We report on measurements of the time dependence of the populations of Rydberg states of Na with n=25–33 produced by stepwise excitation or deexcitation from the initially populated state 28s, stimulated by room-temperature blackbody radiation. We also present a theoretical modeling of the experiments, which mainly consists of solving the set of coupled rate equations for all the states involved. The results of the calculations show that for times of the order of the lifetime of 28s the populations of ns and nd states produced via two-step transitions can be up to 30% of the populations of np states. We also find that np states get repopulated via three-step transitions at the 2–12 % level. A comparison between the data and calculations shows good agreement.

The overlap of classical resonances has been particularly successful in predicting ionization thresholds for hydrogen atoms in strong microwave fields, although not for low scaled frequencies. In this paper, we explicitly relate quantum mechanically computed matrix elements to the classical Fourier amplitudes used in the overlap criterion. The resulting twist to this demonstration of classical-quantum correspondence is that quantum matrix elements can be used to improve predictions of classical-resonance overlap for low scaled frequencies. Conversely, the classical amplitudes are shown to contain delicate cancellations in the quantum matrix elements. In the course of this demonstration, we also introduce a compact numerical method for evaluating high-order multiphoton matrix elements.

In the early experiments on optical pumping and coherent population trapping (‘‘dark resonances’’) increasing buffer gas pressure enhances the effect. In our recent lasing-without-inversion experiments, based on population trapping, we find the opposite behavior, namely, decreasing atomic coherence with increasing buffer gas pressure. We provide a theoretical explanation of this result in agreement with experiment.

A detailed comparison between experimental lifetimes for Rydberg atoms formed by the adiabatic crossed-field method and corresponding theoretical lifetimes has been performed to document that the crossed-field method indeed may be used to generate and control coherent elliptic states of highly excited Rydberg atoms. It is found that core effects play a negligible role except for states of very high eccentricity.

We investigate ultrashort pulse propagation in a dense medium of two-level atoms. We numerically solve the coupled nonlinear Maxwell-Bloch equations by assuming that the fields are slowly varying in time only. We find that while intrinsic optical switching of the atomic inversion persists in extended media, self-phase-modulation effects, coherent energy transfer, and reflections can be large even for films that are only a small fraction of a wavelength thick. If the propagation distance is sufficiently large, a physical boundary that separates fully excited atoms from atoms in the ground state can be created within the medium. In turn, this leads to a rapid spatial modulation of the nonlinear polarization, and a deterioration of the intrinsic optical switching mechanism. We then show that, although the slowly varying envelope approximation in space may be preempted by the fast longitudinal variation of the field and atomic variables, the mean-field approximation remains valid in the regime of ultrafast optical switching, provided the film thickness is sufficiently small such that the medium is nearly uniformly excited. These results are generated by utilization of our calculational method that fully accounts for the longitudinal dynamics of the fields, including reflections.

We show theoretically that optical phase conjugation via four-wave mixing can satisfy the quantitative criteria [Holland et al., Phys. Rev. A 42, 2995 (1990)] for performing quantum nondemolition measurements of a signal field despite the fact that this measurement scheme introduces noise into the signal field and thus does not perform a true quantum nondemolition measurement. The criteria can be satisfied under conditions in which the vacuum field injected in the rear of the phase-conjugate mirror is quadrature squeezed. Using this measurement scheme, it is possible to obtain values of the total information transfer coefficient that are as large as those that can be achieved using quantum nondemolition measurements.

A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.

In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.

Using a photorefractive oscillator, we show experimental optical patterns whose principal features are optical vortices moving around an optical axis on circles. These patterns can be interpreted as simultaneous emission of helical fields with high-charge phase singularities and other rotationally symmetric fields. Patterns with up to nine circling vortices are shown, as well as patterns with two concentric ‘‘wheels’’ of vortices. Mode locking in these rotating patterns corresponds to a stopping of the rotation. An intermediate case between free rotation and locking, in which the pattern ‘‘jumps’’ between certain angular positions, is demonstrated, showing that phase locking of these modes, which is not possible for an isotropic resonator, can come about by small anisotropies.

The propagation of a partially coherent optical beam through dispersive nonlinear media is investigated theoretically by using a phase-diffusion model for the laser beam. Changes in the second-order statis- tical properties during beam propagation depend on whether the nonlinear medium exhibits normal or anomalous group-velocity dispersion. In the case of normal dispersion, the coherence function and the corresponding optical spectrum remain unaffected. By contrast, modulation instability is found to be responsible for noise amplification in the anomalous dispersion regime, enhancing phase fluctuations and causing spectral distortion as well as coherence degradation. Under certain conditions, phase fluctuations exhibit temporal oscillations that lead to the characteristic spectral sidebands associated with modulation instability. The nonlinear Schrödinger equation is solved numerically to study the propagation regime in which the analytic theory becomes invalid.

We analyze two- and three-mode interactions in a cylindrically symmetric class-B laser with a low Fresnel number. Using the method of continued fractions, we derive the steady-state equations for two different kinds of rotating patterns, involving two or three modes. The threshold conditions for bistability in the first case and rotation in the second case are also found. The stability of the two dynamical solutions is investigated numerically. The results are compared with those obtained in some previous works.

The spectral distribution of light generated by a finite cavity with one moving mirror is compared with that produced by a fixed cavity containing a time-varying dielectric. In both cases a motion over a finite time interval is considered. Although the moving mirror is usually considered to be an idealization for the time-varying dielectric, there are qualitative differences in the spectra produced. The spectral distribution for the moving mirror case behaves as 1/${\mathit{n}}^3$, while that for the time-varying dielectric behaves on average as 1/${\mathit{n}}^4$ but is rapidly oscillating.

