Resonant Auger electron spectra from the close lying ${3d}_{3/2}^{-1}5p$ and ${3d}_{5/2}^{-1}6p$ core-excited states of Kr have been measured. The intensities of the transitions to the ${4p}^{-2}5p$ and ${4p}^{-2}6p$ final states have been followed as a function of the exciting photon energy. The effects caused by the lifetime interference between the two Auger decay channels are interpreted by using the one-step picture of the excitation-deexcitation process, with the help of ab initio calculations of the electron wave functions and transition matrix elements. Some aspects beyond the spectator model used are discussed.

We explore a recent proposal [Fedichev et al., Phys. Rev. Lett. 77, 2913 (1996)] for altering the mean interaction strength between ultracold atoms using an appropriately detuned laser. Although care must be taken to minimize laser-driven loss processes, we find large ranges of intensities and detunings where useful changes might be affected. Accordingly, we present simple formulas for the effects of laser light that should prove useful in designing specific experiments. We demonstrate the validity of these formulas by comparison with exact close-coupling models. In particular, we find that useful changes of the mean-field interaction require sufficiently high laser intensities that the rate of laser-induced stimulated emission exceeds the natural spontaneous emission rate.

We analyze the feedback-induced destabilization process of a single-mode laser diode with the wavelet transform (WT). We consider transients following an abrupt switch on of the feedback, for feedback levels strong enough so that the final state of operation of the laser is the coherence-collapsed state. The transient regime involves multiscale interactions that exhibit strong localization in both frequency and time, and we demonstrate that by using the WT we can characterize the transient dynamics and capture the essential features associated with the destabilization process in a relatively simple form.

The polarization properties of the light generated by vertical cavity surface emitting semiconductor lasers are described by means of two different sets of equations, derived, respectively, from a class-$A$ and a class-$B$ approach. We compare the polarization eigenmodes and their stability for arbitrary linear phase anisotropy and pump rates. Inclusion of spontaneous emission noise in the field equations is shown to lead to hopping between the polarized eigenmodes in both cases. By studying both class-$A$ and class-$B$ systems we obtain physical insight into the influence of carrier dynamics on polarization stability and noise-induced polarization hopping.

It is shown that coherent quantum simultons (simultaneous solitary waves at two different frequencies) can undergo quadrature-phase squeezing as they propagate through a dispersive ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ waveguide. This requires a treatment of the coupled quantized fields including a quantized depleted pump field. A technique involving nonlinear stochastic parabolic partial differential equations using a nondiagonal coherent state representation in combination with an exact Wigner representation on a reduced phase space is outlined. We explicitly demonstrate that group-velocity matched ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ waveguides which exhibit collinear propagation can produce quadrature-phase squeezed simultons. Quasi-phase-matched KTP waveguides, even with their large group-velocity mismatch between fundamental and second harmonic at 425 nm, can produce 3 dB squeezed bright pulses at 850 nm in the large phase-mismatch regime. This can be improved to more than 6 dB by using group-velocity matched waveguides.

We observe 30% two-photon optical amplification of a probe laser-field propagating through a laser-pumped potassium vapor. This amplification is spectrally isolated and substantially larger than that of previously reported continuous-wave two-photon amplifiers. The combination of large amplification and spectral isolation of the two-photon gain feature will greatly facilitate precise studies of the photon statistics of this highly nonlinear quantum amplifier and the development and characterization of a two-photon laser based on this gain medium. We also observe spectrally-distinct three-photon amplification $(\sim 5$%) in the same system under different experimental conditions. We present a simple model of the interaction that gives qualitative agreement with our observations and explains the dependence of the two-photon gain on the various system parameters. This model predicts that the size of the two-photon gain is quite sensitive to an interference between two different quantum pathways.

