The squeezing in a mixture of two high-Q cavity modes interacting with strongly driven two-level atoms is discussed for the case in which these two modes are located near the two sidebands of collective resonance fluorescence. The collective effects, cavity damping, and thermal field are accounted for. For suitable values of the parameters of the system, as in recent experiments with Rydberg atoms, a large squeezing can be obtained.

Absorptive, dispersive, and diffractive effects are studied in a nonlinear ring-cavity configuration containing an intrinsically bistable medium modeled generically by a nonlinear oscillator. The output intensity is shown to exhibit steady-state and periodic characteristics for constant input intensity, but no chaotic solutions are found. We find that the plane-wave analysis is inconsistent with the inclusion of diffraction effects and that periodic output characteristics are affected even for Fresnel numbers of order 1000. Our results are contrasted with previously reported experimental and theoretical work.

A general theory is developed that describes continuous state reduction of two quantum-mechanically correlated photon fields by continuous photodetection of one of the fields. The effects of measurement back action and quantum correlation on the state reduction of the other field are highlighted from the viewpoint of continuous photodetection. Nonunitary time evolutions of the density operators and photon statistics are exactly described for both fields. The obtained formulas are applied to parametrically generated photon twins, i.e., signal and idler fields. The continuous state reduction of the signal field by photodetection of the idler field is examined. It is shown that the Manley-Rowe relation can be generalized to the intermediate state under the photodetection process; that is, the initial quantum correlation remains intact throughout the ‘‘destructive’’ photodetection process if we retain the information about the idler readout. The obtained results are compared to the case in which the idler readout is discarded. In this case, the Manley-Rowe relation can no longer hold. This fact demonstrates that retaining the readout information is essential for preserving the established quantum correlation.

The nonlinear response of sodium vapor with a laser tuned near the 4D two-photon resonance is investigated over a large range of sodium concentrations and pump intensities with emphasis on the influence of coherent cancellation effects on the induced polarizations and the primary mechanism for the generation of the new frequencies. Over a wide range of circumstances, the response of the medium is dominated by parametric four-wave mixing as compared to amplified spontaneous emission or stimulated electronic hyper-Raman scattering. Secondary four-wave-mixing fields are generated by stimulated Raman scattering of one parametric four-wave-mixing field and a coupling of these fields with the driving laser field. A sharp onset of saturation of the parametric four-wave-mixing signals with sodium number density and a transition from a quadratic to a linear power dependence is observed. Both effects are explained in terms of the two-photon cancellation effect.

In time-resolved Raman scattering (as well as in degenerate four-wave mixing) the time resolution is in principle determined by the coherence time of the laser pulses involved rather than the pulse widths. In this paper the theoretical time dependence of three different time-resolved Raman-scattering techniques, Raman-fringe decay (RFD), coherent Stokes Raman scattering, and time-resolved stimulated Raman gain, is calculated under various coherence conditions of the fields. Taking RFD generated by temporally incoherent light as the example, it is shown that due to complicated coherence effects the material relaxation time cannot be extracted from the experimental data without careful consideration of the stochastic properties of the fields and the different relaxation parameters of the system. The RFD technique has been experimentally applied to the 524-${\mathrm{cm}}^{\mathrm{-}1}$ mode of ${\mathrm{CH}}_3$I and the 656-${\mathrm{cm}}^{\mathrm{-}1}$ mode of ${\mathrm{CS}}_2$ and coherence effects are indeed observed. The relaxation times are found to be in agreement with previous experimental studies with coherent light.

The generation of a broadband laser field with well-defined and controllable statistical properties, known as the real Gaussian laser field, has been achieved through the random modulation of the amplitude of a stabilized laser beam. The verification of the field-generation technique is provided by measurements of the laser power spectrum (Lorentzian) and by measurements of the intensity autocorrelation function. The latter is shown to decrease exponentially from an initial value of nearly 3 to a final value of 1 with a decay time related to the inverse bandwidth of the field. The techniques for generating this field and for its characterization are discussed in this paper.

We calculate the spectrum of fluctuations in the intensity difference of two weak fields generated in nondegenerate four-wave mixing in an atomic system. The effects of spontaneous emission and Doppler broadening are included. The conditions for optimum noise suppression below the shot-noise level are discussed.

In this paper, the two-photon Bloch equations of a two-level atom in broadband squeezed light are derived. On this basis, we discuss two-photon dynamic Stark splitting of atomic levels and the time evolution of atomic variables. The phenomena of squeezing-induced enhancement and reduction of dynamic Stark splitting of the atomic levels and overdamping of atomic time evolution are obtained.

A study of the influence of the spatial structure and statistics of the pump beams in the phase-conjugation process is made, showing that the reflectivity varies along the phase-conjugation mirror when the phase factor in the coupling equations that describe the process is not constant. The mutual coherence function of the generated field is calculated from the mutual reflectivity of the mirror for two commonly used statistics for the partially coherent pump beams. Finally, the influence of diffractional effects is also analyzed, showing that, in general, the fidelity of the process is degraded.

