We have recently found that the hydrogen atom in a circularly polarized (CP) microwave field possesses an approximate dynamical symmetry and its bounded motion can be well described by a three-dimensional integrable (but nonseparable) Hamiltonian function with a velocity-dependent potential [Raković and Chu, Phys. Rev. A 50, 5077 (1994)]. This finding provides a theoretical foundation for the understanding of the origin of the regularity of Rydberg atom dynamics in CP fields. We describe here the phase space topology of the three-dimensional integrable system relevant to the microwave ionization of the hydrogen atoms in CP fields. Using the integrable system as an approximation to the real system and with the use of the two additional integrals of motion, we are able to trace the deformation of the tori up to the point of bifurcation (ionization). From this, we have determined the classical ionization-field threshold law ${\mathit{f}}_{\mathrm{th}}$≊1/${\mathit{cn}}_0^4$, where ${\mathit{n}}_0$ is the principal quantum number of the initial state of the hydrogen atom and c is almost a constant (≊6 a.u.). These results are in good accord with the existing experimental observations.

Ultrashort, unipolar electric-field pulses have been used to coherently redistribute population between Rydberg states in sodium. The population in several Rydberg states is recorded simultaneously as a function of peak field. In addition, two temporally separated pulses have been used to interferometrically characterize the redistribution process. In the lowest fields, the experimental results are in agreement with the predictions of lowest-order perturbation theory. At slightly higher fields, still well below the ionization threshold, the redistribution process becomes nonperturbative, and a numerical integration of the time-dependent Schrödinger equation must be used to achieve partial agreement between theory and experiment.

We discuss a scheme suitable for the study of strong-field effects on the excitation spectrum of the laser-induced collisional energy-transfer process. The use of a weak radiation field, to induce the interatomic transition, and a strong radiation field, to modify the energy-level position, is found to give rise to a splitting of the resonance peak. The position and the relative intensity of the two spectral components are strongly dependent on the intensity and detuning of the strong field. Line-shape calculations performed for the Eu-Sr system show that the effect is expected to be detectable even for moderate intensities of the strong field.

We demonstrate the laser cooling of an alkali atomic beam using the D1 transition. Stark-effect frequency tuning is used to compensate the Doppler shift. A cesium beam as slow as 20 m/sec has been obtained. We also demonstrate the simultaneous transverse and longitudinal cooling in the deceleration region before the atoms reach their final velocity. This technique could be used to develop a cold atomic beam with high intensity.

We study photonic band gaps in a one-dimensional optical lattice of laser-cooled trapped atoms. We solve for the self-consistent equilibrium positions of the atoms, accounting for the backaction of the atoms on the trapping beams. This solution depends strongly on the sign of the trapping laser detuning. For red-detuned trapping lasers, the resulting lattice exhibits a one-dimensional photonic band gap for frequencies between the trapping laser frequency and the atomic resonance. For blue detuning the stop band extends symmetrically about resonance, typically for hundreds of atomic linewidths, except for the small region between atomic resonance and the lattice frequency, which is excluded. We calculate the reflection spectrum for a lattice of Cs atoms for various trapping laser detunings and interpret its behavior as a function of the lattice size and density. For a mean density of ${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}3}$, and 1000 planes, 55% reflection of a weak probe beam should be observed. We also consider Bragg scattering in a three-dimensional optical lattice as a means of probing the long-range order in the atomic density correlation function.

We present a theory of the two-photon ionization and autoionization in aluminum in the uv wavelength range pertaining to recent experimental results [H. Stapelfeldt, P. Balling, and H. K. Haugen, Phys. Rev. A 46, 1177 (1992)]. The calculation is based on Dirac-Fock theory and shows generally good agreement with experiment.

The stability regions of an ion in a two-dimensional Paul trap are studied by a quantum-mechanical treatment, which is very important for the experiment when the temperature is fairly low. The result is compared with a classical one published before by Paul [Rev. Mod. Phys. 62, 531 (1990)]. It is shown that their properties are quite similar and their differences are related to the quantum effect, which cannot be included within a classical description. All of these properties are discussed in detail.

We present an investigation of the cesium magneto-optical trap, with particular regard to the best combination of atomic density and temperature that can be produced. Conditions in the trap depend on four independent parameters: the detuning and intensity of the light, the gradient of the magnetic field, and the number of atoms trapped. We have varied all these parameters and measured the temperature and density distribution of the trapped cloud. Both the nonlinear variation with position of the restoring force and the reabsorption of photons scattered in the cloud limit the maximum density, and we present an empirical model that takes this into account. This in turn limits the density in phase space ρ (defined as the number of atoms in a box with sides of one thermal de Broglie wavelength). We have observed a maximum ρ=(1.5±0.5)×${10}^{\mathrm{-}5}$, with a spatial density of about 2×${10}^{11}$ atoms/${\mathrm{cm}}^3$.

A subharmonic resonance occurs on irradiation of a three-level (Λ) system by two bichromatic fields when an integer multiple of the common frequency difference matches the Raman detuning between the two lower levels. The occurrence of these multiphoton resonances requires saturation of the Raman transition. The three-level model is applied in order to understand recent experimental studies of subharmonic Raman resonances between vibrational states of optically trapped atoms. I explain the difference between these resonances and the well-known velocity-tuned (Doppleron) resonances in two-level atoms by considering a two-state model with the excited state eliminated. I finally point out a Sisyphus cooling mechanism that is entirely dependent on an additional relaxation of the Raman coherence, comparable to collision-induced resonances.

