The formalism developed recently by Nguyen-Dang, Manoli, and Abou-Rachid [Phys. Rev. A 43, 5012 (1991)] describes nonperturbatively the dynamics of N-level systems in the presence of a laser pulse in terms of a generalized adiabatic evolution. This formalism is adapted to multichannel molecular systems, defining a time-dependent electronic representation for the dynamics of molecular excitations induced by a short, arbitrarily shaped laser pulse. For two-channel systems, this representation is parametrized by an effective pulse area and Berry phases, which depend on nuclear coordinates. Laser-induced nonadiabatic couplings are studied analytically for a hyperbolic-secant pulse. In addition, their effects are examined in numerical studies of wave packets in simple two-channel model systems driven by a short Gaussian pulse.

We analyze the time evolution of the velocity distribution of a collection of atoms decelerated by two laser beams propagating in the direction opposite to that of the atomic beam. The laser frequencies are chirped and the velocity distribution is analyzed in the appropriate moving frame. Starting from a Maxwellian configuration, the distribution evolves toward a two-peaked configuration, in which it remains for all observable times. The same phenomenon arises when the atoms are decelerated by a single laser beam which interacts simultaneously with two nearly degenerate atomic transitions.

The dynamics of a Rydberg electron in a magnetic field is examined for clues to the analytic structure of the electron wave function. A multichannel phase-amplitude formulation proves successful in the intermediate range of radial distances, where the onset of diamagnetism reshapes the Coulomb wave functions. Numerical integration of first-order equations in this range serves to illustrate the evolution of wave functions.

We examine theoretically the behavior of cross sections for laser-induced collisional energy transfer (LICET) over a wide range of detunings and laser intensities for the two-atom pairs Li-Sr and Eu-Sr which have been previously studied experimentally. These two cases are complementary in that the laser and collisional interactions enter in opposite orders, and their level structures are such as to give weak-field line shapes of opposite asymmetry and intensity shift. A three-state model is used and the Bambini-Berman formula for the weak-field quasistatic wing is verified. At high intensities the peak cross section is found to go through a maximum and the LICET profile is found to become symmetric about a shifted center with notable departures from a uniform falloff in the far quasistatic wing, apparently arising from radiative collisional interference effects.

The high-frequency recoil component is suppressed in the optical Ramsey resonance by utilizing optical pumping from the ground state to one of the magnetic sublevels of the upper state. This method requires no extra laser for suppression. With a moderate pump power and an exact tuning of the magnetic field, the high-frequency recoil component of the Ca intercombination line ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_{0\mathrm{-}}^3$${\mathit{P}}_1$ was suppressed completely.

The dynamics associated with a quasiperiodically forced Morse oscillator is studied as a classical model for molecular dissociation under external quasiperiodic electromagnetic forcing. The forcing entails destruction of phase-space barriers, allowing escape from bounded to unbounded motion. In contrast to the ubiquitous Poincaré map reduction of a periodically forced system, we derive a sequence of nonautonomous maps from the quasiperiodically forced system. We obtain a global picture of the dynamics, i.e., of transport in phase space, using a sequence of time-dependent two-dimensional lobe structures derived from the invariant homoclinic tangle of a persisting invariant saddle-type torus in a Poincaré section of an associated autonomous system phase space. Transport is specified in terms of two-dimensional lobes mapping from one to another within the sequence of lobe structures, and this provides the framework for studying basic features of molecular dissociation in the context of classical phase-space trajectories. We obtain a precise criterion for discerning between bounded and unbounded motion in the context of the forced problem. We identify and measure analytically the flux associated with the transition between bounded and unbounded motion, and study dissociation rates for a variety of initial phase-space ensembles, such as an even or weighted distribution of points in phase space, or a distribution on a particular level set of the unperturbed Hamiltonian (corresponding to a quantum state). A double-phase-slice sampling method allows exact numerical computation of dissociation rates. We compare single- and two-frequency forcing. Infinite-time average flux is maximal in a particular single-frequency limit; however, lobe penetration of the level sets of the unperturbed Hamiltonian can be maximal in the two-frequency case. The variation of lobe areas in the two-frequency problem gives one added freedom to enhance or diminish aspects of phase-space transport on finite time scales for a fixed infinite-time average flux, and for both types of forcing the geometry of lobes is relevant. The chaotic nature of the dynamics is understood in terms of a traveling horseshoe map sequence.

