continuous collimated beam of cold ${}^{87}\mathrm{Rb}$ atoms out of a vapor cell. The underlying physics is purely two-dimensional cooling and trapping, which allows for a high flux of up to $6\times {10}^{10}$ atoms/s and a small divergence of the resulting beam. We analyze the velocity distribution of the 2D MOT. The longitudinal velocity distribution of the atomic beam shows a broad feature (full width at half maximum $\simeq 75\hspace{0.5em}\mathrm{m}/\mathrm{s}),$ centered around 50 m/s. The dependence of the flux on laser intensity, on geometry of the trapping volume, and on pressure in the vapor cell was investigated in detail. The influence of the geometry of the 2D MOT on the mean velocity of the cold beam has been studied. We present a simple model for the velocity distribution of the flux based on rate equations describing the general features of our source.

In this work the adiabatic approximation is applied to the propagation of matter waves in confined geometries like those experimentally realized in recent atom optical experiments. Adiabatic propagation along a channel is assumed not to mix the various transverse modes. Nonadiabatic corrections arise from the potential squeezing and bending. Here we investigate the effect of the former. Detailed calculations of two-dimensional propagation are carried out both exactly and in an adiabatic approximation. This offers the possibility to analyze the validity of adiabaticity criteria. A semiclassical (sc) approach, based on the sc Massey parameter is shown to be inadequate, and the diffraction due to wave effects must be included separately. This brings in the Fresnel parameter well known from optical systems. Using these two parameters, we have an adequate understanding of adiabaticity on the system analyzed. Thus quantum adiabaticity must also take cognizance of the intrinsic diffraction of matter waves.

We consider the effects of finite temperature on the scattering of impurity atoms in a Bose-Einstein condensate, showing that the scattering rate is enhanced by the thermal atoms. Collisions can increase or decrease the impurity energy. Below the Landau velocity only the first process occurs, i.e., the collisions cool the condensate. Above the critical velocity the dissipative collisions prevail over the cooling ones for sufficiently low temperatures. These considerations are applied to a recent experiment.

The conditions required for spontaneous parametric down-conversion in a waveguide with periodic nonlinearity in the presence of an unguided pump field are established. Control of the periodic nonlinearity and the physical properties of the waveguide permits the quasiphase matching equations that describe counterpropagating guided signal and idler beams to be satisfied. We compare the tuning curves and spectral properties of such counterpropagating beams to those for copropagating beams under typical experimental conditions. We find that the counterpropagating beams exhibit a narrow bandwidth, permitting the generation of quantum states that possess discrete-frequency entanglement. Such states may be useful for experiments in quantum optics and technologies that benefit from frequency entanglement.

The behavior of a two-level atom in a half-cavity, i.e., a cavity with one mirror, is studied within the framework of a one-dimensional model with respect to spontaneous decay and resonance fluorescence. The system under consideration corresponds to the setup of a recently performed experiment [J. Eschner et al., Nature (London) $413,$ 495 (2001)] where the influence of a mirror on a fluorescing single atom was revealed. In the present work special attention is paid to the regime of large atom-mirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delay-differential equations which contain, for small atom-mirror distances, the Markovian limit with effective level shifts and decay rates leading to the phenomenon of enhancement or inhibition of spontaneous decay. Several features are recovered beyond an effective Markovian treatment, appearing in experimentally accessible quantities like the intensity or emission spectra of the scattered light.

The role of nonresonant (NR) corrections in the resonant photon scattering process on the hydrogen atom is discussed. It is shown that the average energy of the emitted photons may not coincide with the average energy of the incident photons defined by the photon source spectral function. The discrepancy is due to the NR corrections and to the interaction with the vacuum.

It is well known that any entangled mixed state in $2\otimes 2$ systems can be purified via infinite copies of the mixed state. But, can one distill a pure maximally entangled state from finite copies of a mixed state in any bipartite system by local operation and classical communication? This is more meaningful in practical application. We give a necessary and sufficient condition for this distillability. This condition requires that there exist distillable subspaces. According to this condition, one can judge easily whether a mixed state is distillable or not. We also analyze some properties of distillable subspaces, and discuss the most efficient purification protocol. Finally, we discuss the distillable enanglement of a two-qubit system for the case of finite copies.

A simple semiclassical approach, based on the investigation of the anti-Stokes line topology is presented for calculating Regge-poles trajectories for singular potentials, viz. potentials more singular than $r^{-2}$ at the origin. It uses the explicit solution of the Bohr-Sommerfeld quantization condition with the proviso that the positions of two turning points of the effective potential responsible for the Regge poles be relatively close together. We also demonstrate that due to this closeness the Regge trajectories asymptotically approach parallel equidistant straight lines with a slope of $\cot (\phi /m),$ m being the power and $\phi$ the argument of the coefficient of the potential. Illustrative results are presented for the polarization and Lennard-Jones potentials.

We report on the analysis of the line shapes in a two-color, three-photon ionization process of rubidium atoms in a magneto-optical trap. A cw and a pulsed laser are tuned almost at resonance with the $5^2{S}_{1/2}{-5\mathrm{}}^2{P}_{3/2}$ and the $5^2{P}_{3/2}{-6\mathrm{}}^2{D}_{5/2}$ transitions, respectively. The line shapes, recorded as functions of the pulsed laser wavelength, are strongly asymmetric with respect to the near resonance peak positions: in fact, they present long tails only on one side, according to the sign of the detuning of the cw laser. Moreover, the signal is overall stronger for negative than for positive detunings. Theoretical considerations based on the Autler-Townes scheme and computer simulations of the excitation-ionization dynamics show that the main source of asymmetry is the coupling of the two ionization pathways going through the $6^2{D}_{3/2}$ and $6^2{D}_{5/2}$ levels. In order to reproduce the experimental line shapes one must take into account the variability of the pulsed laser intensity and its finite coherence time.

