Calculations of inner-shell photoionization of ${1s}^{2}2p{}^2{P}^o$ and ${1s}^{2}3p{}^2{P}^o$ Li excited states have been performed using recent developments of the R-matrix code with a 29-term target representation for incident photon energies up to 165 eV, with particular emphasis on multiple electron processes. Partial and total cross sections are given for a number of excitation processes including the lower members of 19 hollow atom resonance series. The results are compared with recent experimental measurements of the lowest ${2s2p}^2{}^2{L}^e$ resonance of even-parity hollow lithium states produced by photoexcitation of laser-excited lithium atoms. Experiment and theory are in excellent agreement on a relative scale. The enhancement of the shake-up process increases with initial state excitation, up to 500% over that of the ground state for ${1s}^{2}3p{}^2{P}^o.$ Good agreement is also obtained for K-shell photoionization when comparing branching ratios with available experimental results.

The nonadiabatic phase matrix method offers a unified, systematic treatment of vibrational dynamics in calculations of low-energy inelastic electron-molecule cross sections. This formalism uses fixed-nuclei R matrices to describe the region of configuration space near the target but—unlike its fully adiabatic counterpart, the energy-modified adiabatic method—includes nonadiabatic effects, which are important for resonant scattering and near a vibrational threshold. A most stringent test of this method is $e-{\mathrm{H}}_2$ scattering below 10 eV, where elastic and inelastic cross sections exhibit an enhancement around 3 eV which at the fixed-nuclei level involves a range of physical effects, from nonresonant to resonant scattering, as the internuclear separation varies from the smallest to largest relevant values. Here we describe an implementation of this method appropriate to such systems, an assessment of its accuracy for $e-{\mathrm{H}}_2$ scattering, and an appraisal of the importance of nonadiabatacity for the $\overrightarrow{0}1$ and $\overrightarrow{0}2$ vibrational excitations.

We have discovered theoretically that ionization of a one-dimensional quantum well by an ultrashort subcycle (δ-like) electromagnetic pulse results in photoelectrons propagating both along the field and in the opposite direction in well-separated shells whose velocities reflect quasiresonances in the ionization continuum. For both a quantum well and a three-dimensional hydrogenlike atom, a unipolar, i.e., strongly asymmetrical, δ ionization produces an approximately symmetrical, stratified photoelectron cloud.

We use photodissociation of neutral sodium clusters to measure the recoil pattern of the fragmentation products. The time dependence of the depletion curves reflects the kinetic-energy release that depends on the internal energy, or the temperature, of the cluster. The fragmentation process is treated parallel to the Weisskopf statistical theory of the disintegration of compound nuclei. From the kinetic energies of evaporation, we are able to determine the temperatures of both the daughter and mother clusters. For ${\mathrm{Na}}_{20}$ the temperature is found to be $T=440\mathrm{}\pm 65$ K, which is in good agreement with an estimate based on the evaporative ensemble model. The measured temperature is slightly larger than that found for large ionic clusters. Branching ratios for the evaporation of sodium dimers and monomers from hot neutral clusters are estimated.

We have computed the equilibrium conformations of clusters of up to 100 ions in a spherically symmetric harmonic trap by a simple optimization strategy called seeding in which ions are added or removed from previously discovered minima. In each case, we have found at least as good a minimum as was previously known and believe that we have located the global minimum. We have additionally located a number of local minima and some saddle points. A balancing condition between the Coulomb and trapping terms which all of the critical points of the potential energy surface must satisfy was used to estimate the errors in the computed energies.

Electrons at a fixed density approach a strictly correlated limit as their Coulomb interaction is scaled to infinity. We find the exact energy for strictly correlated electrons in spherical two-electron densities, and a useful gradient expansion for general densities. We also propose a model for the coupling-constant dependence, which interpolates between the weak- and strong-interaction limits. This model defines a density functional which predicts accurate ground-state correlation energies for real atoms and the two-dimensional uniform electron gas.

The velocity selective optical pumping technique has been used to obtain the Doppler-free spectrum of the $D1\mathrm{}$ transition of sodium in the temperature range 110–169 °C. The pump-induced changes in probe transmission across the Lamb dip and crossover resonances first increase and then decrease with temperature. We also observe a reversal in the relative magnitudes of these changes among some of the narrow resonances. These and other temperature-dependent features of the Doppler-free spectrum of the $D1\mathrm{}$ transition of sodium are successfully explained within the framework of the composite five-level model. The degeneracies of the ground-state composite levels and the beam depletion effects at higher temperatures play a crucial role in these investigations.

