The 6${\mathit{P}}_{3/2}$-6${\mathit{P}}_{1/2}$ magnetic dipole resonance transition in ${\mathrm{Pb}}^{+}$ has been observed by cw laser excitation of an ion cloud stored in a Paul trap and subsequent detection of the fluorescence radiation. From the hyperfine-structure splitting of the spectrum we determine the A factor for the ground state, A(${\mathit{P}}_{1/2}$)=12.967(13) GHz, and the excited state, A(${\mathit{P}}_{3/2}$)=0.580(3) GHz. From a contamination of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ in our sample we derived the ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}_{}^{+}{}_{}{}^{}$${\mathrm{-}}^{208}$${\mathrm{Pb}}^{+}$ isotope shift [Δν=311(14) MHz]. A small electric quadrupole admixture giving rise to a ΔF=2 component in the spectrum has been determined to be 6.4(0.5)% of the total transition amplitude.

We develop an optical-Bloch-equation approach for modeling ultracold-atom collisions in optical traps. The method incorporates a molecular picture of the atomic collision, laser-field dressing of the molecular states participating in the dynamics, and decay of the population and polarization due to spontaneous emission of excited states. The last is important to incorporate because the duration of the cold collisions is longer than the excited-state lifetimes. The relative motion of the atoms during the course of the collision is treated semiclassically with corrections for the time-dependent relative motion of the atoms in the various channels. An application of the method to Cs trap loss due to fine-structure-changing collisions is presented. Good agreement with experiment is obtained.

Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.

The matrix exponent method which we applied recently for the solution of the Bloch equations [Sov. Phys. JETP 62, 1125 (1985)] allows us to obtain in the present paper the Bloch-equation solutions when the amplitude and the phase of the exciting field are arbitrary functions of time. The solution’s validity conditions are derived. It is shown that one can also apply the matrix exponent method to the solution of the Maxwell-Bloch equations. The equation describing the evolution of the area of a pulse with modulated envelope and phase is obtained. This equation has an analytic solution which is a generalization of the well-known McCall-Hahn solution.

We investigate the force on a two-level atom interacting with intense monochromatic laser fields which are combinations of standing and traveling waves. We present a continued-fraction solution to the optical Bloch equations. Using this solution to calculate the force on an atom, we have examined the slowing and cooling of a thermal Na atomic beam. We find that the addition of a traveling wave to an intense standing wave can significantly improve the slowing rate and simultaneously decrease the final velocity of the cooled beam.

Ionization of hydrogen atoms by circularly polarized microwave radiation is investigated by means of a classical Hamiltonian model exhibiting chaotic dynamics. An analytic expression is derived for the ionization threshold as a function of the microwave frequency and field strength and is found to agree well with computed Poincaré sections in the high-scaled-frequency regime, ${\mathit{n}}_0^3$ω>1. The results underline the crucial role of core effects in the ionization of nonhydrogenic atoms. For nearly circular orbits forbidden zones of complex eccentricity partition the phase-space torus into disjoint regions.

The generalized states of a quantum system obtained by analytic continuation of a dense subset of density operators and their time evolutions are studied. The time evolution of metastable states is computed using the generalized states. Certain model theories are taken for explicit study. For factorizable Liouville operators the asymptotic states are shown to give line shapes. Nonfactorizable Liouville operators and their generators are investigated. The generic cases are shown to be contractions of suitable isometries of enveloping systems.

The well-known three-level system of Dehmelt [Bull. Am. Phys. Soc. 20, 60 (1975)] exhibits macroscopic dark periods because one of the upper levels is metastable. In this paper we show that one can also have the same phenomenon for a three-level-atom system with both upper states rapidly decaying to the ground state, provided (a) their level separation is very small and (b) their dipole moments for the ground-state transition are parallel. For suitably chosen laser parameters we also exhibit an exact nonradiating solution of the complete time development for atom plus radiation field. This leads to the surprising effect that the atom, after emission of a number of photons, will stop to fluoresce although still irradiated by the laser. The mean number of photons emitted before this switching off of the atom is calculated, as well as the mean duration of the dark periods for the general case.

We present the results of our investigations of the dynamics of a classical hydrogen atom submitted to an intense classical radiation field with a relatively low frequency as compared to the characteristic Kepler frequency of the atomic system. We discuss here the harmonic spectra which can be deduced from a Fourier analysis of the time evolution of the strongly driven atomic dipole, associated either with a single trajectory or with ensembles of trajectories evolving from an initial microcanonical distribution. The spectra obtained from ensemble-averaged atomic dipoles qualitatively reproduce the main features of those recently observed in experiments and allow, in particular, discussion of the occurrence of a plateau in the distribution of harmonic intensities as a function of their order. The possible competition between harmonic generation and multiphoton ionization, which both take place in the same laser-intensity range, is also discussed.

Quantitative results are presented for stabilization of atoms against ionization by strong laser fields over a wide range of frequencies for circular and linear polarization. With circular polarization, stabilization occurs for all frequencies. At high frequency (ω>1 a.u.), the stabilization intensity is predicted by the occurrence of photon thresholds. This mechanism gives excellent numerical agreement both with present calculations and the results of Pont and Gavrila [Phys. Rev. Lett. 65, 2362 (1990)]. A different mechanism operates for ω<1 a.u. Linear polarization differs strongly from circular polarization in many respects.

Statistics of photons emitted by a nondegenerate parametric oscillator (NDPO) operating below threshold are discussed. Analytical expressions for the generating function are obtained when two nondegenerate modes of the NDPO are mixed on a photocathode or when the intensities of the two modes are added. From the generating function, photon-counting distributions and waiting-time distributions as measured by a detector placed outside the cavity are derived. Similarities and differences between the distributions for the NDPO, the degenerate parametric oscillator, degenerate four-wave mixing, nondegenerate four-wave mixing, and thermal light are also discussed.

