We use the quantum theory of feedback developed by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)] and Wiseman [Phys. Rev. A 49, 2133 (1994)] to investigate the photon-number noise properties of the micromaser with direct detection feedback. We find that the feedback can significantly reduce the amount of noise in the photon number. Under the right conditions the feedback locks the systems onto a number state. As opposed to other schemes in the past [P. Meystre, Opt. Lett. 12, 669 (1987); J. Krause, M. O. Scully, and H. Walther, Phys. Rev. A 36, 4547 (1987)], we can fix the number states to which the system evolves. We also simulate the micromaser using the quantum-trajectories method and show that these results agree with the quantum theory of feedback. We show that the noise of quantum island states [P. Bogar, J. A. Bergou, and M. Hillary, Phys. Rev. A 50, 754 (1994)] can be significantly reduced by the feedback.

We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The interaction between the atom and the cavity mode is treated nonperturbatively with the quantized motion of the atom along the cavity axis included. Results are presented for the spontaneous-emission spectrum and the final momentum distribution of the atom. For equal atomic and cavity linewidths analytical results are obtained using a Bloch-state basis (eigenstates of the coupled atom and cavity mode); these are compared with results calculated in the Raman-Nath approximation. The case of unequal linewidths may be solved numerically using the eigenstates of the uncoupled atom and cavity mode as a basis, or analytically by making a secular approximation in the Bloch-state basis. The distribution of final atomic momentum shows that under strong-coupling conditions the atom is diffracted by its radiation reaction field. We compare the spontaneous emission spectra with spectra calculated by treating the motion of the atom classically. Generally there is good agreement when the classical results are averaged over the quantum-mechanical uncertainty in the initial position of the atom. The agreement is lost for sufficiently strong dipole coupling or sufficiently light atoms. Then, spectra that are symmetric in the classical treatment are asymmetric in the quantum treatment due to energy exchange between the internal degrees of freedom and center-of-mass degrees of freedom of the atom.

We investigate the nonlinear dynamics of a nonconventional (i.e., pumped by a mixed-mode wave) modulational instability in a highly birefringent nonlinear dispersive medium. We find that the depleted regime of propagation beyond the linearized stage can be described analytically in a proper region of the parameter space. In this case the governing coupled nonlinear Schrödinger equations, which are not integrable, are reduced to an integrable one-dimensional nonlinear oscillator that rules the propagation of the pump wave and a single sideband pair. This approach permits us to predict the existence of stable and unstable manifolds of time-periodic solutions of the coupled nonlinear Schrödinger equations. The nonlinear dynamics governed by these equations mimics the period-doubling instabilities associated with the homoclinic separatrices in the reduced phase space. Moreover, our approach is also capable of describing the onset of spatial chaos that occurs when the parameter values are such that the additional degree of freedom represented by the conjugated sidebands becomes effective.

Three experiments are discussed in which nonlocal effects can be induced by changing the relative amplitudes of wave packets. Unlike previous experiments, in which nonlocal effects were induced by means of polarizers or phase shifters, in the proposed experiments nonlocal effects can be induced by means of variable beam splitters.

We numerically investigate the classical limit of quantum trajectories in optical second-harmonic generation. This is a dissipative system of two nonlinearly coupled harmonic oscillators, corresponding to the fundamental and second-harmonic optical cavity modes. Classically it is described by a system of nonlinear differential equations which have a range of attractors: fixed points, limit cycles, and chaotic attractors. We consider the field-amplitude mean values corresponding to the quantum trajectory wave functions. We find that in the classical limit of large photon number the trajectories of these mean values approach the corresponding classical attractors. This is because the mean values of operator products factorize into products of mean values in the classical limit.

Based on a trasfer-matrix formalism, photon-assisted tunneling is studied in a strongly driven double-barrier tunneling diode. Two scenarios are considered: A driving potential ${\mathit{V}}_1$cos(ωt) acting on the central quantum well, which may be realized with electrostatic gates close to the quantum well, and a driving electric field across the diode generated by a laser field. Strong quenching of the transmission probability is found for certain parameters {${\mathit{V}}_1$,ω} of the driving field, which can be explained in terms of zeros of fractional Bessel functions, ${\mathit{J}}_{\pm \nu }$(γ${\mathit{V}}_1$/ħω), where γ is a structural parameter. The effect shows a strong similarity to the ‘‘coherent destruction of tunneling’’ recently found in strongly driven quartic double wells.

