It has recently been shown that a field-equation time-derivative approximation that is commonly used in studies of laser-oscillator dynamics is not necessary and can lead to significant errors for some lasers. A related space-derivative approximation is widely used in studies of steady-state laser amplifiers. A more rigorous amplifier formalism is developed here, and the results are exact solutions of Maxwell’s equations. The improved model predicts a spatial instability, single mirror oscillation, and other interesting field behavior.

In a related study the equations governing a high-gain laser amplifier have been solved numerically without making the usual slowly-varying-amplitude derivative approximation in Maxwell’s equations, and thus the field amplitudes are not restricted to vary negligibly in a distance of one wavelength. The results reveal an instability that involves reflections and oscillatory growth of perturbations away from steady state. In the present study steady-state solutions of the field equations are obtained analytically, and transformations are described for converting the equations to alternative intensity-equation sets. These intensity equations are linearized and solved for the growth rate and oscillation period of the perturbations.

The interaction of a two-level atom with a single-mode radiation field through multiphoton transitions is studied in terms of the dressed-state formalism. It is shown that when only certain dressed states are initially excited, population trapping occurs. We particularize these results for some well-known models of one- and two-photon transitions. Photon statistics of the cavity mode is analyzed in terms of the quasiprobability distribution Q(α). It is shown that when population trapping occurs some two-time correlation functions become stationary, which allows one to obtain the resonance spectrum as the Fourier transform of the two-time dipole autocorrelation function.

Higher-order squeezing conditions for squeezed number states are derived using a normal-ordering technique for calculating the moments of the field. Intrinsic higher-order squeezing is also investigated. It is found that the normally ordered moments of the quadrature operators are oscillating functions of the squeeze parameter. Also calculated is the exact nth-order correlation function for an arbitrary squeezed number state. Finally, its behavior for large and weak squeezing is analyzed.

Quantum fluctuations of atomic dipole variables in the two-photon Jaynes-Cummings model are discussed. It is shown that dipole squeezing can be exhibited in certain periods of time evolution of the system for superposition state preparations, and also that the dipole fluctuations cannot be squeezed in atomic spontaneous radiation processes.

I investigate a recently developed method for obtaining bound-state eigenvalues of anharmonic oscillators, and from it derive useful approaches that converge faster. The method consists of writing the eigenfunction as an exponential of a polynomial times a power series, in which the former factor is properly chosen to simplify the resulting recursion relations for the coefficients of the expansion. I also apply the method to central-field models.

It is suggested that a recent experiment verifying the quantum Zeno effect be extended to longer times with weakened laser pulses that make the measurements uncertain. This would show more detailed effects of changes of the atomic state made by the laser pulses. It would test the way the pulses change the density matrix when the measurements are uncertain. It is predicted that when the pulses are sufficiently weak, the transition probability will oscillate in time, as it would if there were no pulses, but the pulses will damp the oscillations the same way they inhibit transitions to produce the Zeno effect. The oscillations could also reveal the change of phase between the atomic states produced by the interaction with the laser beam. Transition probabilities have been calculated as functions of time. Representative results are plotted.

It is shown that, in addition to the Aharonov-Bohm-like phase studied previously [M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984); Y. Aharakov and J. Anandan, Phys. Rev. Lett. 58, 1593 (1987); C. H. Tsai and D. Neilson, Phys. Rev. A 37, 619 (1988)], Berry’s topological phase also appears for purely mechanical reasons in systems rotating at slowly-time-varying angular velocity about a fixed center. A possible experiment to probe this manifestation of Berry’s phase is discussed.

We study the nearest-neighbor spacings (NNS) and spectral rigidities in quantum spectra generated by the equation of multichannel-quantum-defect theory for interacting Rydberg series. For weak coupling near the separable limit, the NNS distributions agree with a Poisson spectrum quite closely, but the spectral rigidities follow the Poisson expectations only for very short stretches of spectrum containing hardly more states than the number of channels involved. For intermediate and strong coupling, both the NNS distributions and the spectral rigidities agree well with the predictions of random matrix theory for the Gaussian orthogonal ensemble case.

The radial electronic density function ${\mathit{D}}_0$(r), has been evaluated in closed form for some low-lying excited ${}_{}{}^2{}_{}{}^{}$S states of the Li i isoelectronic series that are described by Hylleraas-type wave functions. The radial density for each state considered is determined by a set of expansion coefficients, exponent values, and a set of summation limits. Numerical values for each of these are reported for the species Li i, Be ii (3 ${}_{}{}^2{}_{}{}^{}$S and 4 ${}_{}{}^2{}_{}{}^{}$S states) and B iii, C iv, N v, O vi, F vii, and Ne viii for the 3 ${}_{}{}^2{}_{}{}^{}$S states. The nuclear-magnetic shielding constant, the diamagnetic susceptibility and the expectation values 〈${\mathit{r}}_{\mathit{i}}^{\mathit{n}}$〉 (for n=-2 to 8) and 〈δ(${\mathbf{r}}_{\mathbf{i}}$)〉 are evaluated using ${\mathit{D}}_0$(r). The electron-nuclear cusp condition is also examined for each state investigated.

