The close-coupling method is applied to the ${\mathrm{Ps}}^{-}$ system. The scattering phase shifts of $e^{-}+\mathrm{Ps}$ scatterings and the photodetachment cross sections of ${\mathrm{Ps}}^{-}$ are calculated below the first excitation threshold. The scattering equations are solved using a B-spline method. Well converged phase shifts are obtained for s-, p- and d-orbital expansions. The photodetachment cross sections are in good convergence and are nearly gauge invariant.

Through an exact solution of the time-dependent Schrödinger equation for an electron in a static electric field plus the time-dependent electric field of the detaching radiation, the photodetachment cross section of ${\mathrm{H}}^{\mathrm{-}}$ is calculated. Careful attention is paid to ensuring proper limiting behavior as the frequency of the time-dependent field goes to zero. We do not find observable effects of a cross term between the two fields on the detachment cross section. Our results point to possible gauge dependence and other difficulties of S-matrix formulations of multiphoton detachment and ionization.

Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.

Exploring the close analogy between classical electrodynamics and quantum electrodynamics, we have developed a general algorithm to calculate the spontaneous emission rate and the spontaneous emission factor in a microcavity of arbitrary geometry. Both the emission spectrum of the light source and the decay of the electromagnetic modes are taken into account in our model. Assuming a Lorentzian line shape for the emission spectrum, we apply our algorithm to calculate the spontaneous emission rate and the spontaneous emission factor in a dielectric microdisk cavity. We find that the spontaneous emission characteristics in the microdisk are greatly modified by the whispering gallery modes. The influence of the spectral linewidth of the light source on the spontaneous emission rate and the spontaneous emission factor is also discussed.

A method of renormalization-group symmetries is applied for analytical solution to the nonlinear Schrödinger equation which describes the electromagnetic beam self-focusing in a medium with a cubic nonlinearity. The boundary-value problem for the incident Gaussian light beam has been solved analytically in a cylindrical geometry although the method could be applied to other boundary conditions too. The solution describes a detailed structure of wave self-focusing and its global characteristics such as the light power trapped in the singularity, laser beam radius, and self-focusing length. A comparison with the results of previous studies demonstrates advantages of the renormalization-group symmetry method as a tool for the nonlinear electrodynamics theory.

A corrugated magnetic reflector is realized by adding a bias field to a static magnetic mirror. This permits real-time manipulation of a cold-atom cloud on time scales down to 100 μs. We show that rotation of the bias field generates a traveling corrugation of adjustable depth and velocity. Momentum is transferred from the traveling wave to the atoms, resulting in a displacement of the cloud that depends on the wave velocity. This is a step towards a new method of manipulation in which neutral atoms could be transported across the surface by surfing along the moving wave.

We extend the mean-field theory of superfluorescence for a gas system in a bidirectional ring cavity configuration to include atomic center-of-mass motion. This analysis shows that, whereas for stationary atoms the radiation evolution is independent of the sign of the detuning from atomic resonance, for atoms moving under the action of the radiative forces the radiation evolution is strongly dependent on the sign of the detuning. This previously unpredicted behavior is due to the spontaneous formation of a ponderomotive potential simultaneous with the superfluorescent radiation pulses. This potential causes the formation of a strong density grating in the atomic sample.

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. This is connected to the problem of the two-dimensional hydrogenlike atom in the presence of an external magnetic field. For weak magnetic fields, the approximate energy values are obtained by a semiclassical method. In the case with strong magnetic fields, we present the exact recursion relations that determine the coefficients of the series expansion of wave functions, the possible energies, and the magnetic fields. It is found that analytic solutions are possible for a denumerably infinite set of magnetic field strengths. This system thus furnishes an example of the so-called quasiexactly solvable models. A distinctive feature in the Dirac case is that, depending on the strength of the Coulomb field, not all total angular momentum quantum numbers allow exact solutions with wave functions in reasonable polynomial forms. Solutions in the nonrelativistic limit with both attractive and repulsive Coulomb fields are briefly discussed by means of the method of factorization.

