The resonant fluorescent spectrum of an atom driven by an intense laser field is analyzed, taking into account the extended nature of the atom. The angular, spectrum is studied, showing some important differences between the point atom and the extended atom results. In particular, the usual Mollow triplet changes into a quadruplet. Other features in the spectrum, all related to the momentum and energy conservation, are reported. Also, some interference patterns in the power spectrum are shown in the case of a two-peaked Gaussian momentum distribution.

The problem of the interaction of the hydrogen atom with a strong laser pulse has been tackled by solving the time-dependent Schrödinger equation via the state-specific expansion approach [Th. Mercouris et al., Phys. Rev. A 50, 4109 (1994)]. We present above-threshold ionization (ATI) spectra and study the frequency (ℏ${\mathrm{\omega }}_{\mathrm{laser}}$=2–4 eV) and intensity (${\mathrm{I}}_0$⩽2×${10}^{14}$ W ${\mathrm{cm}}^{\mathrm{-}2}$) dependence of the plateaulike structure appearing at high photoelectron energies. Our findings are qualitatively consistent with experimental data recently obtained in rare gases and render support to the proposed tunneling-rescattering mechanism for the interpretation of the observed features. Additional information on the dynamics of the laser-atom interaction is obtained by studying the frequency and intensity dependence of the photoelectron angular distributions (PADs). In agreement with recent experimental discoveries in rare gases, an appreciable sidelobe structure is found in PADs corresponding to high-order ATI peaks, for low laser frequencies (ℏ${\mathrm{\omega }}_{\mathrm{laser}}$⩽3 eV). The connection of the sidelobe structure in the PADs to the ATI plateau is explored and evidence for a common underlying mechanism is produced. Our results suggest that the electron tunneling-rescattering mechanism is not the only one contributing to the appearance of the sidelobe structure in the PADs and the formation of the ATI plateau.

We report the observation of hyperfine-changing collisions and the suppression of their rates in a sample of ultracold sodium atoms. We show that the suppression scheme used in the study of photoassociative ionization of Na [Phys. Rev. Lett. 76, 2033 (1996)] is also able to suppress the hyperfine-changing collisions, producing suppression up to 80%. The experimental results are compared with predictions of a simple Landau-Zener model and of a three-dimensional, multichannel close-coupling calculation. Both theories agree at low intensity, but at high intensity the experiment shows a saturation behavior that is qualitatively described only by the three-dimensional multichannel theory.

A quantum-nondemolition (QND) measurement of the vibrational energy of a trapped ion may be made by placing it at a node of a cavity optical standing wave. In certain parameter regimes there is a backaction evading coupling between the ion's vibrational energy eigenstates and the coherent states of the cavity field. This facilitates a QND measurement of the ion trap state via a homodyne measurement on the cavity output field. This scheme has the advantage that the required measurements minimally disturb the ion.

We present an analytic study of the population dynamics of a two-state system interacting with an external field and subjected to periodic level crossings. We apply an evolution matrix approach to calculate the excited-state population at the crossings (the nodes) and at the antinodes. The results are expressed in terms of only two parameters: the transition probability p for a quarter period from a crossing to an antinode, and the transition probability P for a half period between two successive crossings. We find that the values of the excited-state population at the antinodes can form global (gross) structures. We show that these structures and the population dynamics as a whole are very sensitive to the initial phase φ of the frequency-modulated field, particularly in the limits φ=0 (cosine modulation) and φ=π/2 (sine modulation). We calculate the parameters p and P by using two analytic approaches: one based on the original Landau-Zener model, and the other based on the finite Landau-Zener model. Both approaches unexpectedly lead to the same results. The notion of the global structures and the relevant parametrization in terms of p and P allow us to find various distinctive cases of population dynamics, such as population swapping, completely periodic evolution, superpositional trapping, and stepwise evolution.