The quantum motion of an ion in a quadrupole radio-frequency trap is explicitly solved in terms of coherent states for the dynamical symplectic group in connection with the classical motion. The coherent states are built over extremal and nonextremal weight states. The geometrical Berry phases and the quasienergy spectrum are also obtained.

We study the electronic structures of hydrogen polymolecules ${\mathrm{H}}_{\mathit{n}}$ (n=2,3,4,. . .) in a superstrong magnetic field (B≳${10}^{12}$ G) typically found on the surface of a neutron star. Simple analytical scaling relations for several limiting cases (e.g., large n, high B field) are derived. We numerically calculate the binding energies of ${\mathrm{H}}_{\mathit{n}}$ molecules for various magnetic-field strengths. For n=2,3,4 we employ a Hartree-Fock method to determine the ground-state structure of the molecule in the Born-Oppenheimer approximation. For n=∞ (a bound infinite chain) we use a variational method. For a given magnetic-field strength, the binding energy per atom in the ${\mathrm{H}}_{\mathit{n}}$ molecule is found to approach a constant value as n increases. For typical field strengths of interest, energy saturation is essentially achieved once n exceeds 3 to 4. We also consider the structure of negative H ions in a high magnetic field. For B∼${10}^{12}$ G the dissociation energy of an atom in a hydrogen chain and the ionization potential of ${\mathrm{H}}^{\mathrm{-}}$ are smaller than the ionization potential of neutral atomic hydrogen.

We calculate the two-color ionization profile of atomic hydrogen in the presence of both a weak tunable high-frequency laser field and a low-frequency laser field of moderate intensity. The high-frequency spectroscopic light is used to probe the structure of Rydberg states dressed by the low-frequency field. We construct the photoionization spectrum from the sum of the resonance contributions by calculating the transition dipole moments between the initial state and the dressed Rydberg states, analogous to the study of photoionization in the presence of a dc field carried out by Alvarez and Silverstone [Phys. Rev. Lett. 63, 1364 (1989)].

Mechanisms of two-photon transitions of a molecular ensemble induced by stationary-phase-incoherent light beams are theoretically studied. The time evolution of the vibronic coherence created by the phase-incoherent light beams is analyzed by using the Liouville-space Feynman diagram properly taking into account vibronic dephasings. It is shown that effects of coherence between sequential transitions make a dominant contribution to the time profile of the pump-probe two-photon transition induced by the phase-incoherent light beams. The time profiles are calculated within a simple model to demonstrate differences in the time evolution of the vibronic coherence between the phase-incoherent and pulsed-coherent light spectroscopy. A theoretical consideration is also given to nonresonant two-photon fluorescence of coumarin 440 in solution excited by incoherent light beams, which shows subfemtosecond oscillation with the incident photon-field frequencies.

In this paper we calculate the intensity and carrier-density distribution inside a Fabry-Pérot-type semiconductor laser with arbitrary facet reflectivities. We derive an expression for the linewidth of such a laser operated well above threshold, when the inversion saturates and the carrier-density distribution becomes nonuniform. Results are given for the frequency and carrier-density dependence of the linewidth-enhancement factor of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As lasers. We find that saturation results in substantial nonuniformity of the distributions of the spontaneous-emission factor and the linewidth-enhancement factor. Although these factors codetermine the laser linewidth, their combined effect on the linewidth-power product is found to be negligible in most cases of practical importance. However, a small power-independent contribution to the laser linewidth is predicted for large mirror asymmetries.

Amplitude-noise reduction and diminished losses are found in a laser system in which the lower level of the usual two-level atom is replaced by a coherently prepared doublet, i.e., a λ quantum-beat configuration. The role of atomic coherence between the various levels and regular pumping is investigated. When a portion of the output signal is reflected from a phase-conjugate mirror and reinjected into the laser, the locking phase can be altered and a large phase-noise reduction can be obtained.

A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow’s pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.