We have measured coherent anti-Stokes Raman spectra between crystal-field levels of the ${}_{}{}^2{}_{}{}^{}$${\mathit{F}}_{5/2}$ and ${}_{}{}^2{}_{}{}^{}$${\mathit{F}}_{7/2}$ manifolds of the ${\mathrm{Ce}}^{3+}$ ion diluted in ${\mathrm{LuPO}}_4$ at ∼10 K. The anti-Stokes signal is nearly resonant with the lowest crystal-field level of the 5${\mathit{d}}^1$ configuration of ${\mathrm{Ce}}^{3+}$ at 30 460 ${\mathrm{cm}}^{\mathrm{-}1}$. For a ${\mathrm{LuPO}}_4$ crystal doped with 0.06 mol % ${\mathrm{Ce}}^{3+}$, we found enhancements of the third-order susceptibility ‖${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{R}}$/${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{NR}}$‖ as high as 11.6. This enhancement is over 20 times larger than that seen previously in singly resonant experiments with pure rare-earth crystals.

We investigate the stability of the propagation of bright and dark coupled solitary waves that may travel in the orthogonal polarization modes of a birefringent nonlinear optical fiber. In the anomalous dispersion regime, the coupled-solitary-wave decay is self-induced by modulational polarization instability of the dark component background pulse. In the normal dispersion regime, stable propagation only occurs for distances of the order of one linear beat length. We identify different instability mechanisms such as gray soliton formation, polarization wave breaking, polarization dispersion, and self-stimulated Raman scattering that leads to asymmetric coupled-solitary-wave breakup.

We have discussed the photon statistics of the spectral components of N-atom time-dependent resonance fluorescence. It is shown that in contrast to the stationary limit, sub-Poissonian photon statistics in the sidebands occur for any number N of atoms including the case N≫1. Reduction in Mandel’s parameters ${\mathit{Q}}_{+1\mathrm{}}$ is found with increasing numbers of atoms. The typical time for the presence of sub-Poissonian statistics is proportional to 1/N.

We evaluate the power spectrum of light scattered by a weakly nonlinear Morse oscillator driven by a strong single-mode classical electromagnetic field, taking radiation damping into account as the only relaxation process. The spectrum is calculated in the small-noise limit under a near-resonant condition (the resonance is considered in terms of an effective detuning parameter). We show that the single-peak structure that appears in the weak-field limit splits into a symmetric doublet centering around the driving field frequency in the presence of an intense field when the Rabi frequency far exceeds the natural damping rate.

A non-Markovian model of correlated phase jumps is introduced for phase fluctuations of an electromagnetic field. This generalized jump model (GJM) treats phase jumps of arbitrary size, occurring at random times; but in contrast to previous work, the jumps are allowed to be fully correlated, partially correlated, or uncorrelated. The degree of correlation is defined by a single parameter derived from the theory. The familiar phase-diffusion model, telegraph-noise model, Burshtein model, and Brownian-motion-like model are all obtained from the GJM in the proper limits. The standard way of characterizing the spectrum of a laser has been the assignment of a single parameter—the linewidth. However, in experiments where the details of the fluctuations are important, or where exact line shapes are measured, this single-parameter characterization might be insufficient. This GJM describes most cases by a set of three stochastic parameters: the degree of correlation between the jumps, the characteristic jump size, and the mean time between jumps. In this paper expressions are derived for the correlation function and the spectrum of a stochastic field in terms of these three stochastic parameters. In addition to analytical work, detailed numerical simulations are presented for the various limiting cases of the model, and the agreement between theory and simulation is excellent. Since the stochastic parameters are not a priori known, a procedure is described for extracting the stochastic parameters from measurable quantities such as the field correlation function or spectrum. Since correlated fluctuations are very common in optics (any stabilization feedback procedure involves anticorrelation), the questions of relevance of the present model to problems of current interest in optical communication and nonlinear optics are also discussed.

Strong laser fields, when tuned on resonance to an atomic (molecular) transition, give rise to the well-known triplet of resonance fluorescence. The laser field is normally assumed to be strong and monochromatic, even though the spectrum of real lasers is never a δ function. A standard way to treat laser fluctuations has been to assume a well-defined nominal frequency and a randomly fluctuating phase. Recently we introduced the generalized jump model (GJM) for correlated phase fluctuations, where correlated phase jumps are considered, leading to Markovian as well as non-Markovian stochastic behavior. In the GJM, each phase jump may be correlated to the previous jump, and the degree of correlation, the typical jump size, and the mean time between jumps are the three parameters defining the stochastic character of the laser field. In this paper we apply the GJM model to the case of resonance fluorescence from an atom excited by a stochastic field. The ‘‘standard’’ Mollow triplet is obtained in the monochromatic limit of small jumps, and several new predictions are made in the different limits of the stochastic parameters. In the small-jump limit, a new ‘‘field effect’’ is predicted. The spectral line shape and the triplet separation deviate from the Mollow predictions for a monochromatic field in a substantial way, giving rise to observable differences.