An efficient time-dependent method is presented to obtain, at any time, the nuclear wave functions corresponding to the intense field photodissociation of homonuclear ions, which possess a divergent electronic transition moment, as the internuclear separation increases. It consists of splitting the wave functions into two parts, one part corresponding to the internal region and the second to the asymptotic part. The propagation of the wave packet’s asymptotic part is done analytically even during the field interaction. The advantage of the method presented here is that the extension of the grid, needed to represent the wave packets, is fixed once and for all. Therefore, the numerical effort is reduced to the propagation in a previously fixed region of space, regardless of the duration of the field. The method is applied to calculate the proton kinetic energy spectrum in the photodissociation of the ${\mathrm{H}}_2^{+}$ molecule.

We present a calculation of the probe-transmission spectrum of a two-dimensional optical lattice, in which atoms are cooled by a pair of standing-wave fields with perpendicular polarizations within the plane of incidence. A probe laser is directed along the axis of one of the cooling fields, with a polarization parallel to the incident plane of the cooling fields. The calculated probe-transmission spectrum exhibits both sidebands, which originate from stimulated Raman transitions between different vibrational states of the atoms in the molasses, and a central resonance structure, which originates from Rayleigh resonances among these vibrational states. We also include in our calculation a possible misalignment of the probe field relative to the axis of the cooling field. It is shown that the effrects of the probe misalignment can lead to significant modifications to the central resonance signal.

We study multiple ionization of atoms by a strong laser field using a time-dependent approach based on the Thomas-Fermi model. The evolution of the electron density under the influence of a transient, linearly polarized radiation field is determined by numerical solution of hydrodynamic equations on a two-dimensional grid. We find a threshold ‘‘appearance intensity’’ for a given charge state, i.e., the laser intensity at which such a charge state first appears, which is in reasonable agreement with experimental results for high charge states.

We study the self-pulsing solutions which emerge from the steady state via a Hopf bifurcation in a laser with intracavity second-harmonic generation. Our main result is the construction of periodic solutions and the derivation of explicit amplitude equations which rule the stability of these periodic solutions. In this way, we have been able to substantiate the classification into four classes of periodic solutions with simple phase and amplitude relations. Near the Hopf bifurcation, the periodic solutions are stable and the sum over the individual mode intensities is not periodic but constant, a signature of antiphase dynamics in this system. A fifth class of periodic solutions has been found numerically where the sum over all modal intensities is periodic. Finally, a numerical analysis complements these results and shows that the phase relations which characterize antiphase dynamics are maintained throughout the route to chaos and in the first chaotic domain when the pump parameter is increased.

An exactly solvable lattice version of the Maxwell-Bloch system, which describes resonant interaction of light with a medium of two-level atoms, is derived. The Poisson structures of both the discrete and the continuum limit models are analyzed with and without inhomogeneous broadening, and quantizations of all of these cases are described. The eigenenergy spectra are given.

We solve a problem of spontaneous emission from an atom trapped in a harmonic binding potential for several initial states of the center of mass: the ground state, the thermal state, and the coherent state. The spectral and temporal properties of the emitted light are discussed. We stress the role of the Doppler shift.

We find that the natural antiphasing tendency in linear solid-state laser arrays can be overcome by an injected field, even if the N elements are not identical. We derive a condition for full entrainment that agrees well with numerical simulations using experimentally accessible parameters. The resulting output intensity saturates near the maximum coherent value of ${\mathit{N}}^2$ times that of a single laser. We find that the entrained output can be modulated in a prescribed manner by a suitable choice of the injected field.

We analyze the coupling between the fluctuations of an atomic beam incident on an evanescent wave mirror and the fluctuations of the laser beam producing the evanescent potential barrier. We show that this coupling is equivalent to a crossed Kerr effect between an atomic field and a light field, and that the consistency of the theory requires that both fields be subject to symmetrical commutation relations and quantum fluctuations. We show in particular that the phase shift undergone by the light field during the atomic reflection process permits a quantum nondemolition measurement of the incident atomic intensity.

The statistical properties of a charged oscillator in the presence of a uniform magnetic field are investigated for the case of a time-dependent electromagnetic field. Quite general results are obtained when the time dependence of the external field is not specified. As an example, an oscillating external field is considered. It is found that, depending upon the parameters, this system can show many nonclassical features, such as sub-Poissonian statistics and squeezing.

The theory of photodetection and quantum-optical coherence is formulated in the Heisenberg picture and in such a way that the causal propagation of fields at the velocity of light is manifest. Objections to the standard theory, based on a putative violation of causality, are shown to be unfounded, as is the notion that normal ordering is essential for the elimination of an infinite contribution from the vacuum field. In a similar vein we revisit the Fermi two-atom problem and explicitly demonstrate the causal nature of the interaction without invoking simplifying approximations that have recently been called into question.

The electromagnetic field is quantized in a material whose dielectric function varies with frequency and one spatial dimension. The dielectric function is assumed to have a known form and to be real over the range of frequencies important for a particular application, for example the propagation of an optical signal. General properties of the mode functions are derived and employed in the quantization procedure. Expressions are obtained for the energy and momentum density and current operators, and these are shown to satisfy the appropriate conservation and continuity relations. The general formalism is illustrated by application to the examples of a homogeneous dielectric and two different dielectrics with a sharp interface.