A representation of a Fock state ‖n〉 is given by a superposition of n+1 coherent states. These discrete coherent-state superpositions provide experimental possibilities for generating an arbitrary quantum state of a single-mode electromagnetic field.

We study the propagation of a near-resonant strong laser light with a broad background continuum spectrum in a dense gaseous two-level medium. Due to the nonlinear saturation caused by the driving of the coherent component of the field, spectral regions close to the Rabi sidebands with significant gain exist close to the resonance. The subsequent evolution of the spectrum of the propagating field displays interesting features, and in the stationary limit a broadening of the spectral line always eventually happens in the end which contradicts the coherent narrowing phenomenon for pulsed propagation. This may shed some new light on the mechanisms of cone emission.

The notion of atomic coherent states is extended to the multilevel case. Since the representation based on coherent states is convenient in treating collective interactions of atoms with photons, and since many optical processes involve atoms of three or more levels, it is expected that this extension will play a role in the theory of such processes as cascade superfluorescence and superradiant lasing. Like their bosonic counterparts, atomic coherent states may be used to define a holomorphic representation for atomic states and operators. We discuss this in detail and give examples to illustrate applications.

Resonators driven into self-oscillation via active feedback often form the basis of clocks and other sensitive measurement instrumentation. The phase stability of such an oscillator is ultimately limited by the noise associated with the resonator’s intrinsic losses. However, it is often the case that amplifier noise is the dominant cause of the oscillator’s phase diffusion. Here it is shown that when the resonator possesses a suitable nonlinearity, the phase diffusion due to amplifier noise can be suppressed, allowing one to achieve a long-term phase stability comparable to the ultimate noise limit.

In the analytic Bargmann representation associated with the harmonic oscillator and spin coherent states, the wave functions considered as consisting of entire complex functions can be factorized in terms of their zeros in a unique way. The Schrödinger equation of motion for the wave function is turned to a system of equations for the zeros of the wave function. The motion of these zeros as a nonlinear flow of points is studied and interpreted for linear and nonlinear bosonic and spin Hamiltonians. Attention is given to the study of the zeros of the Jaynes-Cummings model and to its finite analog. Numerical solutions are derived and dicussed.

Phase-controlled homodyne 2(N+R)-port detection with R local oscillators is analyzed with the aim of reconstructing the quantum state of a correlated N-mode signal field. It is shown that both the (N+R)-fold joint count distributions and the N-fold joint difference-count distributions contain all knowable information on the state of the field. In any case, the minimum number of local oscillators is given by the number of different signal-field frequencies. Two Fourier integrals per mode are found to be required to reconstruct the density matrix of the signal field from the joint difference-count distributions measured in balanced homodyning. To illustrate the theory, it is applied to balanced homodyne 4N-port detection (R=N). In this scheme, the joint difference-count distributions directly yield the joint field-strength distributions of a correlated N-mode signal field.

Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.

Solving the tunneling problem in a double-well potential requires knowing the wave function not just of the ground state, but also of the first excited state. A method is described that allows one to construct potentials together with these two wave functions. No approximations are made. To illustrate the method several examples are given. These include potentials that either diverge for large ‖x‖ or become asymptotically flat, with one or two wells, which may be symmetric or asymmetric.

The generalized invariant and the exact quantum motions are found in the Heisenberg picture for a harmonic oscillator with time-dependent mass and frequency in terms of classical solutions. It is shown that the Heisenberg pictures gives a relatively simpler picture that the Schrödinger picture and also manifestly exhibits the time independency of the invariant. We apply this method to the system with a linear sweep of frequency and Paul trap and study the squeezing properties.

The effect of core polarization on fine-structure splitting for the ${\mathit{nf}}^2$${\mathit{F}}_{\mathit{J}}$ levels in ${\mathrm{Kr}}^{7+}$ is investigated in order to explore further the fine-structure inversion of these levels. Core-polarization effects are included via two distinct methods, namely, by performing multiconfigurational Dirac-Fock calculations and single-configuration Dirac-Fock calculations including a core-polarization potential. Both sets of results are compared with presently available experimental values.

The method of obtaining a closed expression of the variational equation for states of arbitrary total angular momentum of two electrons with infinitely heavy nucleus is extended to two electrons and a nucleus with finite mass. An existing variational equation for the P states, which includes the mass polarization term, follows as a special case of the present general formalism.

We show that the energy-averaged entropy localization length for the eigenstates of the Ce atom is well approximated by the prediction of the Wigner ensemble.

We made a classical trajectory Monte Carlo calculation of state-selective cross sections for processes between some light ions and excited helium. The results, useful for analysis of spectroscopic data of fusion devices, are in good agreement with theoretical predictions of scaling laws.

Cross sections for photodetaching an electron from a ${\mathrm{B}}^{\mathrm{-}}$ ion have been determined at photon energies of 1.871 and 2.077 eV. A crossed laser–ion-beam apparatus was used to determine the cross sections of ${\mathrm{B}}^{\mathrm{-}}$ relative to those of the reference ion ${\mathrm{Li}}^{\mathrm{-}}$. The ratios were normalized to previously measured cross sections for the reference ion. The present experiment yields values of σ(${\mathrm{B}}^{\mathrm{-}}$)=24±4 Mb (1.871 eV) and 21±3 Mb (2.077 eV).

We observe the existence of a spatial structure in cold trapped atoms that consists of two concentric rings of atoms. This distribution can be explained through the existence of a coordinate-dependent vortex force in addition to the trapping and damping forces. This vortex force has been used before to explain other structures [Bagnato et al., Phys. Rev. A 48, 3771 (1993)].

We present a quantitative model for coherent on-resonance small-scale self-focusing of laser pulses in atomic media. A vapor-induced diaphragm effect at the edge of the pulse generates a pattern of diffraction rings that modulates the initial transverse profile of the pulse. Practically, because of the spatial asymmetry of the original pulse, this diffraction pattern is perturbed and dots appear superimposed upon the rings. A large-scale self-focusing phenomenon is then initiated from each individual dot and the global transverse energy profile of the pulse evolves in a hot-spot pattern. This final pattern is characteristic of what is usually called small-scale self-focusing. Our theoretical predictions are compared with both the results of an experiment on a ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$ vapor and the predictions of existing models.

Rzazewski and Piraux have investigated the ionization of circular Rydberg states in circularly polarized microwave fields [Phys. Rev. A 47, R1612 (1993)]. They find the threshold higher than for a static field and ‘‘in some cases completely different than the prediction based upon the above barrier escape.’’ We show that above barrier, stable orbits, may exist, which explains, in part, this finding by Rzazewski and Piraux.