We present the theory of a laser in which the transmittivity of one output mirror is controlled by a current derived from a photodetector illuminated by the output light from that end of the cavity. That is, one output port of the laser is controlled by a feedback loop. We calculate the photon statistics inside the cavity. We also calculate the spectrum of intensity fluctuations for the light leaving the cavity through the output mirror not controlled by feedback. We show that intensity fluctuations inside the cavity may be reduced to 50% below the Poissonian limit while outside the cavity the reduction is at best 25% of the shot-noise limit. These optimum results, however, are not achieved under the same operating conditions.

This paper presents a general theory for a continuous quantum-nondemolition measurement of photon number. This theory treats a time-distributed measurement as a sequence of measurements in which at most one photon can be detected in an infinitesimal time, and shows that the average number of photons remaining in the measured field increases when a photon is detected and decreases when no photon is detected. The state of the measured system evolves nonunitarily and reduces continuously to a nunber state whose eigenvalue is uniquely determined by the average rate of photodetection and whose probability distribution coincides with the initial photon-number distribution. Applying the general theory to typical quantum states—coherent, thermal, and squeezed states—shows that the continuous-state reduction towards a number state depends strongly on the initial photon statistics. Despite the nonunitarity of state evolution, an initially pure state keeps its purity: the initial density operator becomes diagonalized only if the readout information is discarded.

A comparison is made of predictions for the phase variances and the phase distribution functions obtained from the Garrison-Wong and Pegg-Barnett formalisms for real field states that include number states, coherent states, and squeezed vacuum states. It is shown that both approaches lead to qualitatively different phase distributions. The Garrison-Wong approach predicts an anisotropy of the phase distribution that is inconsistent with the symmetry of the Wigner and Q functions.

We present a theory of pulsed dressed-state lasers that operate on an inverted transition between dressed states of a coupled atom-field system and are pumped by short laser pulses. We discuss the validity of the adiabatic approach in such a case and generalize the theory beyond the adiabatic approximation. With the help of the generalized theory, we study the competition between various lasing processes, the role of higher-order instabilities, and the role of temporal interference effects. We formulate the physical interpretation of the results by looking at the spectrum of the emitted pulse.

A theory of the photorefractive phase-conjugate oscillator (PCO) is developed. A PCO consists of an optical resonator made up of two planar mirrors (a Fabry-Pérot cavity) containing an intracavity photorefractive phase-conjugate element that is pumped externally by a pair of off-axis counterpropagating laser beams of the same frequency. The two pumps are assumed to be parallel polarized. Phase conjugation of an input beam of slightly higher or lower frequency occurs because of nondegenerate isotropic four-wave mixing. The conjugation process generates a beam of slightly lower or higher frequency so that six waves coexist in the resonator. In the absence of the mirrors, the PCO simply reduces to a photorefractive phase-conjugate mirror (PCM), and in the absence of one of the mirrors, it reduces to a photorefractive phase-conjugate resonator (PCR). Degenerate and nondegenerate self-oscillations are shown to occur for several different cases of practical importance, and the threshold conditions for these cases are derived analytically under the assumption of the undepleted pumps. It is shown that the PCM can exhibit nondegnerate self-oscillations for φ=π/2, where φ is the phase shift between the gratings and the light interference patterns when the gratings are stationary. The coupling coefficient required for degenerate self-oscillation in the PCR is found to be one-half of that for the PCM if the mirror is perfectly reflecting and if the pump beams have equal powers (r=1). It is also shown that one cannot have degenerate self-oscillation in PCO for r=1 and φ=π/2, and nondegenerate self-oscillation for r=1 and φ=0. The self-oscillation conditions for the PCO do not depend upon the position of the photorefractive crystal inside the cavity.