A three-level cascade system coupled to two pulsed, fluctuating multimode laser fields is studied with numerical Monte Carlo simulations. Laser noise is modeled by introducing abrupt, random variations into the field parameters. We show that both phase and amplitude fluctuations may increase the signal through the ac Stark effect, and we demonstrate how noise can change the whole spectral structure of the transitions. As a result that is conveniently produced with simulations but that is often difficult to attain analytically, we also present on- and off-resonance signal distributions at various saturation levels and in different noise scenarios.

Spontaneous parametric down-conversion (SPDC) has been extensively studied for the case of a continuous wave pump. In this paper SPDC is studied for the case in which the pump is a pulse. The pump pulse acts like a clock with an uncertainty equal to its width. This makes it possible to distinguish pairs of photons born at sufficiently different depths inside the crystal with a consequent decrease in two-photon interference. We study this effect in detail for degenerate collinear type-II SPDC and degenerate type-I SPDC. It may be possible in the type-II case to eliminate the clock effect of the pump by judicious choice of materials and wavelengths.

The conditions under which transverse pattern formation in nonlinear optical systems with nonplanar resonators can be described by an order-parameter equation (OPE) are given. It is shown that the same techniques used in the derivation of OPE’s in the case of planar resonators apply to the case of curved mirror resonators, in the limit of small curvatures. Particularly interestingly, this method straightforwardly allows us to know the OPE’s of optical systems previously studied in the limit of plane resonators. Limitations and generalizations of the method are discussed. Applications to the laser and to the optical parametric oscillator are given.

The velocity-dependent spontaneous emission of a two-level atom in a Fabry-Pérot cavity in the strong-coupling regime and the deflection of a beam of two-level atoms in a classical standing wave inside a cavity are discussed using a renormalization group approach. In this way we are able to renormalize the leading-order solutions for both problems through calculations of the corrections at first order. In fact, the first-order terms are not bounded for large times and no sense can be attached to this higher-order correction unless small times are considered. These are like the divergences of quantum field theory. To make them harmless, the condition for the Raman-Nath regime is recovered. The renormalization group methods permit one to eliminate those divergences generating a renormalized leading-order wave function without any condition of applicability. For the spontaneous emission of a two-level atom in a Fabry-Pérot cavity in the strong regime, using a Hamiltonian without losses, it is shown that the unperturbed levels are shifted by a term proportional to the zeroth-order Bessel function with an argument yielded by the ratio of the Rabi frequency and the Doppler-shifted frequency of the mode of the cavity. When the detuning is zero, the correction to the leading-order wave function is not present and known results are recovered. For the beam of two-level atoms in a classical standing wave, when the detuning is much larger than the Rabi frequency, it is shown that the renormalization group equation, which gives the correction for the renormalized leading-order wave function, is a time-dependent Schrödinger equation for a free particle that induces a spreading of the initial Gaussian wave packet.

A complex order parameter description of the spatiotemporal dynamics close to threshold for a single-longitudinal-mode, large-aspect-ratio laser with a weak injected signal is presented in one transverse spatial dimension and for a longitudinal cavity frequency smaller than the atomic resonance frequency. It is shown that, when the frequency of the external signal is tuned close to the atomic resonance frequency, the spatiotemporal dynamics of the laser may be described by two coupled Ginzburg-Landau equations with parametric terms analogous to those derived in hydrodynamics to study excitation of parametric waves in oscillatory convection. As a result of the parametric terms, which physically arise by means of a four-wave-intercation process mediated by the external signal, the bifurcating modes which are superimposed to the forced (homogeneous) mode may be either traveling or standing waves. In particular, it is shown that for small frequency detunings of the injected signal standing waves are preferred to traveling waves close to threshold. Stability analysis of traveling and standing waves beyond threshold within the amplitude equations reveals the emergence of both phase (Eckhaus) and amplitude instabilities.

Optical free-induction decay (FID) of laser-cooled ${}^{85}$Rb has been observed. Considerably good agreements are obtained between experiments and theoretical calculations in the condition of no inhomogeneous broadening. The possibility to apply optical FID measurements to the studies of phase relaxation in a dense atom trap is discussed.