The trajectory predicted by Bohm’s quantum equation of motion, using an initially angle-localized minimum-uncertainty Gaussian wave packet, is compared with the trajectory predicted by Newton’s classical equation of motion for a macroscopic periodically kicked pendulum system. We find that, in violation of the strong form of the correspondence principle, the Bohmian trajectory does not, in general, agree or correspond with the Newtonian trajectory for all times. The Bohm-Newton trajectory correspondence holds as long as the wave packet remains localized in angle. Delocalization of the wave packet in angle triggers the breakdown of the correspondence. The breakdown occurs exponentially quickly if either the Newtonian trajectory that initially coincides with the Bohmian trajectory or one of its classical neighbors is chaotic. In contrast, the breakdown occurs much slower if neither the Newtonian trajectory nor its neighbors are chaotic. These behaviors of the Bohm-Newton trajectory correspondence are generic, or universal, for the class of macroscopic Hamiltonian dynamical systems with bound coordinate space since the kick pendulum is a prototypical member. We predict that neither Bohm’s equation of motion nor Newton’s correctly predicts the experimentally observed and measured trajectory of a macroscopic system after the breakdown of the correspondence, implying that the all-times agreement required by the strong form of the correspondence principle is unnecessary.

We describe strategies for quantum-state estimation based on self-learning algorithms. In contrast to the optimal estimation procedures proposed earlier, our schemes rely on measurements performed separately on each quantum system in a finite ensemble. We numerically simulate our strategies in the case of finite ensembles of qubits and compare the resulting average fidelities to the fidelity of optimal quantum-state estimation.

We have measured the time taken for a magnetically trapped cloud of cold cesium atoms in the ${(F=3,m}_F=-3)$ ground state to rethermalize from a nonequilibrium spatial and velocity distribution. From these measurements we infer the dependences of the elastic scattering cross section on temperature and magnetic field in the ranges $1-30\mu \mathrm{K}$ and 0.05–2.0 mT, respectively. We determine a lower bound on the magnitude of the $(3,-3)+(3,-3)$ s-wave scattering length of ${940a}_0.$

Electron capture resulting from collisions of ${\mathrm{H}}^{+}$ ions with CO molecules has been investigated based on the molecular representation within the fully quantum-mechanical formalism below 10 keV/u. Three different molecular configurations have been considered for collision dynamics, i.e., (i) the proton approaches the center of mass of the CO molecule in the perpendicular configuration, (ii) the proton approaches the C atom in the collinear configuration, and (iii) the proton approaches the O atom in the collinear configuration. Electron-capture dynamics and corresponding capture cross sections depend very sensitively on the molecular configuration, thus revealing a strong steric effect. The capture cross section from the CO electronic ground state is about $1.3\times {10}^{-15}{\mathrm{cm}}^2$ at 10 keV/u, which is in good agreement with experimental findings. Differential cross sections (DCS’s) for three molecular orientations have been examined both for elastic and electron-capture processes, and the DCS averaged over all the configurations was found to agree well with a measurement from 0.02° to 1° at 1.5 keV/u.

Total cross sections for quenching of low-n Rydberg states of Li $(n<\mathrm{}10,$ $l=0)$ in collision with the ground state He have been calculated in the low-energy region $(v<~0.1\mathrm{a}.\mathrm{u}.\mathrm{})$ by employing the molecular orbital approximation. Results for the total depopulation of the parent states, along with those for excitation and de-excitation mechanisms have been presented. Present cross sections exhibit the low-energy Stueckelberg oscillations. Using a model two-state calculation we present a detailed comparative study between the quantum-mechanical and semiclassical findings. Except at very low energies, the semiclassical cross sections agree nicely with their quantum counterparts. The reaction rates at thermal energies are also reported.

Nonlinear relativistic ionization phenomena induced by a strong laser radiation with elliptical polarization are considered. The starting point is the classical relativistic action for a free electron moving in the electromagnetic field created by a strong laser beam. The application of the relativistic action to the classical barrier-suppression ionization is briefly discussed. Further, the relativistic version of the Landau-Dykhne formula is employed to consider the semiclassical subbarrier ionization. Simple analytical expressions have been found for (i) the rates of the strong-field nonlinear ionization including relativistic initial and final state effects, (ii) the most probable value of the components of the photoelectron final state momentum, (iii) the most probable direction of photoelectron emission, and (iv) the distribution of the photoelectron momentum near its maximum value.