This paper is the second in a series describing the theory of photorefractive phase-conjugate oscillators. We apply the formulation developed in Paper I to study the threshold conditions for self-oscillation in the phase-conjugate mirror (PCM), the phase-conjugate resonator (PCR), and the phase-conjugate oscillator (PCO) by considering anisotropic four-wave mixing where the two counterpropagating off-axis pump beams are orthogonally polarized. We consider the two types of situations for orthogonally polarized pump beams corresponding to the two crystal families: one such as the ${\mathrm{Bi}}_{12}$${\mathrm{SiO}}_{20}$ crystal family (sillenite family) and the other such as ${\mathrm{BaTiO}}_3$ and the strontium barium niobate crystal family. Degenerate and nondegenerate self-oscillations are shown to occur for both these types for a number of practically important cases. Threshold conditions for oscillations are derived analytically under the assumption of undepleted pumps for most of these cases. It is shown that for the sillenite family of crystals, the coupling coefficient required for degenerate self-oscillation in PCR is one-half of that for PCM when the mirror is perfectly reflecting and when the pump beams have equal intensities. For PCO, the presence of the second mirror, however, increases the threshold value of the coupling coefficient for self-oscillation by a factor (1+${\mathit{R}}_1$${\mathit{R}}_2$)/(1-${\mathit{R}}_1$${\mathit{R}}_2$), where ${\mathit{R}}_1$ and ${\mathit{R}}_2$ are the power reflection coefficients of the mirrors. For the second type of crystal family, it is shown that PCM also can exhibit self-oscillation. The coupling coefficient required for degenerate self-oscillation in PCR is one-half of that for PCM when ${\mathit{R}}_2$=m and r=${\mathit{m}}^{\mathrm{-}1}$, where m and r are the ratios of the coupling coefficients of the backward and forward gratings and intensities of the backward and forward pumps, respectively.

This is the first of a series of papers on the theory of cone emission from a laser-pumped two-level atomic medium. Starting from microscopic quantum theory for both the active medium and the field, equations for the slowly varying macroscopic quantities are derived. In the steady-state limit, which experimentally corresponds to cw excitation, we find that the sources for the paraxial fields of interest have a long coherence length despite the random nature of spontaneous emission. These radiation sources enter into the equations for the fields in the same form as the source generated by four-wave mixing and therefore may be considered as a ‘‘spontaneous four-wave mixing,’’ since the photons emitted in the Rabi sidebands are correlated. This has far-reaching consequences on the physics of cone emission and also sheds some new light on the fluoresence from strongly driven atomic systems.

We establish a mechanism, which supports Cherenkov-type radiation, as a source of cone emission. This can be considered as an additional mechanism to the previously discussed four-wave mixing (4WM) and initial encoding and follow-up refraction effects. The radiation source is provided by spontaneous emission of the driven atoms at the frequencies of interest. Due to the medium dispersion, the pump field propagates faster than the phase velocity of the field that is generated at the Rabi sideband at lower frequency. Cherenkov radiation is then possible if the source has a long correlation length, which is indeed the case despite the random nature of spontaneous emission. Coherent superposition of the source for the lower-frequency field is in an off-axis direction given by the Cherenkov radiation condition. Differences between 4WM and Cherenkov-type models are consequently resolved.

Comparison between sophisticated R matrix and simple central-field calculations for photoionization of ${\mathrm{Al}}^{6+}$ over a broad energy range is made. Except for the autoionization resonances, which are not included in the central-field model, agreement is excellent. Reasons for, and implications of, this agreement are discussed.

With a view to obtaining an exact analytic solution to the time-dependent Schrödinger wave equation for noncentral harmonic and anharmonic potentials in two dimensions, we make use of an ansatz for the eigenfunction in conjunction with the methods of Burgan et al. [Phys. Lett. 74A, 11 (1979)] and Ray [Phys. Rev. A 26, 729 (1982)]. While the method is found to work well for a restricted class of harmonic potentials, its limitations in the case of anharmonic potentials are pointed out.

The dielectronic-recombination cross sections and rate coefficients of Al-like ${\mathrm{S}}^{3+}$ ion are calculated for the process in which the 3s electron is excited to the 3p state and the projectile electron is captured to a high Rydberg state (nl). The calculations have been done using single-configuration and nonrelativistic Hartree-Fock wave functions in LS coupling. The transitions from the ground state (3${\mathit{s}}^2$3p${)}^2$P and the multiplets of the first excited state (3s3${\mathit{p}}^2$) have been included explicitly. We tabulated our results of the cross sections and rate coefficients to facilitate direct comparison with future experimental data.

