The resonance fluorescence from a system of interacting, identical, and cold (trapped) atoms driven by a laser field is derived. The effects of dressing by the laser field and radiative decay are all included. We examine in detail the applicability of the binary-collision approximation for this problem, which is a special case of resonance broadening. The final result allows a clear physical interpretation and shows interesting features due to the resonant exchange of coherences and excitations. Correspondence with previous work is also discussed.

In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.

The practical aspect of the moment problem of the P function is developed; i.e., a simple explicit expression for the P function in terms of its moments and the derivatives of the Dirac δ function in the complex domain is derived. Its connection with the concept of the nonclassical depth of a quantum state introduced recently is explored. The basic formulas derived are used in the calculations of several specific examples that are popular in the quantum-optics community, such as photon-number state, binomial state, two-photon thermal state, squeezed-vacuum state, etc.

Amplitude fluctuations in the light from a laser and the partition noise attributable to a beam splitter are analyzed using an equivalent-circuit model that incorporates amplitude squeezing. When the energy is not carried by photons but by electrons and also when electrons can be treated as classical particles, the circuit model need not be changed. One simply applies the general circuit model to low frequencies hν≪${\mathit{k}}_{\mathit{B}}$T. Conversion of an electric current to photon flux, and vice versa, converts classical sub-shot-noise spectra of electric currents into quantum squeezing of photon fluxes, and vice versa. The sub-shot-noise character of electric currents, unlike that of quantum squeezing, is not necessarily destroyed by current loss.

The integrability of the vectorial Helmholtz equation describing collinear degenerate four-wave-mixing interactions in isotropic Kerr media of the Maker-Terhune type [Phys. Rev. 137, A801 (1965)] is investigated in an exact fashion. This is done by reducing the underlying Helmholtz equation into an equivalent Hamiltonian form. The Painlevé properties of this Hamiltonian suggest that in general this problem is integrable for only two sets of coefficients of the ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ tensor. For these two cases, integrability is established by explicitly finding the required conservation laws. Possible implications of these results are then discussed.

We investigate the phenomenon of degenerate and nondegenerate two-mode squeezing for a generalized Jaynes-Cummings model with a two-level atom and two modes. The effect of the relative phases between the atomic superposition state and the coherent field on normal squeezing is studied. Different values for the parameters of the atomic coherent state are taken. It is found that the nondegenerate two-mode squeezing is more effective than the one-mode degenerate type, and it recurs at later times.

We have applied a momentum-space method to the solution of the three-dimensional time-dependent Schrödinger equation for electron detachment from a model negative ion, in particular ${\mathrm{H}}^{\mathrm{-}}$. We have studied such phenomena as excess-photon detachment and threshold effects. For selected cases, we obtain excellent agreement with the Floquet calculations. We also present results in regimes of strong interest to experimental efforts.

We derive the wave functions for an electron moving in a quantized circularly polarized standing-wave radiation field. By applying these solutions as the final states, we derive multiphoton ionization transition-rate formulas according to Keldysh-Faisal-Reiss (KFR) theory. Numerical calculations and theoretical analysis show that in the case of two light beams with the same angular momentum, KFR theory does not predict the peak splittings in the photoelectron angular distributions that were observed in an experiment by Bucksbaum, Schumacher, and Bashkansky (BSB) [Phys. Rev. Lett. 61, 1162 (1988)]. A transition-rate formula from a scattering theory developed for the case of single-mode multiphoton ionization by Guo, Åberg, and Crasemann [Phys. Rev. A 40, 4997 (1989)] is extended to the standing-wave case. The theory predicts the peak splitting observed by BSB. Numerical results of the splitting angle from the theory show good agreement with experimental measurements. We also prove that the sine function of the half splitting angle is inversely proportional to the square root of the photoelectron kinetic energy E, i.e., sin(π/2-${\mathrm{\theta }}_{\max }$)∝1/${\mathit{E}}^{1/2}$, where ${\mathrm{\theta }}_{\max }$ is the maximum scattering angle smaller than π/2. Some predictions are made for future experimental observations, such as quantum effects associated with ponderomotive-energy decay.

Pulsating laser oscillations consist of short and intense pulses separated by long regimes with nearly zero intensities. These oscillations appear if the dimensionless relaxation rate of the inversion of population γ is a small quantity (class-B lasers). During the low-intensity regimes, the laser is particularly sensitive to small-amplitude noise. We investigate the effect of noise by studying the limit-cycle oscillations of the laser with a saturable absorber. Specifically, we analyze how the size of the limit cycle is modified as the amplitude of the noise d is progressively increased from zero. We show that if γ≪1 and d>${\mathit{d}}_{\mathit{c}}$=O(exp(-1/γ)), the size of the limit cycle decreases by an O(1) quantity and depends on d. The mathematical problem is a singular perturbation problem that involves two small parameters (d and γ). We first show that the slow evolution of the limit-cycle solution can be studied as a slow passage through a steady bifurcation point. We then analyze the case of a constant imperfection (small injected signal) and the case of additive noise (small-amplitude Gaussian white noise). Both cases lead to the same conclusions.