We study the scattering of an atom beam adiabatically passing through a standing wave laser beam. Contrary to Bragg or Raman-Nath scattering, the adiabatic scattering has an underlying classical process and can be conveniently described by conservation of an adiabatic integral. We discuss the adiabatic scattering in both the classical and quantum approaches as well as the transition from quantum to classical regimes.

Raman-type laser excitation of a trapped atom allows one to realize the quantum-mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multimode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent 'displacement' of the motional quantum state may induce strong amplitude squeezing and quantum interferences.

The conditions for a bifurcation to periodic intensities (Hopf bifurcation) for low values of the pump current are examined using singular perturbation methods. We show that the frequency of the oscillations at the bifurcation point remains close to the relaxation oscillation frequency of the solitary laser until the pump parameter is close to its effective threshold value. This part of our analysis adds substance to previous estimates of the frequency of the oscillations, which were guided by experiments. In the second part of our analysis, we show that, very close to threshold, the frequency exhibits a sharp transition from the relaxation oscillation frequency to a frequency proportional to the external cavity frequency (i.e., 2π/τ, where τ is the external round-trip time).

The photon state created by shifting the photon-number distribution of the thermal state as a whole toward larger photon numbers is called a shifted thermal state. The photon-number distribution of the so-called mazer derived recently by Scully, Meyer, and Walther [Phys. Rev. Lett. 76, 4144 (1996)] is identified as a partially shifted thermal state. Klyshko's criterion for nonclassical states, dubbed 'bump' [Phys. Lett. A 213, 7 (1996)], is used to study the nonclassical effects in this radiation. The criterion is very suitable for our purpose because it involves only the probabilities for detecting three consecutive numbers of photons.

A four-level atom, driven by a coherent field, is considered. We show that under certain conditions complete quenching of spontaneous emission is possible. Hence the population inversion on some specific atomic transitions can be created using a very weak incoherent pumping. We investigate the physics of the effect using bare and dressed states. The proposed scheme may be useful, in principle, for generation of high-frequency and/or high power laser light.

The emission spectrum is calculated for a system of two identical atoms, having relative coordinate r. Initially one atom is in an excited state and the other in its ground state. Both atom and field variables are fully quantized, so that the calculation automatically includes effects related to both retardation and atomic recoil on the absorption or emission of radiation. It is shown that for ${\mathrm{k}}_0$r≫:1 (where ${\mathrm{k}}_0$=2π/λ and λ is the wavelength associated with the resonant excited- to ground-state transition), the emission spectrum can consist of a triplet. The frequency separation between the components of the triplet can be interpreted in terms of the recoil the atoms undergo individually on emitting or absorbing radiation. For ${\mathrm{k}}_0$r≪1, the atoms emit as a composite system and the recoil (while not resolvable) is that associated with a ``molecule'' of mass 2m, where m is the mass of one of the atoms.

A linear theory for optimizing optical fields to achieve a molecular configuration at a chosen time is formulated with an emphasis on the symmetric transformation between time domain and space domain representations. Based on two different measures of control, the yield and achievement functions, two parallel but distinct optimization schemes are derived in a unified algebraic format. Connections are then established to a more conventional optimization procedure as well as the optimization procedure for squeezing wave packets used by Averbukh and Shapiro [Phys. Rev. A 47, 5086 (1993)]. A numerical example of the production of localized wave packets (i.e., squeezed states) demonstrates the effectiveness and feasibility of the proposed scheme.

We discuss quantum interference effects in the resonance fluorescence spectrum of a Λ three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.