We derive the quantum-limited linewidth of a bad-cavity laser, where the cavity-loss rate can be comparable to or larger than the gain bandwidth. We allow for incomplete inversion and arbitrary mirror losses and show how the position-dependent gain, refractive index, and populations co-determine the laser linewidth. The result obtained factorizes in parts that have straightforward physical interpretations. In the bad-cavity regime the laser linewidth is shown to be reduced as compared to the Schawlow-Townes expression as a result of anomalous dispersion associated with the optical gain. Saturation is shown to lead to a power-independent contribution to the laser linewidth; the magnitude of this contribution depends critically on the assumed pumping and decay rates.

Based on the linearization approximation and the conservation of commutation brackets, a general, self-consistent scheme is developed to quantize nonlinear optical-pulse propagation problems. A general computation procedure is developed to calculate the quantum uncertainties of the inner product between any given function and the (perturbed) field operator. As an illustration, a self-consistent quantum theory of the self-Raman effect in optical fibers is presented. The influence of the self-Raman effect on soliton squeezing is examined.

Three-level models of lasers without inversion in V and Λ configurations are studied in a realistic Doppler-broadened gas medium. The intensity of a generated coherent radiation is numerically calculated for a wide range of experimental parameters and the role of the laser cavity is fully taken into account. Different geometrical arrangements of the experiment are compared. Significant differences in lasing properties of the studied models are shown and discussed. An amplification mechanism based on the Doppler shift tuning to dressed-state inverted transitions is discussed.

Spectra of moderately ionized molybdenum atoms were excited in the TEXT tokamak at Austin, Texas. Photographic observations were made with a 2.2-m grazing-incidence spectrograph in the range 40–300 Å. Improved wavelengths were obtained for five electric-quadrupole (E2) lines of Mo xvi of the type 3${\mathit{d}}^9$-3${\mathit{d}}^8$4s lying in the region 51–55 Å. Semiempirical calculations of the wavelengths and transition probabilities confirm the existing identifications of these lines. The transition from the lowest level of 3${\mathit{d}}^8$4s, ${(}^3$${\mathit{F}}_4$,1/2${)}_{9/2}$, to the 3${\mathit{d}}^9$ ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{5/2}$ ground state was found to be anomalously strong. This is thought to be a consequence of the very low density and low electron energy of our plasma and suggests the possibility of using this line as a plasma diagnostic device.

We discuss how an observed neutrality of atoms and observed effects of vacuum polarization can be combined to check CPT symmetry between the electron and positron. Our argument is model independent and generalizes an argument by Müller and Thomas [Phys. Rev. Lett. 69, 3432 (1992)] based on a specific choice of CPT-odd Lagrangian. Our bound is ‖${\mathit{Q}}_{\mathit{e}}^{+}$+${\mathit{Q}}_{\mathit{e}}^{\mathrm{-}}$‖≤2×${10}^{\mathrm{-}18}$e.

We derive relationships between canonical and measured phase distributions for quantum-oscillator states in the semiclassical regime. First, we extend the formalism for the canonical phase to include external measurement-induced uncertainty. We require that a phase shifter shifts a phase distribution while a number shifter does not change it. These axioms determine pure canonical phase distributions uniquely while a noisy distribution can be interpreted as a weighted average of pure phase distributions. As a second step, we show that measured phase distributions, i.e., s-parametrized phase distributions fulfill approximately the axioms of noisy canonical phase, and we derive simple analytical expressions for the corresponding weight functions. Our analysis thus bridges all three conceptions of quantum-optical phase (canonical phase, s-parametrized phase, phase from measurements) and provides important physical insight into the relationship between them.

