The lifetime of an atom in a high-frequency high-intensity laser field is studied. A coupled-channel formalism is developed, based on a well-known high-frequency theory, that describes the behavior of an atom in a laser field. Numerical results are obtained using a finite-difference approximation in combination with a two-center complex scaling technique. The complex scaling method is also shown to be very well suited for calculations on diatomic molecules. Several numerical results are used to illustrate the qualitative features of the method. We show that our theory is formally (though not in practice) equal to other methods that have been used heretofore. It will be shown that, for high-frequency and high-intensity laser fields, the present method can be used to calculate resonance energies using only a few channels.

The problem of laser cooling of a single ion or atom in a harmonic trap is considered. A simple theory of sideband cooling is developed. In the limit that the particle’s secular motion can be treated semiclassically the theory allows the calculation of the logarithmic cooling rate either numerically or, for two special cases, analytically.

A new possible free-electron maser is proposed, which is based on the combination of the guiding-center shift and Doppler shift. In this proposal the electron beam is located at the point where the ordinary gyrotron interaction vanishes, and the initial normalized transverse velocity is chosen to be equal to the reciprocal of its relativistic factor, so as to let the Doppler shift be dominant in the cyclotron resonance condition. Linear analysis of the ${\mathrm{TE}}_{\mathit{m}\mathit{n}}$ mode and nonlinear simulation of the ${\mathrm{TE}}_{\mathit{m}\mathit{n}\mathit{q}}$ mode are presented. The influences of the initial transverse velocity to the axial velocity ratio on the linear growth rate and nonlinear efficiency are discussed in detail. It is found that the hybrid free-electron maser may attain an efficient growth rate and efficiency, and is quite sensitive to the initial transverse velocity to axial velocity ratio.

We develop the quantum theory of a driven, damped intracavity parametric oscillator in the case of nondegenerate signal and idler modes. An analysis of the results of different types of local-oscillator measurements on the outgoing modes is presented. The frequency-domain squeezing is calculated below threshold including the effect of detunings and nonequal decay rates. We also calculate a nonclassical correlation in the quadrature amplitudes of the output beams. The existence of an Einstein-Podolsky-Rosen paradox is demonstrated through violations of the inferred Heisenberg uncertainty principle at causally unrelated locations in the output field. This provides a way of maintaining the commutation relations of the measured operators in the exact form envisaged originally by Einstein, Podolsky, and Rosen.

We show via (1) an approximate, analytical technique, (2) a formally exact matrix continued-fraction analysis, and (3) an analog simulation of the classical Langevin equation of a correlated spontaneous-emission laser (CEL) that noise of nonzero correlation time leads to an enhancement of the characteristic CEL noise quenching.

We calculate the transition rates and the linear and nonlinear-optical properties of a homogeneously broadened two-level system with permanent dipole moments in the presence of two pump fields. We present absorption and emission spectra for the system in the steady state, without making the rotating-wave approximation. Expressions for the nonlinear susceptibilities for wave mixing are derived.

Finite-temperature generalizations of the important, special families of states in quantum optics are constructed using thermofield dynamics. Fermionic coherent states, fermionic squeezed states, and their thermalized counterparts are also constructed. It is shown that all these states possess a generalized thermal annihilation operator, for which these are eigenstates. Typical correlation functions for these states at finite temperature are evaluated.

The distributions, in parameter space, of subcritical Hopf bifurcations and the various attractors of time-dependent motions of optical bistable systems are investigated systematically. The main emphasis is placed on the influence of the variations of the control parameters on the distributions. We have observed the tristability of large-amplitude regular or chaotic motions, periodic pulsations, and the stationary state for the parameters where no instability of the stationary solution exists at all over the complete range of the external field. The problem of how to find the various attractors and how to reveal chaotic motions by adjusting the control parameters is discussed according to the numerical results.

We have presented a semiclassical analysis of four-wave mixing in a system of two-level atoms interacting with a single-mode self-consistent classical electromagnetic field in the presence of a weak probe field. The relevant response functions for the probe wave as well as for the field generated by the four-wave mixing have been calculated over a wide-range coupling constant for the self-consistent field and the atoms. The significant departures from the spectral characteristics associated with the usual four-wave mixing with an external strong pump field arise. The probe wave and the four-wave mixing spectra have been interpreted in terms of simple excitation transfer in the atom–self-consistent-field coupled oscillator model.

We study analytically the generation and propagation of dark-pulse solitons in nonlinear-optical fibers in the normal dispersion regime. We demonstrate that dark-pulse solitons may be created as pairs by an arbitrary dark pulse with equal boundary conditions without a threshold. We also predict soliton generation by a step of an input pulse phase and obtain the parameters of the generated solitons. The case of soliton generation by a random input pulse is described, and probability of the generation for a Gaussian random pulse is calculated. We also consider the case when dark pulses are generated on a background of finite extent. This situation is related to experiments by Krökel et al. [Phys. Rev. Lett. 60, 29 (1988)] and Weiner et al. [Phys. Rev. Lett. 61, 2445 (1988)], who produced dark pulses (e.g., ∼1 psec) on the long bright pulse (e.g., ∼${10}^2$ psec). We demonstrate that in this case dark pulses are not, strictly speaking, solitons, and in terms of the inverse scattering transform they correspond not to bound states (discrete spectrum) but to quasistationary ones lying in a continuous spectrum. We calculate the parameters of the pulses produced and study their dynamics. It is demonstrated that propagation of these dark pulses is similar to soliton motion. We also study the influence of small perturbations on dynamics of dark solitons, e.g., dispersive broadening of a background and dissipative losses.

