We investigate both experimentally and theoretically the energy and angular distribution of fast monoenergetic electrons penetrating very thin foils with a thickness of the order of a few ${\lambda }_f$, the mean free path for free-electron scattering. The measured distribution functions display three distinctive components of zero scattering, single scattering, and multiple scattering, in both angle and energy. The description in terms of a kinetic equation (or equivalently, phase-space master equation) is discussed. Its numerical application is facilitated by a multiple-scattering expansion. Good agreement between experiment and theory is found.

Analytical expressions for the matrix elements 〈v’J‖(r-$r_e$${)}^l$exp[-ma(r-${\mathrm{r}}_{\mathrm{e}}$) ]‖vJ〉 of a rotating Morse oscillator are obtained, where l is a non-negative integer and m is any number. These matrix elements are also obtained by a recursive method that obviates the need for using explicit eigenfunctions. This procedure is based on the hypervirial theorem together with the second-quantization formalism. The results permit the diagonal (v=v’,J=J’) and off-diagonal (v≠v’,J=J’) matrix elements of the operator (r-$r_e$${)}^l$ to be calculated.

The n=3 to 2 transitions in Ne-like, Na-like, and Mg-like bismuth were measured on the UNILAC accelerator at the Gesellschaft für Schwerionenforschung in Darmstadt, West Germany, using the Lawrence Livermore National Laboratory high-resolution double-crystal spectrometer. The measurements cover the region 10–14 keV with precisions of the order of 100 ppm and include electric-dipole and quadrupole transitions. Theoretical multiconfigurational Dirac-Fock calculations were made for the Ne-like system and compared to the experiment. The data exhibit energy shifts of 1.5–2.5 eV from the theory, confirming trends previously observed in tokamak experiments. The Na-like and Mg-like results are compared with unresolved transition array calculations.

Collisional relaxation of the 6s${[3/2]}_1^0$ and 6s’${[1/2]}_1^0$ $m_J$ levels of Xe has been investigated both experimentally and theoretically. Collisional disalignment and dephasing of the $m_J$ levels have been studied by measuring the pressure and laser intensity dependence of the ratio of the ionization from selectively excited $m_J$=0 and ±1 sublevels in a three-photon resonant-ionization experiment via the 6s and 6s’ states of Xe. The selective ionization is achieved by a novel use of two counterpropagating laser beams having parallel and orthogonal polarization, respectively. The pressure dependence of the ionization ratio has been calculated by solving a system of rate equations derived from a full set of density-matrix equations pertaining to the particular experimental conditions. Collisional-relaxation cross sections of the investigated levels have been estimated by fitting the calculated results to the experimental data. The ionization ratio is found to be sensitive to both disalignment and dephasing of the $m_J$ levels.

We treat the selective ionization of one component in a two-component mixture. The ionization is modeled by a two-step process involving a pair of two-level systems. The laser field exhibits stochastic fluctuations in phase, frequency, and amplitude which are described by a pre-Gaussian model. We demonstrate the effect of the parameters of the model on ionization and selectivity. The regions where perturbation theory may be applied are discussed.

We have calculated solutions of the Floquet equations for the photodetachment of an electron bound in a one-dimensional Gaussian potential, by using a discrete basis set that includes continuum waves satisfying appropriate boundary conditions. These different solutions correspond to dominant poles or to shadow poles of the scattering matrix; they originate from bound-state solutions in the zero-field limit. We show that one of the ‘‘extra’’ resonances found in a previous complex-coordinate calculation [J. N. Bardsley, A. Szöke, and M. J. Comella, J. Phys. B 21, 3899 (1988)] can be traced to a shadow pole of one of the bound states of the zero-field system. This example provides further evidence that shadow poles may play an unforeseen and possibly important role in multiphoton processes.