Hyperfine splittings in the 2${\mathit{p}}_6$, 2${\mathit{p}}_7$, and 2${\mathit{p}}_{10}$ states of the 4${\mathit{p}}^5$5p configuration of ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ (I=9/2) have been measured using saturated absorption laser spectroscopy. Computer simulations involving composite line shapes have been employed to reduce resolution difficulties. While the determination of hyperfine-coupling constants A and B in the 2${\mathit{p}}_7$ and 2${\mathit{p}}_{10}$ states is straightforward, this process is complicated by overdetermination in the 2${\mathit{p}}_6$ state. Our measurements of A (2${\mathit{p}}_6$) and (${2\mathrm{p}}_6$,2${\mathit{p}}_7$,2${\mathit{p}}_{10}$) represent the first determinations of these constants. With these measurements, hyperfine couplings for all eight states exhibiting hyperfine structure in the 4${\mathit{p}}^5$5p manifold now exist. The results provide a good test of semiempirical calculations of hyperfine structures.

It is pointed out that the recently proposed set of conjectured solutions [Phys. Rev. A 39, 5082 (1989)] for this problem predicts an unacceptable behavior of the energy function in the perturbative regimes. A modification of the conjectured conditions provides an alternate set of solutions that permits the development of a useful approximation scheme. An appealing approximate description of the entire spectrum that retains the previously obtained desirable features is thereby realized. Only low- and high-field regions are studied. A second derivation of the threshold regime spectrum is furnished.

We identify a mechanism of dynamical pump-noise suppression in lasers. It is based on the recycling of the active laser electron from the lower to the upper laser level by a sequence of incoherent step processes. Although each of these steps corresponds to a Poisson process, i.e., is stochastic, the combination of many incoherent steps leads to a regular (deterministic) recycling of the laser electron and, correspondingly, a pump-noise suppression in the laser. The mechanism predicts sub-Poissonian laser output and intensity fluctuations beyond the shot-noise limit for incoherently pumped systems.

The phase probability curve of a recently proposed photon state consists of a broad background with a sharp central peak [J. H. Shapiro, S. R. Shepard, and N. Wong, Phys. Rev. Lett. 62, 2377 (1989)]. These authors argue that the inverse peak-height phase uncertainty δcphi of this distribution decreases inversely as the square of the mean photon number 〈m〉—an improvement over either coherent or highly squeezed states. We show that the width Δcphi of the best-fitting Gaussian to the central peak–a measure of phase uncertainty tailored to this narrow feature–decreases exponentially with increasing 〈m〉. The importance of this result may be offset by the observation that the area under this peak also vanishes very rapidly.

We have studied the orthonormalized eigenstates of the higher powers ${\mathit{a}}^{\mathit{k}}$ (k≥3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ construct a complete representation with respect to α. (2) None of the orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ shows the squeezing effect in the usual sense. (3) All of the eigenstates of ${\mathit{a}}^{\mathit{k}}$ show the antibunching effect.

The effect of weak higher-order photon absorption on bistable-soliton propagation and switching in a fiber whose intensity-dependent refractive index is described by the linear-plus-smooth-step model is investigated numerically. The choice of model allows the application of the adiabatic assumption and a clear analytic interpretation of all of the observed results.

This Comment precludes any chance of discovering a new potential that would allow one to solve the one-dimensional Schrödinger equation in terms of hypergeometric functions. In particular, it argues that the potential function suggested by Hua [Phys. Rev. A 42, 2524 (1990)] is the well-known Tietz potential, which in turn is a combination of the Rosen-Morse, Morse, and Manning-Rosen potentials presented in a common form.

The model for the origin of the zero-point electromagnetic field by Puthoff [Phys. Rev. A 40, 4857, 1989] is physically interesting but mathematically flawed. Here we give the correct calculation in general relativity and make some comments on it.

In considering an Olbers-type radiation model for the source of vacuum electromagnetic zero-point energy (ZPE), we compare Wesson’s ‘‘time-of-formation’’ interpretation for the range of sources of the ZPE [preceding Comment, Phys. Rev. A 44, 3379 (1991)] with the Puthoff-Santos ‘‘optical depth’’ interpretation, and suggest that the latter may be more compatible with astrophysical constraints.

An error is pointed out in the calculation by Puthoff [Phys. Rev. A 40, 4857 (1990)]. The result obtained is consistent with the interpretation of the zero-point field as dynamically generated by the motion of charged particles, but does not supply any explanation for the cosmic large-number coincidences.