We show through numerical simulations that different kinds of noise have different signatures in the statistical distribution of the intensity peak height as a function of delay time in the turn-on of class-$B$ lasers. Simulations are carried out specifically for a ${\mathrm{CO}}_2$ laser and are compared to the experimental results of H. Grassi et al. [Phys. Rev. A 50, 805 (1994)]. Full qualitative agreement is found with the experiment. These results confirm that noise on the control parameter has a larger influence on the laser behavior than the intrinsic fluctuations. A physical interpretation of the role that the different physical noise sources play in the system is offered.

Both approximate and exact methods exist to determine the density matrix of the field inside an incoherently driven micromaser, but as of yet only a steady-state Fokker-Planck solution has been found for the micromaser with injected atomic phase [Phys. Rev. A 34, 2032 (1986)]. Since Fokker-Planck solutions have been shown not to represent the effect of trapping states on the cavity field adequately, other solutions must be sought. In this paper, we present both a highly accurate approximate analytical solution and a more computationally complex numerical solution based on the exact methods of Lu [Phys. Rev. A 47, 1347 (1993)], both of which demonstrate symmetry breaking in the phase. Since the spectra of the injected phase micromaser will be the same as that of the incoherently pumped case, we present numerical comparisons of our two solutions via the phase variance.

We present an optical resonator with modified properties due to a nonabsorbing highly dispersive medium. The steep nonabsorbing dispersion is created with an additional pump field in an atomic beam using the effect of coherent population trapping. The linewidth of such a resonator depends on the slope of the dispersion line, which in turn depends on the atomic density and the intensity of pump and probe field. In the experiments presented here, the cavity linewidth is reduced by a factor of more than 50 relative to the linewidth of the empty resonator. We have studied the influence of the relative intensities of pump and probe field on the line profile. Due to the dispersion of the medium, the resonance frequency is nearly independent of the geometrical length of the resonator.

We propose a method for generating collective atomic Schrödinger-cat states formed as superpositions of the Bloch (or atomic coherent) states in the context of cavity QED. We then study the properties of these states and show the effects of the superpositions on spontaneous and stimulated emission, the atomic dipole moment, spin squeezing, and coherence.

Pattern formation near threshold in large-aspect-ratio, single-longitudinal-mode, two-level lasers with plane mirrors under the action of a weak injected plane-wave field resonant with the atomic transition frequency and tilted with respect to the laser cavity axis is analytically investigated in terms of the amplitude equations for the system. It is shown that, when the laser emission occurs off-axis, the appearance of resonances among the injected signal field and the unstable emerging tilted waves drastically changes the pattern selection properties of the free-running laser. As a result new transverse patterns, which include singly and doubly periodic stripes and undulating hexagons, may be stabilized by the injected signal. These patterns arise from the superposition of the forced mode with either one, two, or three traveling waves on the critical circle of the free-running laser. This is a distinctive feature from similar structures more commonly found in passive optical systems, where complex patterns always arise as a superposition of standing waves. The stability properties of the various patterns and their selection rules are analytically investigated within the amplitude equations.

Interference of electric charges in the presence of a time-dependent magnetic flux $-Vt+{\sum }_{i=1\mathrm{}}^m{A}_i\sin ({\omega }_{i}t+{\theta }_i)$ is considered. It is shown that higher-order correlations detect interference only if the voltage takes one of the values $\nu eV={\sum }_{i=1\mathrm{}}^m{N}_i{\omega }_i.$ The results are interpreted in terms of highly nonlinear processes of multiphoton frequency conversion.

In this paper we propose a way to get the approximate ground-state wave function by the variational method and thence determine the superpotential $w$ that is necessary for the supersymmetric WKB quantization condition. By this approach, the supersymmetric WKB method can be applied for any potentials. Two examples are given: (i) the anharmonic potential and (ii) the Hulthén potential including the centrifugal potential.

The differential equation determining the $n$th-shell one-electron density of a bare Coulomb problem is solved explicitly.

The ground bound state in the positronium hydride molecule (HPs) is determined from extensive variational four-body calculations with the James-Coolidge four-body variational expansion in the relative coordinates $r_{12}{,r}_{13}{,r}_{23}{,r}_{14}{,r}_{24}$, and $r_{34}.$ For the positronium hydride with the infinitely heavy nucleus ${(}^{\infty }\mathrm{HPs})$ the total energy found, $E=-0.7891369$ a.u., is one of the lowest variational values published to date. A number of bound-state properties have been calculated also, including the $\delta$-function expectation values, two-body cusps, and the two-photon annihilation rate.