We have measured absolute differential cross sections of atomic hydrogen by electron impact. A modulated crossed-beam method was used. The energy and angular range measured were from 40 to 200 eV and from 12° to 156°, respectively. Atomic hydrogen was generated by a microwave discharge device. The present results were compared with the previous measurement by Williams [J. Phys. B 8, 1683 (1975); 8, 2191 (1975)] and a few theoretical results. There is relatively good agreement in the forward scattering, but a signficant discrepancy has been found in the extreme backward direction in this energy region. In general, the present results are larger than the previous measurement and theoretical results by more than a factor of 3 at extreme angles. The present results of the integrated cross sections are in good agreement with the previous measurement and theoretical predictions, even though there are disagreements in the backward scattering due to the very small differential cross sections in the backward angles.

Calculations of photoionization amplitudes and phases for the 4d subshell of xenon are carried out in the relativistic random-phase approximation for photon energies ranging from 80 to 140 eV. These calculations account for correlations within and between the 4d, 5s, and 5p subshells as well as relaxation of the 4d subshell. The resulting theoretical amplitudes are compared with a recent experimental measurement of photoionization amplitudes and phases for the 4${\mathit{d}}_{5/2}$ subshell at 94.5 eV.

An error in an earlier paper [Phys. Rev. A 40 2276 (1989)] of the theoretical expression for the trace of the collision-induced polarizability tensor of hydrogen pairs (${\mathrm{H}}_2$-${\mathrm{H}}_2$), which is based on the dipole-induced-dipole (DID) approximation, is corrected here. The analysis of the measurement of the binary collision-induced trace Raman spectrum of hydrogen gas is reconsidered. However, a discrepancy between the measured trace spectrum and the computation based on the revised theoretical expression remains unresolved. It is not clear whether the lowest-order DID model used here is inadequate or the measurement of the very week trace spectrum is in error.

Optical pumping of the ground state of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}_{}^{+}{}_{}{}^{}$ ions, confined in a Paul ion trap on the weak 6${\mathit{P}}_{1/2\mathrm{-}}$6${\mathit{P}}_{3/2}$ M1 transition at λ=710 nm, and consequent magnetic-dipole transitions between the ground-state hyperfine Zeeman levels have resulted in an A factor of 12 968 180 601.61(0.22) Hz and linewidth of 0.5 Hz. The value includes corrections of Zeeman shifts from residual magnetic fields and second-order Doppler shifts in the several-eV-deep trap potential, while the ions were cooled by He buffer gas. Two M1 quanta have been applied simultaneously in a double-resonance experiment.

We give a field-theoretical derivation of the explicit probability distribution of photon emission by identical N noninteracting atoms (sources), which has been applied to study the tendency of photons to form collimated beams. More precisely, given that each source emits one photon with some given energy, due to the same atomic transition, we derive the conditional probability that the N photons have momenta in arbitrary directions. Each source is assumed separately to emit photons of momenta with uniform distribution for their directions, and no assumption is made on the sources being pointlike.

The frequency-dependent density-density response function for a semiclassical gas has been calculated from its defining equation of linear-response theory. The particular form of the response function appears to be relevant to optic-data inversion using Kramers-Kronig relations. Also the zero-frequency limit of the response function, being the static susceptibility, is a bounded function. The susceptibility for the semiclassical gas model provides a unique opportunity to test the bounds analytically. This study further suggests a slightly different derivation of the lower bounds, perhaps less abstract than by convexity theory via Jensen’s inequality.

Shape changes of a fluid membrane with fixed area modeled by a curvature Hamiltonian and a boundary line tension are investigated. The zero-temperature energetics are studied using a variational principle in the space of axisymmetric shapes. For zero spontaneous curvature, the only energy minimizing shapes are the disk and the sphere. The energy barrier heights between these configurations are determined as a function of the Hamiltonian parameters. Thermal fluctuations of the shape are studied by means of a Monte Carlo simulation. The ‘‘phase transition’’ from open to closed topology is determined as a function of the rigidity and line tension at nonzero temperature. The transition is found to persist even at zero membrane rigidity. The energetics of the transition are shown to be related to the branched polymer scaling behavior of the fluid membrane.