We analyze the physical origin of the inversionless amplification in four-level atoms driven by a Raman field and identify the existence of two different mechanisms for the predicted gain. The first mechanism is connected with the appearance of a population inversion between the atomic states dressed by the coherent pump, while the second is linked to the buildup of coherence among these states. Proper selection of the relaxation parameters can make either the first or the second mechanism dominant over the other although usually both coexist.

We report an experiment of the time-delayed Raman-enhanced nondegenerate four-wave mixing (RENFWM) with a broadband laser in carbon disulfide (${\mathrm{CS}}_2$). We studied the RENFWM signal intensity as a function of the relative time delay τ between two beams which originate from a single broadband laser source. Our results indicate that the temporal behavior of the RENFWM is asymmetric with the maximum of the signal shifted from τ=0. Furthermore, unlike the corresponding coherent Stokes Raman scattering (CSRS) no coherent spike appears at τ=0. From our experimental results the relaxation time of the Raman mode can be extracted directly. We present a second-order coherence function theory to elucidate the physics of the basic features of the time-delayed RENFWM. We also discuss the difference between the RENFWM and the CSRS from a physical viewpoint.

The transverse instability of counterpropagating waves in nonlinear media with a photorefractive or Kerr-type nonlinearity is studied. The problem is formulated for a sluggish nonlinear medium that responds much slower than the optical frequency. In this limit, a general dispersion relation, valid for arbitrary longitudinal variation of the optical intensities, is obtained and solved numerically for several representative cases. It is found that, while photorefractive media provide sufficient nonlinear coupling for the observation of transverse instabilities, such observations may be difficult due to the presence of strong amplified incoherent scattering (fanning) in photorefractive media.

We study the refractive index of a system of two-level atoms driven by a strong coherent external field. We show that this system can produce a large index of refraction accompanied by vanishing absorption.

The paper deals with a system of two single-mode radiation fields copropagating through a nonabsorbing Kerr medium modeled as an anharmonic oscillator. The quadrature squeezing of the signal light is investigated and the phase dynamics, including the distribution, shift, and variance of the phase of the probe light, is studied using the Pegg-Barnett Hermitian phase operator. The results show that the squeezing is considerably influenced by the coupling between the two fields and the phase dynamics shows new features compared with that predicted by the Susskind-Glogower phase formalism.

We present a calculation of one-dimensional sub-Doppler cooling of neutral atoms, in which the atomic center-of-mass motion is quantized. The cooling field consists of a pair of counterpropagating, linearly polarized laser beams, with their polarizaton vectors at an angle θ with respect to each other. The steady-state atomic density matrix is analyzed as a function of θ. It is shown that, depending on the internal atomic level scheme, the equilibrium population of the quantized ground state of atomic center-of-mass motion can either increase or decrease significantly when θ is reduced from π/2. These effects are interpreted based on the spatial localization of atoms in the light-induced potential wells.

The phase properties of pair coherent states in the two-mode Jaynes-Cummings model are investigated based on the Pegg-Barnett phase formalism. The general expressions of the properties for the phase-sum operator of the two correlated fields are presented, in which the Stark shifts are considered. Analytic results are given in the strong-field approximations. It is found that the phase properties such as the variance of the phase-sum operator and the variances of the cosine and the sine of the phase-sum operator exhibit characteristic periodic oscillations in which the period is determined solely by the Stark shifts.

The internuclear-axis angular distribution is investigated in a nonresonant multiphoton process. This is done for diatomic or symmetric-top molecules and for singlet molecular states or any state which is well described by Hund’s case (a) electronic coupling. The electric dipole approach is used for the description of the interaction of the electromagnetic radiation with the molecule and explicit expressions, either for resolved or unresolved magnetic levels, are derived. The obtained simulated results are compared with excitation spectra available in the literature.