We predict that vibration-rotation coupling in diatomic molecules will lead to cross-revivals of vibrational wave packets—provided lifetime effects and collisions can be eliminated. Analytical conditions for full cross-revivals of systems governed by the minimal Hamiltonian exhibiting rotation-vibration coupling are found and the influence of higher-order cross terms is studied. Finally, generality of the phenomenon of molecular cross-revival is investigated by doing numerical calculations for several molecular potentials and temperatures. For expansion-cooled molecules strong cross-revivals are obtained in all cases. In the particular example of cold ${\mathrm{Li}}_2$ in the $A^1{\Sigma }_u^{+}$ state nearly complete cross-revivals are observed. These cross-revivals survive thermal averaging and reach at an initial temperature of 900 K an amplitude which is close to half the beat amplitude at zero time delay. The “rotational cooling” mechanism facilitating this, by reducing the effective rotational temperature of the wave packet, is explained in terms of the molecular rotational constants and laser wavelength bandwidth.

The finite depth $\mathcal{E}$ of an atom trap results in an upper bound for the energy transfer in collisions with the background gas that will result in heating but not in loss of an atom. The energy transfer rate is accurately predicted as function of the well depth by applying a versatile semiempirical model function for the small-angle differential cross section, covering the full range from pure diffractive scattering to classical scattering. Simple scaling laws for the energy transfer rate are presented that can be readily applied. For the diffraction dominated regime we find an energy transfer rate proportional to $(\mathcal{E}/{\mathcal{E}}_{\mathrm{ref}}{)}^2$ with ${\mathcal{E}}_{\mathrm{ref}}{=(k}_B{T}_b\hspace{0.5em}{\theta }_0^2/4),$ a system-dependent energy determined by the ambient temperature $T_b$ and the diffraction angle ${\theta }_0.$ In the classical regime we find the usual result of an energy transfer rate proportional to $(\mathcal{E}/{\mathcal{E}}_{\mathrm{ref}}{)}^{5/6}.$

We show that there are three possible phases for a spin-2 spinor Bose condensate, one more compared to the spin-1 case. The order parameters of these phases are the spontaneous magnetization and the singlet pair amplitude. Current estimates of scattering lengths show that all three phases have realizations in optically trapped alkali atoms. There is also a one-to-one correspondence between the structure of a spin-2 spinor Bose condensate and that of a d-wave BCS superfluid.

In this article, we propose a simple approach to deal with the fluorescence of a quasi-three-level system in $\Lambda$ configuration in which one of the “levels” is actually a band with possibly a large width. By solving this quasi-three-level molecule model, we obtain an analytical expression for the microcavity-modified fluorescence decay rate suitable for arbitrary cavities with any geometrical shape under a strong coupling condition. Applying the general result to a microsphere, we express explicitly the fluorescence decay rate’s dependence on the cavity radius, emission linewidth, and the quantities characterizing the involved cavity modes, and find it in remarkable agreement with the recent fluorescence experiment by Barnes et al. [Phys. Rev. Lett. 76, 3931 (1996)]. In addition we briefly discuss the suitability of the approach for other microcavity-modified optical processes such as lasing and Raman scattering.

The Ni-like Gd X-ray laser is investigated in detail primarily through a 1.5-dimensional combined fluid and atomic physics code EHYBRID. Directly measurable parameters are calculated using a combined optical raytracing and saturation calculation code RAYTRACE. As experimental data for Gd are not widely available, we compare the predictions of our model with experimental results for Sm. There has been considerable success reproducing the results of experiment with this model. Much has been made of the similarities between the operating conditions for Ne- and Ni-like lasers. This approach has been quite successful from an experimental viewpoint. In this paper we consider the degree of similarity. Areas of difference are highlighted particularly the relative stability of the lasant ion stages.

We report an experimental study of coherent population trapping and four-wave mixing via multilevel dark states prepared in the ground hyperfine states of ${}^{87}\mathrm{Rb}$ atoms. The dark states are created by Λ-type coupling chains driven by a linearly polarized pump laser tuned to the $D_1$ $F=2\mathrm{}\leftrightarrow F^{\prime }=1\mathrm{}$ transition. The Doppler shift in the coupling chains is compensated by the left- and right-circularly polarized components of the pump laser. The multilevel dark states are explored by a probe laser and their existence is manifested by a strong dependence of the probe excitation and four-wave-mixing emission on the probe polarization. Our experiment shows that coherent population trapping in multilevel dark states of a degenerate atomic system should be useful in the coherence control of optical nonlinearity.