Using semiconductor Maxwell-Bloch equations, we analyze the response of an ensemble of $1s$ excitons driven by a femtosecond optical pulse beyond the traditional approach of slowly varying amplitudes and phases. For optical pulses of a given duration, we show that the off-resonance optical field can evolve into a stable soliton. Besides hyperbolic-secant solitons, we find a single soliton with nonzero asymptotics that is stable against low-amplitude perturbations and whose form is not affected by collisions.

We apply the geometric phase theory to the dissipative system of a set of nonlinear coupled oscillators. We found an area theorem for the geometric phase, which provides a direct and simple geometric method for observing the geometric phase of this system. The area theorem shows evidence that the geometric phase is related to certain dynamical features of the systems.

We demonstrate theoretically and experimentally the manipulation of spatial localized structures (spatial solitons) of a laser with saturable absorber in a self-imaging resonator. We show the on-off bistability of the solitons, their movement by phase gradient forces, the parameters of their existence, the limits of their stability, and periodic soliton nucleation and dynamics.

We theoretically describe a pump-probe scheme for detecting the optical Stark effect on two-level atoms with a fully quantized pump field. The probe absorption reflects the photon statistics of the pump field for both the single-atom and multiatom case. Nonclassical features, without counterpart in the single-atom case appear in the multiatom absorption and result in strong variations of the absorption amplitude and nonclassical gain or absorption.

Perpendicular reflection of low-power, near-resonant radiation at a sapphire–Rb-vapor interface (selective reflection) has been measured for Rb densities of $3\times {10}^{14}–3\times {10}^{17}/{\mathrm{cm}}^3$. At the lowest density the eight hyperfine components are essentially isolated, and at the highest pressure they are highly blended. The data have been fitted to a coherent superposition of the reflected field amplitudes of the eight components, including the well-known starting transient and wall interaction. At low to moderate densities this yields a good fit to the data, and a result for the Rb-Rb collisional shift. At the higher densities the rapid attenuation of the incident field has a major effect on the reflection spectrum, and an approximation to this is included in the calculation, assuming exponential attenuation at the equilibrium-vapor rate. This provides improved fits to the data and allows the apparent Lorentz-Lorenz plus collisional shift to be evaluated. However, the data do not fully fit this calculation, and a complete self-consistent-field calculation appears necessary to fully understand the high-pressure results.

The properties of coherent nonlinear gain are utilized for generating stable pulses with durations shorter than the inverse spectral width of the gain profile. A passive cw mode-locking technique making use of the coherent gain and the coherent absorber is proposed as the basis for a self-induced transparency soliton laser. The basic features of pulse evolution including the pulse shortening effect are described.

Three-photon resonance enhancement of third-harmonic generation and multiphoton ionization have been studied in xenon under excitation by the Bessel and the focused annular laser beams. It has been shown that the transformation of a Gaussian beam into a Bessel or an annular one leads to significant changes of third-harmonic excitation profiles and ionization spectra. These changes result from a principal difference of the beams, where either collinear (Gaussian beams) or noncollinear (Bessel and focused annular beams) excitation geometries are realized. It has been shown that the noncollinear ring-type phase matching shifts the maximum of the generated third harmonic to the longer wavelength toward the atomic resonance. Numerical calculations of third-harmonic excitation spectra have been carried out and compared with experimental results. The efficiency of frequency tripling in collinear and noncollinear excitation geometries have been compared. Cancellation of the three-photon $6s$ resonance and the influence of harmonic photons on the excitation of the four-photon $4f$ resonance in the Bessel beams are discussed.

We consider spatiotemporal dynamics in an optical system containing a thin film of nonlinear medium having binary-type refractive nonlinear response and a feedback mirror. Steady-state output transverse patterns consist of a set of localized states, and strongly depend on the initial spatial phase modulation (seeded phase image). These steady-state solution properties can be used for nonlinear image processing and edge detection. System dynamics are studied both theoretically and through numerical simulation.