We calculate the spontaneous-emission characteristics of a quantum-well exciton embedded in the center of a planar microcavity and compare them with the emission characteristics in a single-mode cavity with lateral confinement of the electromagnetic field. The results indicate that because the modal structure of a planar microcavity consists of a spectrally dense continuum, the exciton decays into the cavity continuum with a time constant close to the free-space spontaneous-emission lifetime, even under conditions in which its spectrum displays the vacuum Rabi splitting. This behavior contrasts with the case of cavities with lateral in-plane confinement of the field, in which the vacuum Rabi splitting is the signature of a dramatic modification of the spontaneous-emission lifetime. The technological implications of this difference are discussed.

Using the two-mode realization of the su(1,1) Lie algebra, we define new states that equalize the su(1,1) uncertainty relation. We refer to these as two-mode intelligent SU(1,1) states. Due to strong correlations between modes, these states exhibit nonclassical properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, squeezing in the superposition of the modes, and sum squeezing. We also study the phase distributions of the states and propose a mechanism by which they may be generated.

A generalized Bloch-Maxwell formulation for laser-field-coupled semiconductors is derived from a two-band model which includes direct Coulomb interactions. The momentum-dependent, microscopic, electron-hole equations of motion in the time-dependent Hartree-Fock approximation and neglecting interband exchange interactions form the starting point for the formulation. A self-consistent set of coupled equations in four dynamical variables for the medium, together with the electric-field amplitude coupled through the Maxwell wave equation in a semiclassical approximation, are obtained to lowest order in the coherent Coulomb exchange interaction and the density-of-states distribution. Intrinsic optical bistability is predicted in a steady state due to a carrier density-dependent redshift of the band edge due explicitly to coherent Coulomb exchange. Integration of the dynamical equations for conditions which correspond to the ultrafast time regime exhibit intrinsic adiabatic inversion, adiabatic following, anomalous Rabi cycling, and unique, as well as fast, optical switching, all of which depend upon the coherent Coulomb exchange interaction.

Photorefractive oscillators are shown to have the same transverse properties as class-A lasers, in spite of the different mechanisms of light amplification in both systems and the different microscopic physics. A laser Ginzburg-Landau equation for the order parameter of photorefractive oscillators (PRO) is derived and correspondences between parameters of PRO’s and class-A lasers are given. The close similarity between these two systems is evidenced by numerical calculations. Experimentally, a PRO is found to emit stationary patterns such as pure mode patterns and vortex lattices, and to display a periodic motion of vortices, all of which are characteristic of lasers.

We have found that an intense shot-noise-limited laser beam tuned near the 4 ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$⇆4 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ potassium resonance transition acquires excess noise after passing through an atomic-potassium vapor cell. The noise is maximum for laser detunings of approximately ±1 GHz and falls to nearly the shot-noise limit for detunings greater than ±3 GHz. We describe the production of this noise in terms of a forward four-wave mixing process involving the laser field and its side modes, which are initially in the vacuum state. We present a fully quantum-mechanical theory of forward four-wave mixing in a system of two-level atoms and use it to predict the noise properties of the transmitted laser beam. The predictions of this theory are in good agreement with the experimental data.

Based on proposals to measure squeezing by homodyne cross correlation [Ou, Hong, and Mandel, Phys. Rev. A 36, 192 (1987)] and by homodyne intensity correlation measurements with a weak local oscillator [Vogel, Phys. Rev. Lett. 67, 2450 (1991)], the method of homodyne correlation measurements is considered in detail for the case of weak local oscillators. Aside from the feasibility of measuring squeezing in low efficiency detection, it appears possible to record the correlation of the noise of two noncommuting observables, namely, the intensity and the electric field strength of the signal field. The separation of the different contributions to the measured correlations is considered and spectral correlation measurements are analyzed. Local oscillator noise, which is not balanced out in such a scheme, is found to be attenuated effectively by decreasing the local oscillator field. In particular, in the homodyne cross correlation scheme, it is of interest to use a beam splitter that significantly differs from a 50%:50% partition.

The phase properties of an initially coherent field propagating through a Kerr medium are examined using two different measures of phase uncertainty: (i) variance of periodic functions and (ii) the entropy. The variance of a periodic function of phase (with period 2π/m) is found to be minimized only at the times when the field evolves into a discrete superposition of n distinguishable coherent states (Schrödinger-cat states) where n is a factor of m. The phase entropy is found to be more sensitive, as it is minimized at the times when the field evolves into a superposition of an arbitrary number of distinguishable coherent states. The sum of the photon number and phase entropies is found to display behavior very similar to the Wehrl entropy for the evolving field, i.e., the sum is minimal at the times the cat states occur, and at these times it has a value that indicates the number of component coherent states in the cat states.

We characterize the nonlinear dynamics of a semiconductor laser subject to optical injection. The key characteristics of measured optical spectra are reproduced in calculations based on a single-mode model that includes spontaneous-emission noise. The laser exhibits chaos over a bounded range of injection levels. As the chaotic regime is approached from both lower and higher injection levels, a period-doubling route to chaos is followed, although the route is obscured by spontaneous-emission noise. A new, bounded regime of period-doubling occurs for injection levels well above the region of chaotic dynamics. Optical injection strongly modifies the carrier-field resonance coupling frequency.

A photon number density operator proportional to the dot product of the electric field and the vector potential is introduced as an alternative to the Mandel operator. In the Lorentz gauge it is the time component of the four-vector obtained by contracting the electromagnetic field tensor with the vector potential. Its other components can be interpreted as a current-density vector, and these number and current-density operators satisfy a continuity equation. The photon density operators introduced here are all products of operators that satisfy Maxwell’s equations and whose Lorentz and gauge transformation properties are well known.