In the highly correlated small-jump limit, which is approximated by the Kubo oscillator model, the previous results are corrected to include nonzero line shifts and extended to the case of non-Lorentzian line shapes. In all regions, even input fields of the same line shape (which would be considered identical in the one-parameter linewidth description) give rise to very different output spectra, justifying the more complete stochastic description. Effective relaxation constants ${\mathrm{\Gamma }}_1^{\mathrm{*}}$ and ${\mathrm{\Gamma }}_2^{\mathrm{*}}$ that simplify the description of the spectrum are calculated in all appropriate cases, and ${\mathrm{\Gamma }}_1^{\mathrm{*}}$ is found to equal the input laser linewidth. In addition to predicting the resonance fluorescence spectra, the present analysis provides a way to extract the stochastic parameters from the nonlinear measurement in those cases where the linear characterization of the input field cannot do it. The analytic work is fully supported by extensive numerical simulations.

In a laser with an injected signal (LIS), the phase of the laser field can be constant (phase locking) or grow unbounded (phase drift) or vary periodically (phase entrainment). We analyze these three responses by studying the bifurcation diagram of the time-periodic solutions in the limit of small values of the population relaxation rate (small γ), small values of the detuning parameters (small Δ and Θ), and small values of the injection field (small y). Our bifurcation analysis has led to the following results: (1) We determine analytically the conditions for a Hopf bifurcation to stable time-periodic solutions. This bifurcation appears at y=${\mathit{y}}_{\mathit{H}}$ and is possible only if the detuning parameters are sufficiently large compared to γ [specifically, Δ and Θ must be O(${\gamma }^{1/2}$) quantities]. (2) We construct the periodic solutions in the vicinity of y=${\mathit{y}}_{\mathit{H}}$. We show that the phase of the laser field varies periodically. We then follow numerically this branch of periodic solutions from y=${\mathit{y}}_{\mathit{H}}$ to y=0. Near y=0, the phase becomes unbounded. (3) A transition between bounded and unbounded phase time-periodic solutions appears at y=${\mathit{y}}_{\mathit{c}}$ (0<${\mathit{y}}_{\mathit{c}}$<${\mathit{y}}_{\mathit{H}}$). This transition does not appear at a bifurcation point. We characterize this transition by analyzing the behavior of the phase as y→${\mathit{y}}_{\mathit{c}}^{+}$ and as y→${\mathit{y}}_{\mathit{c}}^{\mathrm{-}}$. (4) We find conditions for a secondary bifurcation from the periodic solutions to quasiperiodic solutions. The secondary branch of solutions is then investigated numerically and is shown to terminate at the limit point of the steady states. (5) We develop a singular perturbation analysis of the LIS equations valid as γ→0. This analysis allows the determination of a complete branch of bounded time-periodic solutions. We show that the amplitude of these time-periodic solutions becomes unbounded as y→0 provided that Δ and Θ are sufficiently small compared to γ [specifically, Δ and Θ are zero or O(γ) quantities].

Dissociation probabilities, energy absorption, and ground-state populations are calculated numerically for interaction of a Morse oscillator with a resonant ultrashort (${\mathit{t}}_{\mathit{p}}$<${10}^{\mathrm{-}12}$ sec) intense laser pulse as a function of intensity and pulse area in order to investigate the sensitivity of coherence phenomena to delocalization and chaos in molecule-radiation field systems. It is concluded that a zero-area pulse can reduce considerably energy absorbed by a molecule as well as dissociation probabilities for intensities below and near the chaotic region. It is found that the two-level model (describing the interaction of light resonant with the ground to first excited level transition) works well up to the intensity ${10}^{12}$ W/${\mathrm{cm}}^2$, above which transitions to higher levels must be considered.

A theory for ultrafast pump-probe spectroscopy of large polyatomic molecules in condensed phases is developed. A multimode Brownian oscillator model is used to account for high-frequency molecular vibrations and local intermolecular modes as well as collective solvent motions. A semiclassical picture is provided using the density matrix in Liouville space. The pump field creates a doorway state that propagates for a specified time interval, and the spectrum is calculated by finding its overlap with a window state, prepared by the probe pulse. The doorway and the window states are wave packets in phase space. For high-frequency modes and with long pulses they are expanded in the vibronic eigenstates, whereas for low-frequency modes and with impulsive pulses the Wigner (phase-space) representation is more adequate. Conditions for the observation of quantum beats, spectral diffusion, and solvation dynamics (dynamical Stokes shift) are specified.

Modifications of the first-gradient correction to the Thomas-Fermi kinetic-energy (KE) functional have been proposed based on its global correlation with the Weizsäcker energy functional. The self-consistent solution of the Thomas-Fermi-Dirac equation containing the modified first-gradient KE functional and a Wigner-type local-correlation-energy functional leads to acceptable energy values when one considers the computational simplicity.

The ground-state energy, fusion rate, and sticking probability are calculated using a Laguerre polynomial basis. The results are compared with previous calculations, and the advantages are pointed out.