Master equations are derived for the time evolution of density-matrix elements characterizing atoms interacting with classical radiation fields that drive transitions between electronic-state manifolds of levels. The atomic center-of-mass motion is quantized and recoil accompanying absorption, stimulated emission, and spontaneous emission is included. An adiabatic elimination of the optical coherences is used to obtain quantum rate equations for ground- and excited-state density-matrix elements. Subsequent adiabatic elimination of excited-state density-matrix elements results in rate equations for the slow evolution of ground-state density-matrix elements. It is shown that recoil during spontaneous emission mixes spatial and internal atomic degrees of freedom. © 1996 The American Physical Society.

By varying an intensive parameter in a nonlinear optical system with two-dimensional feedback the wave front displays a transition from a uniform to a patterned state, and eventually to space-time chaos. A nonlocal interaction, introduced by means of a feedback rotation, is the source of the observed phenomena. The observed space-time chaotic behavior is characterized by a rapid decay of correlation. We study the possibility that the system eventually evolves from space-time chaos to a turbulent regime. © 1996 The American Physical Society.

The theoretical basis for electromagnetically-induced focusing (EIF), which is caused by spatial variations in the coupling laser strength in an electromagnetically-induced transparency (EIT) experiment, is studied in detail. Using a numerical model it is shown that radial changes in both absorption and refractive index are important in predicting the probe beam’s propagation conditions. Detailed calculations of the focusing and defocusing during EIF under various conditions are presented and compared with appropriate experiments. Diffractionlike patterns are predicted for, and observed on, a probe beam after propagation through a smaller EIT aperture. © 1996 The American Physical Society.

The bistable response of linear molecular aggregates modeled as linear chains of two-level systems is shown. We carry out analytical and numerical calculations of the aggregate population by means of the system of coupled nonlinear equations for the density matrices of individual molecules. Our conclusion is that bistable behavior of the population results from the dependence of resonance frequency of the aggregate on the number of excited molecules. © 1996 The American Physical Society.

We discuss nonclassical effects in the fluorescence from a simplified model of laser-cooled neutral atoms in one-dimensional optical molasses. Despite the randomness characteristic of these atomic systems, squeezing takes place according to a well defined spatial pattern within a small solid angle whose width essentially depends on the molasses size and geometry. We also address the issue of the measurability of such an effect. © 1996 The American Physical Society.

We exploit analogies between tunneling electrons and evanescent electromagnetic waves to construct and operate an optical Larmor clock. In the electronic Larmor clock, the tunneling time is proportional to the amount of precession the electronic spin undergoes while interacting with a weak, barrier-confined magnetic field. In the optical scheme, the analogy to the spin is made via Stokes parameters, and an optical retarder is shown to be analogous to the magnetic field. A magnetized tunnel barrier consists of a thin film of uniaxial liquid crystal between two high-index prisms. To operate the clock, we measure the Stokes parameters of the polarized laser beam transmitted through the barrier. By varying the wavelength of the incident light, we use the clock to study tunneling through barriers of various thicknesses. © 1996 The American Physical Society.

We report on the analysis of experiments on a neodymium-doped yttrium aluminum garnet laser with an intracavity frequency-doubling crystal. Three modes of the laser were excited in differing polarization configurations. The total intensity of infrared light was observed and then analyzed using methods of nonlinear-time-series analysis. We present clear evidence using global false nearest neighbors that when all polarizations are parallel, the intensity is chaotic with two positive Lyapunov exponents and the system can be embedded in dimension 7. The noise level in this operating condition, which we call type I chaos, is small. When one of the polarizations is perpendicular to the others, the intensity is again chaotic with positive Lyapunov exponents, but there is substantial noise in the signal of high dimensional origin, and no finite embedding dimension appears possible. We call this type II chaos. We suggest that the origin of this phenomenon is the intrinsic quantum noise associated with the generation of green light, which is 25 times more intense in the type II operating configuration than in the first. In past experiments with this system we have found that the type I chaos can be controlled to unstable periodic orbits while type II cannot. In each type of chaotic laser operation we use local false nearest neighbors to demonstrate that the local dimension of the dynamics is 7. This means seven differential equations can capture the full dynamics of these regimes of the laser. We evaluate local and global false nearest neighbors to support our conclusions and determine the Lyapunov spectrum of each type of chaotic behavior. The predictability of type II chaos is shown to be much less than that of type I, and we make local polynomial models in reconstructed-state space to demonstrate that we can predict rather well for type I chaos. Finally we suggest a fairly standard model for the interaction of the infrared light with the nonlinear frequency doubling medium and with a two-level of the active medium. © 1996 The American Physical Society.