We present explicit analytic expressions for adiabatic dressed states which, in suitable limits, produce complete population transfer between initial and final states of a four-state excitation chain without ever placing appreciable population into intermediate states. The population-transfer scheme is a generalization of the three-state stimulated Raman adiabatic passage that makes use of counterintuitive pulse sequences. We demonstrate analytically and numerically that the four-state system differs in a very significant qualitative way from previously studied N-state systems with odd N. In particular, we find that the presence of modest detuning from single-photon resonance is critical to the success of population transfer.

We solve numerically the dynamics of a system related to the problem of k-photon down-conversion with a quantized pump. We analyze in detail the statistical properties of the field modes. We show that the fields exhibit sub-Poissonian statistics and anticorrelation. The influence of different initial Fock states as well as their coherent superpositions on the field statistics and squeezing of the modes is analyzed in detail.

Quantum-mechanical phase distributions are investigated for some nonlinear optical phenomena which, at a classical level, involve only changes in the phase of the electric field. The phenomena investigated include reflection from a phase-conjugate mirror and propagation through an optical fiber. It is found that, while the peaks of the respective phase distributions exhibit the expected classical behavior, the widths of the phase distributions also undergo substantial changes. The relation between the input and the output phase distributions in the two cases mentioned above is investigated analytically as well as numerically. The results are compared with a phase distribution defined via the Wigner function.

In this paper we explore theoretically and experimentally the effect of fluctuations in the instantaneous frequency of a pulsed laser on the shape and position of two-photon transition spectra. The usual procedure of characterizing a pulsed laser by its frequency energy spectrum is insufficient for precision measurements. The nonlinear nature of the two-photon transition produces a systematic shift of the atomic spectrum with respect to the laser frequency spectrum that is dependent on the phase evolution of the laser pulse. In fact, any nonlinear process (e.g., second-harmonic generation) may result in displaced or distorted spectra. We also find that Fabry-Pérot filtering a laser pulse can result in large frequency chirps. We use an optical heterodyne technique to measure the instantaneous frequency of our excimer-pumped dye-laser system to an uncertainty of 1.3 MHz and determine the effect of the inherent frequency chirps of this system on a two-photon transition. We conclude that with this technique, precision nonlinear spectroscopy to the level of 1 MHz may be achieved with pulsed lasers.

Recent experiments have found abrupt changes in the intensity of laser light scattered off single ions and atoms. These abrupt changes have been interpreted as resulting from Bohr’s ‘‘quantum jumps’’ of the ion or atom from one state to another. In Bohr’s description, such quantum jumps are not predicted by the Schrödinger equation and are introduced by additional postulates into quantum theory. We consider here an alternative explanation of these experiments using only properties of solutions of the Schrödinger equation and avoiding Bohr’s added postulate.

Photon antibunching in intracavity second-harmonic generation and intracavity atomic absorption inside a high-Q optical cavity is discussed. A linearized description of quantum dynamics in the weak-field limit is used because the system size, as characterized by the number of photons ${\mathit{n}}_0$ needed to probe the nonlinearity of the system, is often quite large for realistic parameters. In both cases standard results are recalled that demonstrate that antibunching is a small effect given by ${\mathit{g}}^{\mathrm{}\left(2\right)\mathrm{}}$(0)-1≊-1/${\mathit{n}}_0$ for large values of ${\mathit{n}}_0$. We show that when higher-order terms that are usually ignored in linearized treatments are retained, ${\mathit{g}}^{\mathrm{}\left(2\right)\mathrm{}}$(0) satisfies the lower bound ${\mathit{g}}^{\mathrm{}\left(2\right)\mathrm{}}$(0)≥0 even for small values of ${\mathit{n}}_0$. It is further shown that by employing a high-Q cavity to suppress the coherent part of the spectrum of field fluctuations, perfect antibunching can be achieved even for large systems. Conditions under which this is possible are derived and curves are presented to illustrate the behavior.

Phase-space pictures have proven to be useful in analyzing standard squeezing. Here such pictures are developed for amplitude-squared squeezing, a form of higher-order squeezing. They are used to examine amplitude-squared squeezing of the squeezed vacuum state and to suggest a method of producing amplitude-squared squeezed states using a nonlinear interferometer. The phase-space representation of a variable which is a mixture of the usual amplitude-squared squeezing variables is also discussed.