Combining high-resolution laser and electron spectroscopy, we have measured angular distributions of electrons emitted from autoionizing Rydberg states close to the 6p ${}_{}{}^2{}_{}{}^{}P_{1/2}^{}{}_{}{}^{}$ and 6p ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{3/2}^{}{}_{}{}^{}$ ionization limits of barium. Starting from 6sns ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ (12≤n≤100) Rydberg levels, [6$p_{1/2}$n’s${]}_{J=1\mathrm{}}$ (24≤n’≤50), [6$p_{1/2}$n’d${]}_{J=1\mathrm{}}$ (22≤n’≤49), and [6$p_{3/2}$ns${]}_{J=1\mathrm{}}$ and [6$p_{3/2}$n’d${]}_{J=1\mathrm{}}$ (11≤n’≤99) autoionizing Rydberg states were reached by exciting their 6$p_{3/2}$ns components. Alternatively, by inducing the transition 6s→6$p_{1/2}$ of the (${\mathrm{Ba}}^{+}$) ionic core, the [6$p_{1/2}$24s${]}_{J=1\mathrm{}}$ and the neighboring [6$p_{1/2}$22d${]}_{J=1\mathrm{}}$ and [6$p_{1/2}$23d${]}_{J=1\mathrm{}}$ states were excited starting from the 6s24s ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ Rydberg level.

We have observed pronounced resonances in the asymmetry parameters β corresponding to the final ionic states ${\mathrm{Ba}}^{+}$ 6s ${}_{}{}^2{}_{}{}^{}S_{1/2}^{}{}_{}{}^{}$, 5d ${}_{}{}^2{}_{}{}^{}D_{3/2}^{}{}_{}{}^{}$, and 5d ${}_{}{}^2{}_{}{}^{}D_{5/2}^{}{}_{}{}^{}$. These resonances appear in the vicinity of the [6$p_{1/2}$n’s${]}_{J=1\mathrm{}}$, [6$p_{1/2}$n’d${]}_{J=1\mathrm{}}$, and [6$p_{3/2}$n’d${]}_{J=1\mathrm{}}$ autoionizing Rydberg states and are caused by configuration interaction with the [6$p_{3/2}$ns${]}_{J=1\mathrm{}}$ Rydberg series. Above the 6p ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{1/2}^{}{}_{}{}^{}$ ionization limit the shape of the β resonances was found to be independent of the principal quantum number. In contrast, the β resonances associated with [6$p_{1/2}$n’s${]}_{J=1\mathrm{}}$ and [6$p_{1/2}$n’d${]}_{J=1\mathrm{}}$ autoionizing Rydberg states change their shapes within the contour of the [6$p_{3/2}$12s${]}_{J=1\mathrm{}}$ perturbing state. In addition to angular distributions we have measured the yield of electrons, leaving the ion in its ground state as well as the total ion yield by scanning the (third) laser across the [6$p_{3/2}$12s${]}_{J=1\mathrm{}}$ perturbing resonance.

In addition, kinetic energies of emitted electrons were measured at fixed total excitation energies falling within the contour of the perturbing resonance. Total ion yields, partial ion yields, and electron yields corresponding to the ${\mathrm{Ba}}^{+}$ ground state as well as branching ratios to the ${}_{}{}^2{}_{}{}^{}\mathrm{S}_{1/2}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{3/2}^{}{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{5/2}^{}{}_{}{}^{}$ final ionic states exhibit pronounced resonances which have been correlated with the resonances observed in the asymmetry parameters. For each final ionic state a simple multichannel quantum defect model was used to calculate the asymmetry parameter β as a function of excitation energy. Good agreement with asymmetry parameters derived from experiment was achieved.

In this work we report resonance parameters in electron-hydrogen scattering converging on the N=7 hydrogen threshold. Resonance energy positions and widths for states with both parities (${\mathrm{-}1)}^L$ and (${\mathrm{-}1)}^{L+1\mathrm{}}$ are calculated by using a method of complex-coordinate rotation. Results for intrashell resonances (both electrons occupying the same shell) below the N=7 threshold are included in this work, with approximated quantum numbers K and T assigned to each state. These results can be used to construct supermultiplet structures of the doubly excited resonances of hydrogen negative ions, and to study the triatomic (XYX) molecularlike characters.

The polarizations of sodium atoms optically pumped by a single-mode cw ring dye laser were measured as a function of the pumping power, sodium-vapor thickness, and external magnetic field for Pyrex glass and copper walls with and without dry-film coating. Observed quantities were analyzed by a simple optical pumping model in which the effect of the radiation trapping was taken into account. Assuming that the depolarization of the sodium atom was mainly induced by the local magnetic field at the sodium atom during its adsorption on the wall surface, the calculations could successfully reproduce the observed polarizations.