Circular and nearby Rydberg states in parallel electric and magnetic fields are studied using semiclassical and exact quantum-mechanical methods. A wide range of external field strengths is considered including regimes close to and beyond the classical ionization thresholds. When the tunneling decay rates due to the presence of the electric field are negligible, semiclassical eigenvalues and wave functions represent very good approximations. The combination of the complex-coordinate method with a discrete variable representation and the Lanczos iterative scheme provides an efficient way to calculate exactly the complex eigenvalues corresponding to the resonances emerging from the quasibound circular and nearby Rydberg states. Magnetic fields have in general a stabilizing effect, diminishing the decay rates, although there are cases showing the nonmonotonic (oscillatory) dependences of the imaginary parts of the eigenvalues with increasing magnetic field strength.

We study the counterpart to the multiphoton down-conversion in the quantized motion of a trapped atom. The Lamb-Dicke approximation leads to a divergence of the mean motional excitation in a finite interaction time for k-quantum down-conversions with $k>~3,$ analogous to the situation in the parametric approximation of nonlinear optics. We show that, in contrast to the Lamb-Dicke approximation, the correct treatment of the overlap of the atomic center-of-mass wave function and the driving laser waves leads to a proper dynamics without any divergence problem. That is, the wavy nature of both matter and light is an important physical property that cannot be neglected for describing the motional dynamics of a trapped atom, even for small Lamb-Dicke parameters.

Numerical solutions of the time-dependent Schrödinger equation for the one- and two-electron linear molecular ions ${\mathrm{H}}_3^{2+}$, ${\mathrm{H}}_3^{+}$, ${\mathrm{H}}_4^{3+},\hspace{0.5em}{\mathrm{H}}_4^{2+},$ ${\mathrm{H}}_5^{4+}$, and ${\mathrm{H}}_5^{3+}$ at fixed internuclear distance and parallel to the laser polarization have been obtained in intense laser pulses $(I>~{10}^{14}\hspace{0.5em}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2)$ in order to examine the effect of electron-electron interactions on high-order harmonic generation in extended (delocalized) systems. It is found that, in general, two-electron effects produce longer plateaus at large internuclear distances, thus enhancing harmonic generation well beyond the $I_p{+3U}_p$ atomic maximum order cutoff law, where $I_p$ is the ionization potential and $U_p$ the ponderomotive energy. A second plateau is usually found at critical distances $R_c=(\pi /2){\alpha }_0$ with a cutoff at energy $I_p{+6U}_p$ in one-electron systems and $I_p{+12U}_p$ for two-electron systems, where ${\alpha }_0$ is the ponderomotive radius. Initial delocalized states, such as molecular orbitals, are shown to create longer harmonic generation plateaus and one can therefore attribute enhancement of harmonic generation plateaus by electron repulsion due to the increased separation and delocalization of electrons in extended systems by correlation effects.

A generalized eikonal approximation in the relativistic quantum theory of Dirac particle scattering on an arbitrary electrostatic potential in the field of strong electromagnetic waves is developed. An analytic formula for the particle wave function is obtained. The essence of the approximation is that quadratic scattering potential terms $\left[\sim U^2\right(\overrightarrow{r}\left)\right]$ are considered small.

On the basis of the generalized invariant formulation, the invariant-related unitary transformation method is used to study the evolution of the quantum Dirac field in a time-dependent spatially homogeneous electric field. We solve the functional Schrödinger equation for the Dirac field and obtain the exact solutions and corresponding total phase. The total phase includes both the dynamical phase and geometric phase (Aharonov-Anandan phase).

We analyze N-level systems for population transfer by counterintuitive pulse delay, in which $N-2$ intermediate states are strongly coupled by dressing laser fields. We have carried out specific analysis for the four- and five-level systems using a dressed-state picture, as representatives for even-N- and odd-N-level systems, respectively. We have found that the dynamics of the systems are essentially different for even-N- and odd-N-level systems, and that complete population transfer assisted by dressing fields is more restrictive for even-N-level systems than for odd-N-level systems.