Semiclassical models for lasers typically incorporate a fundamental simplification called the rotating-wave approximation. In this study the rotating-wave approximation is reexamined, and its implications for the simplest problem of a steady-state laser oscillator are considered in detail. It is found that for practical laser operating conditions the errors resulting from this approximation may not always be negligible.

The anticorrelated fluctuation of the intensity of a driver beam pumping a Λ-like three-level system in the first transition from the initial to the intermediate level and that of the intensity of the radiation generated in the second transition from the intermediate to the final level initiated by noise is observed in an experimental arrangement designed for the investigation of far-infrared Dicke’s superradiance. The fluctuation is interpreted as the result of a two-photon back-and-forth transition between the initial and the final level, emitting (absorbing) and absorbing (emitting) photons in the first and the second transition depending on the direction of the two-photon transition. The influence of this two-photon back-and-forth transition on the Dicke’s superradiance is discussed.

We show theoretically that by interfering two independent, equally squeezed vacuum fields on a simple 50-50 beam splitter one can produce twin beams with perfect intensity correlation. Using a broadband theory of traveling-wave, parametric down-conversion, we calculate the noise statistics of the difference intensity of the two fields leaving the beam splitter as a function of the relative phase between the two independent squeezed fields. The noise statistics are found to vary from twin photon beams to superthermal fluctuations for a broad range of electronic detection frequencies near zero frequency (dc). In the case of ideal detectors, essentially perfect noise cancellation is predicted for arbitrary degrees of squeezing when the two beams are mixed with the proper phase. The results are fairly robust with respect to the effects of imperfect detection efficiency and unequal squeezing strengths in the two fields.

Harmonic generation and above-threshold ionization are both consequences of the nonlinear response of atoms to intense laser fields. In this paper, we examine what happens to the single-atom harmonic spectrum at high intensities, when multiphoton absorption ceases to be the dominant process of ionization. At these intensities, ionization can occur by the electron wave packet passing directly over the resultant barrier of the atomic potential and the incident electric field. In consequence of this, the harmonics produced are of a lower strength and can be swamped by the production of a large background to the harmonic spectrum. This background is caused by the ionized electron rescattering from the nucleus in the presence of the laser field.

The nonstationary (time-dependent) problem of the longitudinal modulation instability of the fundamental mode of a cylindrical waveguide with a nonlinear (Kerr-law) dielectric susceptibility is analyzed numerically and analytically using some integral relations. The cases of low and high intensities for the initial cw beam for different core radii are considered. In the case of high intensities, diffraction has an important role, and the growth-rate curves have special features corresponding to the effect of modulation instability in an unbounded nonlinear medium. These features are investigated analytically using integral relations. In the case of low intensities, diffraction is suppressed and the effect is known to be described by the nonlinear Schrödinger equation. The explicit procedure for deriving the growth-rate curves, as well as the equation for the field-envelope function based on the integral relations, is suggested for this case.

The definition of an effective polarizability associated with a dipole transition is shown to result from the use of a dyadic Green’s function in solving the electron equation of motion obtained from a classical model of spontaneous emission that takes into account the presence of nonhomogeneities in the electric permittivity. This polarizability provides access to the line shape associated with the transition; it also provides a generalized procedure for studying the effects of changes in the electromagnetic environment on line shapes, frequency shifts, and transition rates.

It is shown that many types of two-mode squeezing are based on reducible representations of the SU(1,1) or SU(2) groups. In these cases it is possible to squeeze independently each irreducible sector and generalize the concept of squeezing. The related concept of Bogoliubov quasiparticles is also generalized. The information transmitted by two-mode states is calculated as a sum of the information in the two modes and the information in the correlation. Special emphasis is given in the effect of squeezing on the correlation between the two modes. Higher correlations in three-mode systems are also studied in the context of information theory.

We study the nonlinear optical response of molecular assemblies consisting of coupled two-level molecules with arbitrary geometry including inhomogeneous broadening and exciton dephasing. An analytical expression for the third-order optical susceptibility is derived based on a certain closure of the equation-of-motion hierarchy. An exact expression for the third-order response of small crystalline aggregates with exciton population relaxation is derived, and used to show that for low relaxation rate Γ the cooperative part of the nonlinear response scales as ${\mathrm{\Gamma }}^{\mathrm{-}1/2}$ in d=1, and up to logarithmic corrections, as ${\mathrm{\Gamma }}^{\mathrm{-}1}$ in d=2 and 3. We show that cooperative enhancement is caused by exciton scattering. This is to be contrasted to other cooperative effects such as superradiance, which are related to the size of molecular coherence domains and therefore scale as ${\mathrm{\Gamma }}^{\mathrm{-}\mathit{d}/2\mathrm{}}$. In a numerical study for dipole-dipole interactions in d=1, 2, and 3 dimensions we find that the local-field approximation is valid only in selected cases, and in general fails to reproduce the magnitude and the resonance structure of ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$.

We present a complete account of our recent work [Phys. Rev. A 44, 31 (1991)] in which we investigate the theory of cancellation by interference between the absorption of three fundamental laser photons and one third-harmonic photon. The theory is formulated in terms of the density matrix so as to take detunings, dephasing, and laser bandwidth into account. The result is a theory of cancellation for finite detuning that explains how four-photon resonances can be canceled by a three-photon mechanism if there is an atomic level at near-three-photon resonance. The treatment is extended to focused beams and the interplay between phase matching and cancellation is investigated. We obtain explicit conditions for cancellation to occur, and perform calculations pertaining to a recent experiment where cancellation of 4+1 resonantly enhanced multiphoton ionization has been observed.