The mathematical form of the observables for spin relaxation of hydrogen-atom isotopes by electron spin exchange with unpolarized paramagnetic dopant gases is presented using a Boltzmann-equation approach. Hydrogen-maser, muon-spin-rotation, and stored atomic beam experiments are considered. Depending on the experimental technique, different relaxation rates are experimentally observed, but these are all related to the same intrinsic collision rate. In particular, for an unpolarized dopant, all relaxation rates are proportional to the same spin-flip cross section, and all H-atom experimental results appear to be consistent with each other, contrary to past statements in the literature.

We here present the theory of lasing without inversion for systems with a split upper laser level. We show that the effect of amplification without inversion may be realized for at least two different situations. In the first situation, the effect is due to the asymmetry of radiative characteristics of quasidegenerate transitions. In the second situation, the effect can be provided without any asymmetry and is achievable for the definite phase of the transfer of coherence between the quasidegenerate levels (quasiparametric amplification). We also show that for laser amplification without inversion, the rate (frequency) of mixing of the quasidegenerate levels should be significantly higher than the linewidths of these levels. This mixing of quasidegenerate levels can be realized by low-frequency electromagnetic radiation or by interaction with an auxiliary third level. In addition, we derive the conditions for providing laser action for such systems rigorously, and we give some specific examples for the realization of this effect in gaseous and solid-state media. One of the most promising configurations may be realized in solid-state media when two narrow quasidegenerate levels are embedded in quasifree states (low-density state conduction band). We also discuss the use of a parametric mechanism for the creation of spatial gratings and for the construction of new types of electro-optical devices.

We find that the exponential operators U=exp[-i(${\lambda }_1$${\mathit{Q}}_1$${\mathit{P}}_2$+${\lambda }^2$${\mathit{Q}}_2$${\mathit{P}}_1$] and W=exp[-i(${\lambda }_1$${\mathit{Q}}_1$${\mathit{Q}}_2$-${\lambda }_2$p${\mathrm{P}}_1$${\mathit{P}}_2$)] (where ${\lambda }_1$ and ${\lambda }_2$ are real; $P_i$ and $Q_i$ are coordinate and momentum operators, respectively; and i=1,2) are two types of generalized squeezing operators responsible for generating two types of one- and two-mode combination squeezed states, respectively. The coordinate and/or momentum representations of U and W are presented, and their normal product forms are first derived in terms of the newly developed technique of integration within an ordered product, which provides us with a direct approach to constructing these new squeezed states. The fluctuations in quadrature phases for these states are analyzed.

We present three additional theoretical signatures of quantum jumps displayed by the behavior of the Mandel Q(T) function, transient squeezing, and the time-dependent spectra, for a Raman system resonantly driven by coherent fields. As in our earlier formalism we assume that one or both of the driving fields are intense and invoke the secular approximation to derive a Markovian master equation for the atomic-density operator. This is then used to obtain analytical expressions for Q(T), transient squeezing parameters, and the time-dependent spectra. These analytical results provide further characteristics of the quantum jumps.

We present a detailed quantitative theory of transient multiwave mixing effects in a nonlinear medium produced by two incident coherent laser beams. Our theory accounts for all the relevant parameters such as laser pulse widths, medium response times, nonlinearities, interaction length, intensities, beam ratio, phase-modulation effects, losses, side diffractions, and explicitly shows how the dynamics and the multiwave mixing processes are interrelated with these parameters. The crucial role played by the diffracted beams and the time-dependent phase shifts among the beams and the interplay among the various intensity and index gratings are explicitly evaluated. In particular, the gain experienced by a weak incident probe beam via these mixing effects from the incident strong pump beam is investigated as a function of the aforementioned parameters.