Numerically determined ionization rates for the field ionization of atomic hydrogen in strong and short laser pulses are presented. The laser pulse intensity reaches the so-called “barrier-suppression ionization” regime where field ionization occurs within a few half laser cycles. Comparison of our numerical results with analytical theories frequently used shows poor agreement. An empirical formula for the “barrier-suppression ionization” rate is presented. This rate reproduces very well the course of the numerically determined ground-state populations for laser pulses with different length, shape, amplitude, and frequency.

We review the information on the interactions between cold ground-state Na atoms following from ${\mathrm{Na}}_2$ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length $a_{1,-1}$ of Na atoms in the $|1,-1〉$ hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths $a_S$ and $a_T,$ $a_{1,-1},$ scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find $a_S=(19.1\mathrm{}\pm {2.1)a}_0,a_T=(65.3\mathrm{}\pm {0.9)a}_0,$ and $a_{1,-1}\mathrm{}(B=0\mathrm{})=(55.4\mathrm{}\pm {1.2)a}_0.$

The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, Phys. Rev. A 46, 1426 (1992)] and the collective atomic recoil laser (CARL) [R. Bonifacio and L. De Salvo, Nucl. Instrum. Methods Phys. Res. A 341, 360 (1994)] are compared. Both theories can be used to derive expressions for the gain experienced by a probe field interacting with an ensemble of two-level atoms that are simultaneously driven by a pump field. It is shown that the underlying formalisms of the RIR and CARL are equivalent. Differences between the RIR and CARL arise because the theories are typically applied for different ranges of the parameters appearing in the theory. The RIR limit is one in which the time derivative of the probe field amplitude, ${\mathrm{dE}}_2/dt,$ depends locally on $E_2\mathrm{}\left(t\right)\mathrm{}$ and the gain depends linearly on the atomic density, while the CARL limit is one in which ${\mathrm{dE}}_2/dt={\int }_0^t{f(t,t}^{\prime }{)E}_2{(t}^{\prime }{)dt}^{\prime },$ where f is a kernel, and the gain has a nonlinear dependence on the atomic density. Validity conditions for the RIR or CARL limits are established in terms of the various parameters characterizing the atom-field interaction. The probe gain for a probe-pump detuning equal to zero is analyzed in some detail, in order to understand how gain arises in a system which, at first glance, appears to have a symmetry that would preclude the possibility for gain. Moreover, it is shown that these calculations, carried out in perturbation theory, have a range of applicability beyond the recoil problem. Experimental possibilities for observing CARL are discussed.

Our recent approximate analytical results on the evolution of the initial state and the excitation from this state of a band of high Rydberg states by an optical pulse [Phys. Rev. A 55, 2144 (1997)] are compared with more exact numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spacing of high Rydberg states, applied in the analytical model, are removed in the numerical model. We find that the approximate analytical model is not able to reproduce all the results of the more exact numerical model, if the laser pulse is very short (i.e., much shorter that the Kepler period of the resonantly excited high Rydberg state) or very intense (i.e., when the Rabi period for the resonant transition is substantially shorter than the above Kepler period). This mainly concerns the redistribution of the population over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespective of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg states. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydberg states and the evolution of the initial state, imitating at least qualitatively the results of the numerical model in certain time and intensity scales.

We discuss how split-operator techniques may be applied to calculate normalized wave-function solutions to the three-dimensional time-dependent Dirac equation on a space-time lattice grid. This approach can be used to investigate various field-free dynamics of electron wave packets as well as the interactions of atomic electrons with space-time varying electromagnetic radiation. We demonstrate this technique by analyzing the time-resolved Klein paradox and the Zitterbewegung.

We study the laser cooling of one atom in a harmonic trap beyond the Lamb-Dicke regime. By using sequences of laser pulses of different detunings we show that the atom can be confined into just one state of the trap, either the ground state or an excited state of the harmonic potential. The latter can be achieved because under certain conditions an excited state becomes a dark state. We study the problem in one and two dimensions. For the latter case a different cooling mechanism is possible, based on the destructive interference between the effects of laser fields in different directions, which allows the creation of a variety of dark states. For both, one- and two-dimensional cases, Monte Carlo simulations of the cooling dynamics are presented.

We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ’s). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to $\pi \hspace{0.5em}(\pi$-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of ${}^3\mathrm{He}-B$ and the internal Josephson effect in ${}^3\mathrm{He}-A$ are also discussed.