Four-wave mixing in homogeneously broadened, two-level atoms, driven by time-delayed, correlated phase-diffusing optical fields is investigated. The spectrum of the driving field has an arbitrary bandwidth, i.e., it can have a Lorentzian or a Gaussian profile or an intermediate profile (Voigt). A time delay between the strong pump and weak probe field provides a partial correlation between the fields, and this time delay makes the composite field seen by the atoms non-Markovian. It is shown that the calculation of the four-wave-mixing signal reduces to the solution of six coupled Langevin equations with multiplicative noise; Monte Carlo techniques are utilized to study the response of the atoms to non-Markovian fields. A technique for numerically simulating phase-diffusing fields with colored frequency fluctuations is shown. The four-wave-mixing profiles are found to be significantly different from those for which the driving field is chaotic. The profiles show oscillatory behavior as evidence of the Rabi frequency, a feature not seen in previous works. For some parameter values, a revival of the signal is seen for an increasing time delay, analogous to the revivals seen in chaotic field signals [Phys. Rev. A 44, 6009 (1991)].

A lossless beam splitter (a dielectric interface, a passive interferometer, or a linear coupler) changes the quantum state of two incident modes by an SU(2) transformation. Apart from phase shifting, the argument of the quadrature wave function of the system undergoes a rotation. Quasiprobabilities are changed by the inverse mode transformation. The use of balanced beam splitting allows the simultaneous measurement of conjugate quadrature components via homodyning the emerging beams with two strong coherent reference fields that differ in their phases by π/2. The measured probability distribution is given by a generalized Q function. It depends on the state of the field entering the second beam-splitter port. For a vacuum, the Q function will be obtained. The use of unbalanced beam splitting allows the measurement of a squeezed Q function without using squeezed states. Dissipation in Gaussian reservoirs corresponds exactly to a heuristic beam-splitter model. As a mathematical tool, the Fokker-Planck equation of damping in phase-sensitive reservoirs and the corresponding quantum master equation were solved. The dissipative decay of a Schrödinger-cat state was studied as an example. The sensitivity of quantum coherence with respect to damping can be interpreted geometrically.

Homogeneous silica-based and heterogeneous semiconductor-doped glasses were optically encoded with circularly polarized beams for efficient second-harmonic generation (SHG) at 532 nm. SHG growth rates for circularly polarized writing beams with both the same and opposite helicity show that ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$(0;ω,ω,-2ω) mixing symmetries are well obeyed in semiconductor microcrystallite-doped glass but not in homogeneous silicate glasses. The radiated second-harmonic free-space mode and ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ tensor symmetries for cohelically encoded gratings in SK5 glass determined an electric field which possessed a radial component as well as a component which had a constant direction across the readout beam axis. The results are discussed in light of present theories.

We present a quantum-nondemolition measurement scheme in which one component of the momentum of an atom traversing a propagating light wave is measured by monitoring a quandrature phase of the field. We show how a selective version of the measurement may be used to reduce the transverse momentum spread of an atomic beam and we suggest how this scheme could be used to transversely cool a beam of atoms in the absence of spontaneous emission.

It is shown that if the initial photon distribution is narrow (sub-Poissonian), long-time behavior of the atomic inversion is dominated by very spectacular and almost-periodical superstructures. These superstructures generalize phenomena described previously (fractional revivals). They result from beating of not-nearest-neighbor eigenstates of the system, and we show which beats lead to particular types of revivals. In addition, the cavity field develops macroscopically distinguishable states (optical Schrödinger-cat states). These stages emerge when the fractional revivals with a frequency of 2/${\mathit{t}}_{\mathit{R}}$, 3${\mathit{t}}_{\mathit{R}}$, and 4/${\mathit{t}}_{\mathit{R}}$, where ${\mathit{t}}_{\mathit{R}}$ is the single-revival period, appear for the second, fourth, sixth, etc., time in the superstructure pattern.

We report on experimental investigations of stimulated Brillouin scattering (SBS) in single-mode optical fibers, taking fully into account the influence of external feedback from the fiber ends. A threshold condition for arbitrary external reflectivity is derived. Detailed time-series analysis reveals that for the limiting case of vanishing external reflectivity, the dynamics is purely stochastic. For finite reflectivities, the observed dynamics is periodic provided environmental perturbations are suppressed. These findings settle a recent discussion about whether there are deterministically chaotic features present in the dynamics of SBS in fibers.