The dynamical origin of the quantum defect Δ of the valence electron of alkali-metal atoms is attributed solely to an unspecified potential of the inner core, and it is demanded that Δ is stationary with respect to variation in the values of atomic core radius ${\mathit{r}}^{\mathrm{*}}$. It is seen that this conjecture, when supplemented by a reasonable description of the core interaction, simultaneously produces numbers for ${\mathit{r}}^{\mathrm{*}}$ and Δ that help visualize the conceptual aspects of the problem. Corrections to the quantum-defect data due to core polarization are considered from a slightly different point of view. Problems in extending the present model for multivalent atoms are discussed.

The triply excited ${\mathrm{He}}^{\mathrm{-}}$ 2s2p2p ${}_{}{}^4{}_{}{}^{}$P state is studied. The resonance position and width are calculated to high precision with a saddle-point complex-rotation method. The relativistic corrections and fine structures are also calculated. The absorption wavelength and oscillator strength from the ${\mathrm{He}}^{\mathrm{-}}$ 1s2s2p ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ state is computed to facilitate the observation of this resonance in synchrotron-radiation experiments.

Ionization by impact of protons on hydrogen targets in different initial states, with principal quantum number n=1–5, is studied at collision energies from 10 up to ${10}^3$ keV/amu. Total cross sections are calculated employing the first-order-Born approximation and the continuum-distorted-wave–eikonal-initial-state model. Scaling laws predicted by the generalized correspondence principle are analyzed.

Charge-analyzed ${\mathrm{He}}^{+}$ and ${\mathrm{He}}^{2+}$ ions are measured in coincidence with convoy electrons for collisions between ${\mathrm{He}}^{+}$ ions and carbon foils of 3 and 10 μg/${\mathrm{cm}}^2$. The bombarding energy of the projectile ${\mathrm{He}}^{+}$ ranges from 17.5 to 25 keV/amu. The results are independent of the thickness of the carbon foils. The cross section of convoy electrons for ${\mathrm{He}}^{2+}$ is about 3% of that for ${\mathrm{He}}^{+}$ in a state of equilibrium resulting from multiple excitations and deexcitations. The transport length ${\lambda }_{\mathit{c}}$ of the convoy electrons is about 2.0±1.2 Å, which is close to the mean free path of free electrons of the same speed in the carbon foil. This implies that the convoy electrons are produced in the bulk of the foil and survive scattering in a 2.0±1.2-Å-thick last layer.

In a recent paper, Reisfeld and Asaf [Phys. Rev. A 49, 348 (1994)] suggested a simple model explaining an observed correlation between the electron scattering lengths and electric polarizabilities of rare-gas atoms. They proposed an electron-target interaction potential consisting of a short-range hard-core repulsive part plus a long-range dipole polarization potential, and used the Born approximation to evaluate the scattering length. We show that for this model the scattering length may be evaluated analytically and that theoretical predictions based on an exact expression disagree with experimental data.

The Xe 4${\mathit{d}}_{5/2}$:4${\mathit{d}}_{3/2}$ branching ratio has been determined in the photon energy range 80–250 eV using high-resolution electron spectroscopy and undulator radiation at the new Finnish beamline at the MAX I storage ring. The results were found to be in a satisfactory agreement with the calculated literature values obtained with the relativistic random-phase approximation. A few discrepancies between the theoretical predictions and our experimental results indicate additional correlation effects not accounted for in theory. The branching ratio is now shown to have a maximum of about 1.6 at around 230 eV. Lifetime widths of 114(4) and 121(4) meV are obtained for the 4${\mathit{d}}_{3/2}$ and 4${\mathit{d}}_{5/2}$ core hole states, respectively.

We examine the operator Φ${\mathrm{^}}_{12}$ proposed by Luis and Sánchez-Soto [Phys. Rev. A 48, 4702 (1993)] as a possible description of the phase difference between two electromagnetic fields. We show that there is a difficulty in directly representing the phase difference between arbitrary fields by this operator, but conclude that the incorporation of the operator into an alternative definition of phase difference constitutes a valuable alternative approach to the quantum description of phase.

In response to the objection raised by Pegg and Vaccaro [the preceding Comment] we point out that their example is not a difficulty in directly representing the phase difference by the ${\mathrm{\Phi }}_{12}$ operator. In fact, we argue that it is a property common to a wide range of phase descriptions, including the Pegg-Barnett formalism.