Results are presented for the lifetimes of the $6p$ levels in Yb II, viz., 8.07±0.09 ns for the $j$=$\frac{1}{2}$ level and 6.15±0.09 ns for the $j$=$\frac{3}{2}$ level. These are compared with previous experiments and calculations. Our values are in excellent agreement with previous experiments, but show a significant improvement in precision. The results from previous calculations show a rather wide scatter but the experimental values are still consistent with the means of the calculated values within that scatter. However, there does still appear to be a need for a more complete calculation for the ${\mathrm{Yb}}^{+}$ ion.

We perform relativistic many-body perturbation theory calculations through third order to study amplitudes of the principal transitions in copperlike, silverlike, and goldlike ions. For low ionicities, semiempirical corrections are given for the omitted fourth- and higher-order terms. Comparisons with experiment are made.

Errors in relativistic correlated ab initio results for the “${}^{5}D$” $J=2\mathrm{}$ to $J=3\mathrm{}$ $M1\mathrm{}$ transition, which is nearly constant with $Z$, have been reduced from 5% to 1.5% (400 ${\mathrm{cm}}^{-1})$, on average. Beyond the Dirac-Coulomb level, the principal contributions are from the magnetic operator and certain $n=3\mathrm{}$ single and double excitations (correlation effects).

A formal theory for the evaluation of the cross section for the excitation of many-electron atomic ion within the framework of the Coulomb-Born approximation is formulated in non-partial-wave version, in which the multiple expansion of the transition matrix element is decomposed into two parts: the target form factor and the projectile distortion form factor. These are the matrix elements of the tensor operators between quantum states, so that any complicated wave function for the target ion can be employed. Thus it becomes possible to apply Coulomb-Born theory to treat the excitation of many-electron atomic ions for impact by charged particles, especially heavy particles. As an illustration, the $1s$-$2s$ and $1s$-$2p$ excitation cross sections of hydrogenlike ions by electron impact are calculated for a wide range of energies using the Coulomb-Born formal analysis.

Elastic phase shifts and scattering cross sections for electron-hydrogen scattering below the $n=2\mathrm{}$ threshold are carefully evaluated using the hyperspherical close-coupling (HSCC) method. The results are compared to other benchmark calculations to illustrate the convergence properties of the HSCC method. Elastic and inelastic scattering cross sections between the $n=2\mathrm{}$ and $n=3\mathrm{}$ thresholds are also calculated and compared to other benchmark calculations.

We generalize our recent model calculations on the generation of higher harmonics at metal surfaces by a powerful femtosecond laser pulse [Phys. Rev. A 54, 3245 (1996)] for the case in which a bichromatic field of frequencies ω and 2ω is applied, where both components are out of phase by an angle φ, and we discuss the coherent phase control of the harmonic generation process, relating our results to those obtained for harmonic generation by shining a bichromatic laser field on atoms.

It is shown that the system of a three-level atom coupled to two modes of quantized cavity fields in the Ξ configuration with arbitrary detunings can be exactly reduced to a two-level system with an effective coupling which depends nonlinearly on the intensity of the two cavity fields.

Rates for photodetachment from a model potential are calculated in the Floquet approach, with and without allowance for the shift in channel wave numbers induced by the finiteness of the number of multiphoton channels included in the calculation. The two sets of results converge to the same limit when more and more channels are taken into account. Convergence is faster in calculations using shifted wave numbers.

There is currently a great deal of experimental interest in the trapping of alkali-metal atoms in magnetic traps. In this Brief Report we present a method for calculating nonadiabatic spin-flip transitions in such traps. We show that for realistic traps currently being used the loss rate due to this mechanism is exponentially small.

Angular distributions have been measured of Cl${}^{+}$ fragment ions resulting from dissociative ionization of polyatomic molecules CCl${}_4$, CHCl${}_3$ and CH${}_2$Cl${}_2$ induced by linearly polarized laser pulses of intensity 10${}^{13}$ W cm${}^{-2}$. Pronounced anisotropy is exhibited in all cases, with Cl${}^{+}$ detected mainly along the direction of the laser’s polarization axis, indicative of field-induced spatial alignment of the precursor molecules. The directional properties of the average linear polarizability of the precursors appear to play a key role in determining the extent to which such alignment occurs.

The high-field ionization rate of a one-dimensional atomic model using a Gaussian potential well is calculated classically. The results are in qualitative agreement with quantum calculations; for sufficiently strong fields the ionization rate decreases, in an oscillatory manner, with increasing field strength. In addition, some apparent disagreements in the literature are resolved by pointing out the distinction between interpretations of suppression as a reduction in ionization rate or as a reduction in ionization probability. Similarly, the relation between ionization suppression and stabilization is discussed, and as an example it is shown that the present results do not contradict earlier claims of no stabilization in short-range potentials.