In a recent microlaser experiment [K. An et al., Phys. Rev. Lett. 73, 3375 (1994)], a thresholdlike transition of intracavity mean photon number as a function of intracavity mean atom number has been observed. In this paper the behavior is explored with quantum trajectory simulations. It is shown that the transition is caused by enhanced atom-cavity Rabi interaction due to the increase of the intracavity photon number as the intracavity atom number is increased. The transition is further accentuated by the position-dependent variation of the coupling constant in the Fabry-Pérot cavity. In addition, it is demonstrated that multiatom collective effects are negligible in the microlaser under consideration, in which atoms are injected into the cavity at random times and the product of the coupling constant and atom-cavity interaction time is much less than π. In this case the analytic theory of the one-atom micromaser [P. Filipowicz et al., Phys. Rev. A 34, 3077 (1986)] can be extrapolated into the multiatom region, assuming uniform atom-cavity coupling throughout the cavity and monovelocity atomic injection. Finally, simulations are performed which account for spatial variation of coupling constant, velocity distribution of injected atoms, and spontaneous atomic decay in the actual experiment. The results are in good agreement with experiment.

Fabry-Pérot spectroscopy was used to observe a spectral broadening of 1.3±0.2 MHz in laser light forward scattered through a colloidal solution. Light from a single-mode argon-ion laser was collected after scattering through water to which measured amounts of diatomaceous earth or 0.08-μm-diam polystyrene spheres were successively added. The broadening is attributed to coupling between fluctuations in particle concentration and spontaneous thermal fluctuations. Though spontaneous fluctuations exist in all pure fluids, they are very weak in water. However, the presence of the particles induces temperature gradients in the fluid, which in turn induce fluctuations in particle concentration.

We report the observation of the quantum effects of competing ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ nonlinearities. We also report classical signatures of competition, namely, clamping of the second-harmonic power and production of nondegenerate frequencies in the visible. Theory is presented that describes the observations as resulting from competition between various ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ up-conversion and down-conversion processes. We show that competition imposes hitherto unsuspected limits to both power generation and squeezing. The observed signatures are expected to be significant effects in practical systems.

We analyze the quantum fluctuations of second harmonic generation at the Hopf bifurcation and in the limit-cycle regime near the critical point using many-body techniques. The many-body approach does not make use of linearization approximations and can thus be used to study finite-size effects. Finite-size corrections reduce the amount of squeezing at the Hopf bifurcation and eliminate infinities predicted by the linearization approach at this point and in the self-pulsing regime. The characteristic frequencies of the linearized fluctuation spectra in the self-oscillation regime are shifted and new spectral structures are observed.

Experimental evidence of scattering of second-harmonic light from the surface of spherical particles of optical dimensions is presented. This mechanism for second-harmonic generation is observed in a suspension of monodisperse spherical colloidal particles, ordered in a centrosymmetric crystalline lattice. In this periodic structure the mechanism of phase matching is provided by the bending of the photon dispersion curve near the Bragg reflection band. A simple theoretical analysis based on the Rayleigh-Gans scattering approximation shows that constructive interference of the second-harmonic light scattered from different portions of a single-sphere surface leads to a nonvanishing field with a quadrupolar distribution intensity pattern.

We describe the time evolution of a wave function in the infinite square well using a fractional revival formalism, and show that at all times the wave function can be described as a superposition of translated copies of the initial wave function. Using the model of a wave form propagating on a dispersionless string from classical mechanics to describe these translations, we connect the reflection symmetry of the square-well potential to a reflection symmetry in the locations of these translated copies, and show that they occur in a ``parity-conserving'' form. The relative phases of the translated copies are shown to depend quadratically on the translation distance along the classical path. We conclude that the time-evolved wave function in the infinite square well can be described in terms of translations of the initial wave-function shape, without approximation and without any reference to its energy eigenstate expansion. That is, the set of translated initial wave functions forms a Hilbert space basis for the time-evolved wave functions.

Simulating two-dimensional optical pattern formation in sodium vapor, we show that hexagonal patterns can be unstable against their own spatial harmonics or subharmonics. The instability results in ultrahexagons or subhexagons, respectively. The formation of ultrahexagons is due to interaction with a second solution branch with a wave number nearly resonant to the harmonics of the primary hexagon. The mechanism of the instabilities is discussed on the basis of order parameter equations obtained from symmetry considerations.