We investigate the noise in a fundamental soliton state constructed from the exact energy eigenstates of the quantized nonlinear Schrödinger equation. It is shown that such a state has statistical properties that are substantially different from those of a coherent state with the same mean field. We can construct, for example, a fundamental soliton state that has initially minimum fluctuations for the four linearized soliton operators (particle number, phase, momentum, and position). We also show that the linearized noise analysis is not valid for nonlinear phase shifts larger than ${\mathit{n}}_0^{1/4}$, where ${\mathit{n}}_0$ is the average number of particles in the fundamental soliton. © 1996 The American Physical Society.

A first-principle calculation of the signal and the noise for Ramsey spectroscopy with nonclassical light sources is given. It is found that the signal-to-noise ratio can be enhanced by using fields with sub-Poissonian statistics. © 1996 The American Physical Society.

The spontaneous Raman scattering from liquid samples of ${\mathrm{C}}_6$${\mathrm{H}}_6$ is investigated in the Casimir topology of a microscopic optical Fabry-Pérot cavity terminated by Bragg reflectors tuned at the emitted Stokes wavelength. The given general quantum scattering theory is based on a complete set of mode functions describing the cavity-confined field in its vacuum state. The coupling of the field with the normal CH ring stretching mode at Δν=3062 ${\mathrm{cm}}^{\mathrm{-}1}$ (totally symmetric species ${\mathit{A}}_{1\mathit{g}}$) of the benzene molecule is given via the related Raman tensor, which leads to the appropriate form of the coupling Hamiltonian. A detailed experimental investigation of the spontaneous Raman scattering for the mode is then reported. The results confirm the relevant predictions of the scattering theory, namely, the effect of the vacuum confinement on the enhancement and inhibition of the total and differential cross sections, on the angular distribution of the scattered radiation, and on the molecular depolarization ratio. © 1996 The American Physical Society.

A model for Raman lasers including several longitudinal modes is analyzed. Depending on the choice of the parameters the system can exhibit single-mode emission, wide bistability domains, and self-pulsing. The latter is often characterized by two frequencies, which are clearly related to single-mode and multimode instabilities, in agreement with the interpretation of earlier experimental results. © 1996 The American Physical Society.

This paper deals with a system exhibiting quantum interference in the two-photon coupling between its ground state and the continuum through two quasiresonant intermediate levels by two modes of the electromagnetic field. We show that this system can generate quantum coherence among the two field modes, the internal and the external degrees of freedom. Two applications are discussed: generation of photon-number correlations between the two modes, and selection of atoms in a given velocity class. © 1996 The American Physical Society.

It is shown that distinct atomic beams can be entangled when they interact with quantum superpositions of macroscopically separated micromaser fields. Experimentally feasible tests of complementarity are proposed, detecting Ramsey interference (or not) in one and ‘‘Welcher Weg’’ information (or not) in the other entangled beam. Available information and fringe contrast can be manipulated using classical and quantum fields. The ‘‘quantum eraser’’ is realized in the former case, while it is only a special feature in the latter one. Other applications of entangled atoms are also suggested. © 1996 The American Physical Society.

In this work we analyze the quantum phase properties of pairs of electromagnetic field modes. Since phases differing by 2π are physically indistinguishable, we propose a general procedure to obtain the correct mod(2π) probability distributions for the phase difference. This allows us to investigate the properties of a number of phase approaches. This procedure provides deeper insight into the quantum nature of the phase difference. We relate this problem to the representation of nonbijective canonical transformations in quantum mechanics. © 1996 The American Physical Society.