We present a quantum analysis of the interaction of a multimode electromagnetic field with a Kerr nonlinear beam splitter. In the limit of weak nonlinearity, we use an input-output formalism to relate the statistics of the scattered fields to those of the input signal, and obtain a general input-output relation for the second order correlation function. For thermal input fields, we find that strong attenuation (optical tunneling) may lead to pronounced photon antibunching in transmission. In contrast to a linear beam splitter, the nonlinear device is predicted to strongly suppress photon-number noise.

We study high-order harmonic generation at a high pumping energy using a long focal length lens. We identify different saturation regimes of the harmonic emission, revealing the interplay between phase matching, absorption, and laser defocusing. In the optimal conditions, high conversion efficiencies are obtained, resulting in an increase of at least one order of magnitude of the harmonic energies compared to previously reported values. In xenon, microjoule energies are reached, opening new perspectives for the applications of this ultrashort coherent radiation.

We propose a “programmable” quantum device that is able to perform a specific generalized measurement from a certain set of measurements depending on a quantum state of a “program register.” In particular, we study a situation when the programmable measurement device serves for the unambiguous discrimination between nonorthogonal states. The particular pair of states that can be unambiguously discriminated is specified by the state of a program qubit. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subsets it can be very close to the optimal value.

Total cross sections for the positive and negative fragments resulting from dissociative collisions with He of vibrationally relaxed ${\mathrm{H}}_3^{+},$ ${\mathrm{D}}_3^{+},$ and ${\mathrm{HD}}_2^{+}$ molecular ions have been measured in the energy range 3–9.8 keV. The measured absolute total-cross-section values are more than one order of magnitude smaller than those previously reported with the molecular ions without vibrational relaxation. When the cross sections are plotted as a function of the projectile speed and normalized to compensate for the relative fragment yield, the values for the production of deuterium fragments are higher than those for hydrogen ions in the energy range of the present study. These results are consistent with the theoretical predictions for the behavior of triatomic molecular ions with high rovibrational excitation.

The energy loss of neutral Ne atoms with keV energies scattered under a glancing angle of incidence from a flat LiF(001) surface is investigated by means of a time-of-flight method. Under these scattering conditions, i.e., surface channeling, electronic excitations of the insulator surface as well as charge-exchange processes play a negligible role, so that the elastic energy transfer of projectiles to atoms of the target surface can be studied. Our data are interpreted by Monte Carlo computer simulations based on quantum-chemical interaction potentials. The simulations show that thermal vibrations of lattice atoms play an important role for a quantitative description of projectile energy loss under channeling. From our simulations we derive a surface Debye temperature of $250\pm 50\mathrm{K}$ for the LiF(001) surface.

We investigate the classical and quantum properties of ultracold sodium atoms in a one-dimensional optical lattice and a three-dimensional harmonic trap. The energy versus crystal momentum dispersion relation for the lowest energy band of the optical lattice, together with the harmonic potential, define an effective Hamiltonian that we use to calculate classical atom paths. When one of the symmetry axes of the harmonic trap is aligned with the optical lattice, the atoms follow stable trajectories. But tilting this symmetry axis away from the optical lattice direction creates an unusual type of mixed stable-chaotic classical dynamics, which originates from the intrinsically quantum-mechanical nature of energy bands. In this regime, the density of quantized energy levels for the system exhibits periodic fluctuations associated with both stable and unstable periodic classical orbits. One of the unstable orbits also produces well-defined scar patterns in a subset of eigenfunctions. Wave functions with distinct spatial forms are identified and related directly to particular parts of the classical phase space using a Wigner function analysis.

We explore the analogy between two-component quantum alkali-metal gases and spin-polarized helium systems. Recent experiments in trapped gases are put into the frame of the existing theory for the Castaing instability in transverse channels and the formation of homogeneous precessing domains in spin-polarized systems. Analogous effects have already been observed in spin-polarized ${}^3\mathrm{He}$ and ${}^3\mathrm{He}{-}^4\mathrm{He}$ mixture systems. The threshold effect of the confining potential on the instability is analyzed. Additional experimental possibilities for the observation of a transverse instability in a trap are discussed.

We have measured the $6s-{7p}_{1/2,3/2}$ transition probabilities in atomic cesium using a direct absorption technique. We use our result and other previously measured transition rates to derive an accurate value of the vector transition polarizability $\beta$ and, consequently, reevaluate the weak charge $Q_W.$ Our derived value $Q_W=-72.65\left(49\right)\mathrm{}$ agrees with the prediction of the standard model to within one standard deviation.

We show that a system of $2n$ identical two-level atoms interacting with n cavity photons manifests entanglement and that the set of entangled states coincides with the so-called SU(2) phase states. In particular, violation of classical realism in terms of the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimoni-Holt conditions is proved. We discuss a property of entanglement expressed in terms of local measurements. We also show that generation of entangled states in the atom-photon systems under consideration strongly depends on the choice of initial conditions and that the parasitic influence of cavity detuning can be compensated through the use of Kerr medium.

We have combined B-spline basis sets with R-matrix theory for the description of photoionization in two-electron systems and applied this combination to the study of irregularities in He photoionization when doubly excited resonances up to the $N=9\mathrm{}$ threshold of ${\mathrm{He}}^{+}$ are reached. Both total and partial photoionization cross sections have been obtained. Since the magnitude of the resonance effects is very similar for all partial cross sections, we believe that experimental investigations of photoionization cross sections leaving ${\mathrm{He}}^{+}$ in a highly excited state could provide the most information about possible long-range fluctuations in the photoionization cross sections.