The finite bandwidth of a short laser pulse often overlaps several initially unpopulated low-lying excited states of an atom. We show that when such a pulse is used to photoionize an atom, the low-lying levels may be pumped into a coherent superposition that inhibits or prevents excitation of the atom, effectively trapping population in the initial state of the atom. The existence of the effect was first noted in a numerical study of short-pulse excitation of hydrogen. Here we explore the effect through a series of simple models that demonstrate the physics of the effect in the simplest possible situations.

We have performed nonperturbative (Floquet) calculations of partial and total rates for ionization of H(1s) by linearly polarized 532-nm light at intensities up to and above the threshold intensity (1.4×${10}^{13}$ W/${\mathrm{cm}}^2$) at which the minimum number of photons required to ionize the atom increases from 6 to 7. Results are presented for partial seven- and eight-photon ionization rates, and for angular distributions in the seven-photon channel. (In accord with current conservation, the partial rates sum to the total rate.) We analyze, in some detail, the role of intermediate six-photon resonances between the 1s level and high Rydberg sublevels. Associated with each Rydberg manifold, specified by the principal quantum number (≥9), are two resonance peaks in the ionization rate; one peak is very sharp, and corresponds to an avoided crossing of the quasienergy eigenvalues originating from the 1s level and some high Rydberg sublevel, while the other peak is broad (and smaller) and corresponds to a true crossing of the eigenvalues. The intermediate resonances significantly affect the angular distributions, and reveal the orbital angular momentum quantum number of the Rydberg sublevel involved in each resonance peak. Results are presented for the ionization yield and angular distribution produced by a realistic pulse, taking into account the temporal and spatial variation of the intensity, as well as ponderomotive scattering.

A theory of degenerate four-wave mixing in the Raman-Nath approximation is developed that includes transverse effects and excitation-dependent optical material properties. A microscopic model is used for the nonlinear absorption and refractive-index changes of laser-excited semiconductors. Diffusion of the excitation density is assumed to be the dominant transverse coupling mechanism. Numerical simulations of the Raman-Nath scattering spectrum are presented for the example of room-temperature bulk GaAs using steady-state illumination. The shortcomings of the standard analysis at high excitation are demonstrated.

The main-wave one-dimensional modulational instability due to the dispersive terms of the wave equation in a free-electron laser is introduced and analyzed. We derive the appropriate dispersion relation and compare its associated growth rate with one due to wave-particle energy exchange alone, as obtained by Davidson and Wurtele under the deep trapping assumption [Phys. Fluids 30, 557 (1987)]. It is found that, depending basically on the relation between some characteristic parameters, the modulational instability may be governed by wave dispersion. We also discuss the effects of waveguides on these instabilities and the behavior of the unstable modes as a function of the mentioned characteristic parameters.

We report detailed studies of the dynamic response of spin coherence to a step input of optically resonant narrow-band laser radiation in the presence of a static transverse magnetic field. The evolution of the spins is observed with a cw optical probe beam using polarization-selective detection of the transmitted light. In extension of previous optical-pumping experiments, the dynamics of the system are studied systematically as a function of optical-resonance detuning and intensity. Our experiments are performed on the 3s ${}_{}{}^2{}_{}{}^{}S_{1/2}^{}{}_{}{}^{}$ ground state of sodium, using the $D_1$ line for optical excitation. The experimental data are compared with theoretical predictions based on a Bloch-type equation of motion for an optically driven spin system in a J=(1/2 ground state.

An algorithm for calculating the time-resolved evolution operator of a multilevel system dipole interacting with a Gaussian-shaped laser pulse is developed through use of a compound Magnus expansion in compliance with Maricq’s convergence criterion. In conjunction with the Leverrier-Bateman resolvent method, the algorithm allows the frequency spectrum for the interaction of the multilevel system with a train of identical phase-coherent Gaussian-shaped laser pulses to be readily evaluated. Furthermore, the algorithm renders possible the expeditious averaging of operator expectation values over the spectral bandwidth of the laser field. A prescription for gauging the accuracy of the algorithm is provided.

Phase operators and phase states are introduced in the Hilbert space $H_{2j+1\mathrm{}}$ associated with the SU(2) group. The phase operators obey the SU(2) algebra and play a dual role to the standard angular-momentum operators. A finite Weyl group plays a fundamental role in those ideas. In the SU(1,1) case the exponential of the phase operators is nonunitary, and the phase states form an overcomplete set which is used to formulate an analytic representation.

The spatial properties of the optical field and hence the performance of a free-electron laser depend on the fact that the electron beam, which acts as both an amplifying and a refractive medium, is transversely nonuniform. Under certain circumstances, optical guiding may be realized, where the optical field is stably confined near the electron beam and amplified along the beam over many Rayleigh ranges. We show that the three-dimensional evolution of the optical field through the interaction region can be determined by a guided mode expansion before saturation. Optical guiding occurs when the fundamental growing mode becomes dominant. The guided mode expansion is made possible by implementing the biorthogonality of the eigenmodes of the coupled electron-beam optical-wave system. The eigenmodes are found to be of vectorial form with three components; one specifies the guided optical mode and the other two describe the density and the energy modulations of the electron beam.

Dynamical transient response and longitudinal spatial evolution of the first-order phase transition are presented for intrinsic optical bistability of a system of interacting spatially distributed, coherently driven two-level atoms. It is shown that a discontinuity in the nonlinear dielectric function is established internal to the medium due to transient response to a coherent, externally applied, time-dependent driving field, following the attainment of a critical value for the input intensity. If the externally applied field intensity reaches the steady state, beyond the critical value, the discontinuity of the nonlinear dielectric function in the medium reaches a stable stationary condition and forms a spatial boundary between states of high and low polarization in the medium. Thus it is shown that intrinsic optical bistability corresponds to a spatial as well as a temporal first-order phase transition in light-matter interactions, far from thermodynamic equilibrium, where the spatial boundary between different phases is established by transient dynamical response to the incident field.