The problem of the formulation and simulation of quantized optical systems using the positive-P representation is considered. We show that feasible computational strategies are determined mainly by the eigenstructure of the system of stochastic differential equations that correspond to the positive-P Fokker-Planck equation. We demonstrate analytically that the stability and accuracy of numerical solutions are generally much improved by adopting time-centered implicit schemes. These findings are then related to the specific problem of second-harmonic generation. It is shown that the eigenstructure of the stochastic system possesses interrelationships that can lead to severe difficulties in numerical simulations. In particular we show how the problem of ‘‘spiking’’ encountered at high levels of quantum noise can be related to the numerical ‘‘stiffness’’ of the problem. We also demonstrate the advantages of time-centered implicit methods by highlighting the distortions that can occur in the Euler-type simulation of limit cycle solutions. Of physical interest is the fact that the phase-space morphology of the quantized second-harmonic generator admits families of limit cycles. This is in marked contrast to the purely classical picture in which, for a given parameter set, there exists only a single limit cycle. Finally we demonstrate by direct analytic solution that, under the conditions of adiabatic elimination, the positive-P representation for the second-harmonic generator with zero driving field fails, in the sense that it produces nonphysical results. This failure is in all respects analogous to the breakdown encountered in the problem of nonlinear optical damping.

We study in detail the electron energy spectrum produced by the interaction of atomic hydrogen initially in the 2s state with a femtosecond laser pulse. As a first step, we treat the problem within second-order perturbation theory. For that purpose, we analyze in the first instance the off-diagonal continuum-continuum transition matrix elements and derive asymptotic expressions when both the initial- and final-state energies are very close to the ionization threshold. We also consider the diagonal divergence and extend a recent calculation of Madajczyk and Trippenbach [J. Phys. A 22, 2369 (1989)]. By means of a proper analytical regularization of these matrix elements, we show that they may be considered as a distribution, which, in addition to a δ function and its first derivative, involves three principal parts. When this distribution is acting on a given function of energy, it is shown that the calculation of these three principal parts may be carried out fully analytically. We then present results for the electron energy spectrum. Various pulse shapes are considered, and a detailed discussion is given on the contribution of the intermediate continuum states to the second-order probability amplitude.

The exact quantization of the asymmetric top using quantal action-angle variables is demonstrated. The implications for studying the quantization of nonlinear, nonintegrable systems are discussed.

It is shown that the Harbola-Sahni exchange potential ${\mathit{w}}_{\mathit{x}}$ is not generally independent of path for nonspherical densities. Requirements for corrections to ${\mathit{w}}_{\mathit{x}}$ are put forth.

We have investigated the two-particle time-dependent Schrödinger equation with a central form of the potential. We have found that the potentials can be divided in four classes according to the symmetry group that keeps the form of the equation invariant.

As the mechanical counterpart of the Aharonov-Bohm effect and the Aharonov-Cashier effect in a magnetic field, the existence and possibility of observation of a quantum interference effect between the split paths of a coherent particle beam in a uniformly rotating frame have been studied previously. The discussion is now generalized to the case of a reference frame rotating at arbitrarily time-varying angular velocity about a fixed center. The phase difference between the split beams of particles and the resulting interference pattern depend not only upon the speed, but also upon the orientation of the axis of rotation. The conclusion may have, therefore, inferences on gyroscopic applications.

We calculate the ground-state energies of muonic molecules formed by deuterium-deuterium, tritium-tritium, and deuterium-tritium nuclei plus a negative muon confined in a two-dimensional (2D) region. We show that the equilibrium distance between nuclei is a factor of 4 smaller and the vibrational energies are about a factor of 5 higher than the corresponding three-dimensional (3D) muonic molecules, thus favoring fusion reactions. In fact, the estimated d+t fusion rate is found to be three orders of magnitude higher in 2D than in 3D.

Relations involving radial, 〈${\mathit{r}}^{\mathrm{\alpha }}$〉 and momentum 〈${\mathit{p}}^{\mathrm{\beta }}$〉 expectation values of fermionic systems are found. These relations are based on semiclassical relations for fermionic systems, extended for more realistic atoms, molecules and nuclei. The inequalities obtained are studied and numerically analyzed for atoms within the Hartree-Fock framework.

Partial doubly differential cross sections ${\mathit{d}}^2$${\mathrm{\sigma }}^{\left(\mathit{n}\right)}$/dEdΩ for the production by electron impact of argon ions having charge states from n=1 to n=4 have been measured as a function of the angle of ejection θ in the range 40°<θ<113°, with the energies of the incident and ejected electrons being 1.0 keV and 200 eV, respectively. A comparison has been made with similar data from the literature and explanations have been offered for the behavior of the measured angular variations.

The energy dependence of the ionization produced in silicon by recoiling silicon atoms was measured in the 4–54-keV energy interval. It is found that the fraction of the recoil energy that is dissipated as ionization follows an ${\mathit{E}}^{1/2}$ dependence which agrees well with the predictions of the theory of Lindhard et al. [Mat. Fys. Medd. 33, 10 (1963)].