The existence of positive well-defined quasiprobabilities is known to be related to the measure of nonclassicality for a given field state. We test the coincidence of the loss of well-known nonclassical properties with the appearance of the positive well-defined quasiprobabilities for various fields influenced by phase-insensitive reservoirs. For Gaussian fields the appearance of a positive Glauber-Sudarshan P function coincides with the loss of nonclassical properties in quadrature fluctuations and in photon statistics. We find that when an initial Fock state dissipates or is amplified the initial field loses its nonclassicality in photon statistics before the P function becomes positive, which is different from the Gaussian field. The Wigner function may be positive even when the decaying Fock state is sub-Poissonian. For the amplification of the Fock state, however, the Wigner function is positive only when the field is super-Poissonian. For the dissipation and amplification of the Fock state the point when a certain quasiprobability function becomes positive definite depends only on the average number of photons N of the heat bath. © 1996 The American Physical Society.

We consider the classical and quantum-mechanical processes of three-wave interactions in different phase regimes and present numerical calculations for the quantum case, where all three modes are sizably excited from the beginning. These excitations are coherent so that various important phase regimes can be adjusted. In addition, one mode can also be prepared in a squeezed or Kerr state. The classical solutions are well known and are briefly summarized, but certain phase regimes are classically unexplored and we show here that they give interesting and surprising results. In the out-of-phase regime (where the photon numbers do not change in the first order of time) we get, with an initial Kerr state, strongly sub-Poissonian photon statistics in the signal after a short interaction time. This effect is limited by the classically described phase shifts that are present even in the parametric approximation. This nonclassical phenomenon (due to the Kerr state) helps us to understand similar nonclassical effects generated by entangled states of the pump and signal during sum-frequency generation. © 1996 The American Physical Society.

The spatiotemporal dynamics of a laser consisting of a thin layer of active material, whose thickness is less than the lasing wavelength, and feedback mirror, has been analyzed on the basis of derived complex order-parameter equations, namely, Cross-Newell, Newell-Whitehead-Segel, and Swift-Hohenberg equations. We have shown that the thin-layer laser can have an output in the form of traveling waves and that they are stable in a wide region of control parameters. Numerical simulations carried out for two-dimensional laser dynamics demonstrate the possibility of spontaneous formation of rhomboid patterns, and domains containing traveling waves with different orientations. © 1996 The American Physical Society.

A continuous photon-number measurement has been assumed in the idler mode output from parametric down-conversion for an initial coherent state. The states generated in the signal mode due to the mode entanglement and the effects of both the destructive and the ideal reduction are described in terms of a quasidistribution of the complex field amplitude as well as of the density-matrix elements. The resulting near-number states in the ideal case are suitable for the study of the dynamics of phase and quadrature distributions rotated by the actual preferred phase. These states exhibit both number and quadrature squeezing. © 1996 The American Physical Society.

The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an experiment was performed by Itano et al. [Phys. Rev. A 41, 2295 (1990)] in which an atomic-level measurement was realized by means of a short laser pulse. The relevance of the results has given rise to controversies in the literature. In particular, the projection postulate and its applicability in this experiment have been cast into doubt. In this paper we show analytically that for a wide range of parameters, such a short laser pulse acts as an effective level measurement to which the usual projection postulate applies with high accuracy. The corrections to the ideal reductions and their accumulation over n pulses are calculated. Our conclusion is that the projection postulate is an excellent pragmatic tool for a quick and simple understanding of the slow-down of time evolution in experiments of this type. However, corrections have to be included, and an actual freezing does not seem possible because of the finite duration of measurements. © 1996 The American Physical Society.

The effect of electromagnetically induced transparency in resonant four-wave-mixing schemes is investigated in an analysis that goes beyond perturbation theory in the coherent driving field. In addition we examine the case where the two-photon pump field is sufficiently strong to necessitate a nonperturbative treatment. This allows us to examine the cases where either one or both of the driving fields are strong. Phase matching is included in a plane-wave propagation treatment that matches the situation most likely to be encountered in actual experiments. The calculations are in part intended to model real experimental situations and thus incorporate driving and pump-field linewidths via the phase-diffusion model and Doppler broadening. With a strong pump-field laser, large enhancements in the efficiency of light generation occur at frequencies corresponding to the Autler-Townes satellites induced by the strong driving field. In this situation gain and high four-wave-mixing efficiency are simultaneously present, resulting in the production of a large intensity of coherent radiation. © 1996 The American Physical Society.