A theory is presented that describes radiative effects in beam propagation at interfaces separating two (or three) self-focusing dielectric media. The nonlinear interface is formed by two media, both of which are nonlinear, so that in both media the nonlinear wave packet representing the self-focused channel (optical beam) may be described by a soliton solution of the nonlinear Schrödinger equation (NLSE), the interface being a steplike inhomogeneity. Assuming the perturbation to be small, we apply the perturbation theory for solitons based on the inverse scattering technique and study adiabatic and radiative effects stipulated by the soliton scattering. In the adiabatic approximation the scattering is described by equations for the soliton parameters that correspond to a motion equation for a classical particle in an effective potential. The reflection coefficient of the beam (the NLSE soliton) is related to a radiation during the scattering, and calculated in the Born approximation of the perturbation theory for the cases of a single and two nonlinear interfaces. An analytical comparison with the scattering of a linear wave packet is carried out. In particular, it is demonstrated that the nonlinear reflection coefficient may be sufficiently smaller than the linear one. We predict also the nonmonotonic dependence of the single-interface reflection coefficient versus the beam power, and analytically describe the nonlinear resonant scattering by two interfaces.

The different roles played by multiplicative white and colored noise in a single-mode dye-laser model are investigated through the concept of first-passage-time (FPT) distributions. An analytic result for the skewness of the FPT distributions is presented and compared with experimental measurements and numerical simulations. The effects of multiplicative white and colored noise on the mean, variance, and coefficient of skewness are discussed. The simplified theoretical model can well describe the transient process of a dye laser.

We discuss methods for computing first-order matrix elements involving continuum wave functions variationally. Specifically, we show that the trial wave function obtained from the Kohn method will give a variational result for any first-order property. We also discuss a variational technique for computing the squared modulus of a first-order matrix element based on approximating the resolvent. We explain why the resolvent method will converge more slowly in certain cases and illustrate our remarks with calculations on a model problem.

A recent calculation of the spectrum of the n=2 states of lithiumlike uranium is improved by a more accurate treatment of the effect of finite nuclear size and a more complete calculation of higher-order corrections to Breit and mass-polarization contributions. Predictions for the 2$s_{1/2}$-2$p_{1/2}$ and 2$p_{1/2}$-2$p_{3/2}$ splittings, incorporating a phenomenological treatment of radiative corrections, are presented.

We observe that the expressions for the single-particle exchange-energy density $e_{\mathrm{x}}$ and the orbital-dependent exchange potentials $v_{\mathrm{x}{}^{\left(i\right)}}$ diverge at the nodes of the single-particle densities when the self-interaction-correction (SIC) method is applied to the conventional expression for the exchange energy $E_{\mathrm{x}}$ in the gradient-expansion approximation (GEA). An expression for $E_{\mathrm{x}{}^{\mathrm{GEA}}}$ is constructed that reduces to the conventional form in the slowly varying density limit and leads to convergent SIC expressions for $e_{\mathrm{x}}$ and $v_{\mathrm{x}{}^{\left(i\right)}}$. When this gradient-expansion-approximation self-interaction-correction (GEASIC) functional is employed in the calculation of the total energy for atoms with closed subshells, the results are significantly closer to the Hartree-Fock results than those obtained from either the GEA or the local-spin-density self-interaction-correction (LSDSIC) approximation. Furthermore, when the recently derived value for the GEA constant, i.e., (10/7 of Sham’s value, is employed, the results are found to be further improved. In addition, we show that the construction of a single (i.e., orbital-independent) Kohn-Sham potential from these GEASIC potentials leads not only to accurate exchange-only total energies but to reasonably accurate results for ${\varepsilon }_{\max }$ as compared to experimental ionization energies when the effect of correlation is included in the LSDSIC approximation.

Within the boundary-corrected first Born approximation to the exact electron-transfer amplitude, a simple model is presented for representing the complex interactions between the projectile and the target nucleus plus nonactive electrons existing in an ion-atom collision. The one-electron Hartree-Fock density derived from the occupied orbitals is used. For proton-helium scattering comparison is made with the results obtained using strictly Coulomb potentials and with other screening results.

A relationship between the location of Cooper minima and the difference between the quantum defect of the initial state and the threshold phase shift (in units of π) of the final state in excited photoionization has been suggested earlier [Phys. Rev. Lett. 48, 473 (1982)]. The existence of a shape resonance in the final state is shown to modify this relationship.

The semiclassical approximation for the ionization cross section is obtained for a generic nlm substate in the limit of low projectile velocities.

We have performed ab initio calculations of several autoionizing double-Rydberg states of Ba. We have also investigated the effects due to electron configuration mixing. These calculations are based on the Hartree-Fock atomic model. Numerical results are presented and are compared with the experimental data for msn’s and msn’d states. Although our calculated quantum-defect values are in excellent agreement with experimental values, they do not yield the same dependence of the scaled autoionization rates on the core principal quantum number as deduced from experiment.

A new approach to developing the series expansion of the density operator of quantum optics is given, and the result is applied to finding the second-order polarization vector. Coherent, number, and squeezed states are each investigated and the results compared.

Based on inequalities derived from the partial ordering by majorization, some higher-order criteria for the existence of nonclassical effects in photon statistics are introduced. These generalize the well-known concept of two-photon antibunching to many-photon antibunching. The photon-number distribution of the famous two-photon coherent state is used to illustrate these new criteria.