We investigate the time evolution of squeezing in the signal mode of the undamped parametric amplifier. Both the degenerate and nondegenerate cases are considered. These are the simplest models that give limits to squeezing caused by both the intrinsic pump noise and pump depletion. Conflicting analytic expressions have been reported. We resolve this by the use of exact numerical methods, employing both number state and stochastic techniques. Our central result is that in both cases we find that the minimum in the squeezed quadrature variance scales as N${\mathrm{¯}}^{\mathrm{-}1/2}$, where N¯ is the initial coherent pump photon number. This bound on the amount of squeezing obtainable, coupled with the loss in energy due to the conversion efficiency, serves to limit the phase information in the squeezed channel to no more than that of the coherent pump. We believe this to be a fundamental limit for using the squeezed radiation generated in coherently driven parametric amplifiers.

A model is formulated to investigate quantitatively how near-resonant degenerate four-wave mixing (DFWM) in a vapor of homogeneously broadened two-state atoms is affected by radiation scattered from the pump beams. The spectral intensity distribution of the scattered radiation in the interaction volume is obtained by solving the equation of radiative transfer and a detailed treatment of the modification this fluctuating field causes on the optical dipole induced by the coherent laser fields is presented. For a broad parameter regime, this modification can be expressed via a single quantity that incorporates the energy of the fluctuating field together with bandwidths and frequency offsets from the atomic resonance. Numerical solutions are given which show that the scattered field causes the DFWM reflectivity to be depressed by a signficant amount, depending most strongly on a characteristic transverse length of the interaction volume. Approximate analytic expressions for the reflectivity are also given which assist in physically understanding the underlying mechanisms.

A model describing the dynamics of a white- and colored-noise injected-signal, single-mode, homogeneously broadened laser in the semiclassical limit is presented. The system has a Hopf bifurcation above the threshold where phase locking occurs. This bifurcation point is characterized by a simple relation between gain and loss parameters, detuning, and external-driving-field intensity. The stochastic normal form of the system near the bifurcation point is found and the contribution of the harmonics of the bifurcation frequency in the spectrum is thus analytically determined. As a result of gain saturation and phase-excursion phenomena the resonances become apparent before reaching the bifurcation point for low driving-force values. Above this bifurcation point, the spectrum is that of a frequency-locked laser in the presence of noise. These results are consistent with numerical experiments carried out with both white and colored noise. In the case of colored noise, resonances are wider than in the white-noise case, depending on the correlation time of the multiplicative and the additive terms into which noise has been decomposed.

We analyze the quantum-fluctuation properties of second-harmonic radiation generated in the high-efficiency conversion process used in a recent experiment by Hakuta, Marmet, and Stoicheff [Phys. Rev. Lett. 66, 596 (1991)]. We extend their work by studying the second-harmonic generation inside an optical cavity. The active medium inside the cavity is modeled by three-level atoms with degenerated upper levels (1s, 2p, and 2s states of atomic hydrogen) interacting with a strong constant electric field. An enhancement of the conversion efficiency and a reduction of the added noise are found as a result of an electromagnetically induced transparency. We show that the scheme is capable of producing light in a squeezed or coherent state close to a minimum-uncertainty state with a large mean amplitude.

We have constructed the multimode bosonic realization of the su(1,1) Lie algebra, on the basis of which the su(1,1) generalized coherent state in the multimode Fock space is derived. It is shown that the multimode coherent state is, in fact, the generalized multimode squeezed vacuum state discussed by Lo and Sollie [Phys. Rev. A 47, 733 (1993)], and that the unitary displacement operator can be identified as the generalized multimode squeezing operator. Hence, similar to the single- and two-mode cases, our multimode bosonic realization of the su(1,1) Lie algebra has immediate relevance to the squeezing properties of boson fields.

We investigate the resonance fluorescence spectrum from two identical atoms driven by a strong standing-wave field. We find interesting modifications of the Mollow spectrum, caused by interferences between the two atoms, and in particular a succession of ‘‘dark’’ and ‘‘bright’’ states as one of the atoms is moved to successive nodes of the field. Large enough separation between the atoms leads to their decorrelation and the disappearance of these interferences, the atoms acting then as independent radiators. From a technical viewpoint, we also illustrate how the use of superoperators in Liouville space keeps the discussion transparent and provides a convenient tool for numerical calculations.