Perturbative corrections are derived for the rotating-wave approximation (RWA) for the single-photon and multiphoton resonance profiles due to the interaction between a two-level molecule, with nonzero permanent dipoles, and a sinusoidal time-dependent electric field. The derivation is carried out through the use of a Floquet secular equation that introduces the effects of the permanent dipole moments into the problem through the argument, d⋅e^scrE/ω, of Bessel functions contained in molecule-laser coupling parameters; here d=${\mu }_{22}$-${\mu }_{11}$, where ${\mu }_{\mathrm{ii}}$ is the permanent dipole of molecular state i, and scrE, e^, and ω are the field strength, direction of polarization unit vector, and the circular frequency of the electromagnetic field (EMF). Expansions for the N-photon resonance profiles and the associated resonance frequencies and full widths at half maximum, in powers of the couplings between the transition and permanent dipole moments and the applied EMF, are obtained by expanding the Bessel functions in the perturbative results and are compared with those in the literature (available mostly for d=0 only). The perturbative results, and a series of exactly calculated two-level model absorption spectra, are used to discuss (1) the ability of the explicit perturbative corrections to the RWA to explain the differences between exact and RWA resonance profiles (for example, the positive or negative Bloch-Siegert shifts and dynamic backgrounds absent in the RWA), (2) the usefulness of the perturbative corrections in general, and (3) the effects of permanent dipoles on single-photon and multiphoton absorption spectra.

Based on a classical inequality, which is a generalization by Muirhead [Proc. Edinburg Math. Soc. 21, 144 (1903)] of the arithmetic-geometric mean inequality, and the expression for factorial moments of photon numbers in the P representation, the concept of two-photon antibunching is extended to involve many photons from the same mode, or from two different modes, of the radiation field. A systematic study is carried out to examine the conditions for the existence of many-photon antibunching in pair coherent states introduced recently by Agarwal [J. Opt. Soc. Am. B 5, 1940 (1988)]. It is proved analytically that the intramode antibunching always exists and that intermode antibunching occurs whenever a certain condition is satisfied by the relevant parameters; otherwise, numerical study shows that it occurs only when the eigenvalue of the pair-annihilation operator is large enough. The pair coherent states are then generalized by using a more realistic initial condition for their generation through the competition of different nonlinear processes in a two-photon medium. It is again established analytically that intramode antibunching always exists in these generalized pair coherent states; and numerical study reveals the general features of the intermode antibunching.

The radiative emission of strongly driven, two-level-like barium atoms into the modes of a confocal optical cavity is studied as a function of barium density. As the barium density is increased, the spatial profile, intensity, and spectrum of light emitted out the ends of the confocal cavity display dramatic changes indicative of a transition from fluorescence to lasing. In this novel two-level system, laser action can be explained in terms of an inversion between the dressed atom-field states or in terms of a type of stimulated hyper-Raman scattering in which atoms lase from the ground to the excited atomic state. A simple dressed-atom rate-equation analysis of this two-level-atom laser is presented. It is pointed out that this same system may provide a means of realizing two-photon-like laser action.

We show that the Langevin equation for a nonlinear-optical system may be obtained directly from the Heisenberg equation of motion for the annihilation operators, provided a certain linearization procedure is valid. We apply the technique to the parametric oscillator used to generate squeezed light and compare our results to those obtained from Fokker-Planck-type equations. We argue that, only when the Wigner, as opposed to the P or Q, representation of quantum optics is used, do we get a correct description of the underlying stochastic process. We show how the linearization procedure may be carried out to describe the operation of the parametric oscillator both below threshold, where a squeezed vacuum state results, and above threshold, where we find a squeezed coherent state. In the region of the threshold a heuristic extension of the method leads to a possible description of the system by means of a nonlinear Langevin equation.

We examine the level shifts and radiation rates of an atom near an infinite, perfectly conducting plane. Following the work of Dalibard, Dupont-Roc, and Cohen-Tannoudji [J. Phys. (Paris) 43, 1617 (1982); 45, 637 (1984)], we distinguish between the effects of radiation reaction and vacuum fluctuation. This separation provides some new physical insight into the nature of ‘‘cavity’’ modifications of atomic properties. In particular, we are able to identify the Casimir interaction as entirely due to the vacuum fluctuations.

We discuss the situation in which idler beams from two parametric down-converter crystals are allowed to interfere. We show that, when two mutually coherent signal beams derived from a common laser are injected into the down-converters, the two idler beams can become mutually coherent also. Moreover, the resulting interference pattern can, in principle, have 100% visibility when the number of injected photons per unit down-converter bandwidth is large. This is just the condition for stimulated down-conversion to dominate over spontaneous down-conversion.