An adiabatic approximation for the Liouville density-matrix equation which includes decay terms is developed. The adiabatic approximation employs the eigenvectors of the non-normal Liouville operator. The approximation is valid when there exists a complete set of eigenvectors of the non-normal Liouville operator (i.e., the eigenvectors span the density-matrix space), the time rate of change of the Liouville operator is small, and an auxiliary matrix is nonsingular. Numerical examples are presented involving efficient population transfer in a molecule by stimulated Raman scattering, with the intermediate level of the molecule decaying on a time scale that is fast compared with the pulse durations of the pump and Stokes fields. The adiabatic density-matrix approximation can be simply used to determine the density matrix for atomic or molecular systems interacting with cw electromagnetic fields when spontaneous emission or other decay mechanisms prevail.

We relate the phase distribution of a quantum state obtained by integrating its corresponding Q function over radius (1) to a specific measurement scheme using a linear amplifier and (2) to a particular phase operator. A simple relation between the P distribution of the amplified macroscopic state and the Q function of the initial unamplified microscopic state allows us to prove the identity of the phase distributions obtained by integrating the corresponding distributions.

The optical bistability in a dye-ring cavity has been investigated by using the derived Maxwell-Bloch equations based on the band model. It is shown that the bistable conditions and behavior are closely related to the band structure of the dye molecules.

Group-velocity dispersion (GVD) places a fundamental limitation on the resolution possible when measuring the propagation time of short optical pulses through dielectric media. We show that due to a nonlocal, quantum-mechanical effect, a surprising cancellation can occur in fourth-order interference, allowing the time interval between photons emitted in spontaneous parametric down-conversion to be measured without significant degradation of the resolution due to the spreading of the individual photon wave packets. This may also prove useful for measuring the higher-order contributions to GVD.

When subpicosecond solitons propagate in an optical fiber the soliton self-frequency shift occurs. We have made observations of this effect in standard telecommunication fiber, which show a strong departure from the predicted behavior. This difference is shown to be due to the residual birefringence in the standard fiber. Results are also presented on the power and length dependence and detailed comparisons with numerical simulations are made.

We present a detailed analysis of the noise properties of a potential lasing scheme employing a coherently driven three-level system in the Λ configuration inside an optical cavity. We derive expressions for the steady-state laser intensity and the width of the intensity fluctuations and show that the output fields exhibit sub-Poissonian statistics for suitable operating conditions. The fundamental mechanism responsible for noise suppression is identified as increased intensity dissipation inside the cavity through emission and absorption by the atoms, which counteracts the intensity fluctuations.

Experimental investigations of two-photon enhanced stimulated hyper-Raman and parametric four-wave-mixing emissions are described for tuning unfocused laser beams near two-photon resonance with 3D and 4D states in sodium vapor. Over wide ranges of vapor pressures, path lengths, and laser power densities, the gains for stimulated hyper-Raman (SHR) scattering and for parametric four-wave mixing (PFWM) can become very greatly reduced from values expected from simple considerations. The suppression of gain can arise from interferences produced at two-photon and three-photon resonances, and from ac Stark shifts produced by internally generated near-resonant fields. Quantitative comparisons are made between observed and theoretically predicted values for SHR and PFWM production. Of 12 predicted consequences of the interferences and Stark shifting on the nonlinear behavior, ten are demonstrated through the experiments.

The similarity between the system of the plane rotator and that of the optical oscillator (mode) has been exposed. In both the systems special states have been examined, which minimize the usual and unusual uncertainty relations. Number-sine-cosine uncertainty relations for these systems have been derived and the number-sine minimum-uncertainty states have been investigated in greater detail than in the literature.

We consider a lossless two-photon micromaser with atomic polarization. We find that for particular values of the atomic flight time, the field evolves to a pure state which can be made of a superposition of even-photon-number states or odd-number states. These states approach to a perfectly squeezed state as the upper limit of the ‘‘trap’’ increases.

The two-photon absorption by a pair of two-level atoms interacting with an incident field is examined. If the laser field is weak, then the existence of the dipole-dipole interaction-induced two-photon resonance follows from the higher-order Fermi golden rule. The effects of spontaneous emission and intense fields on the dipole-dipole interaction-induced two-photon resonance is studied using density-matrix methods. The presence of an intense field is shown to result in a significant enhancement of the two-photon resonance. Numerical results for the probability of simultaneous excitation of two atoms, for the atomic correlations, and for the radiated field intensity are presented.

We describe a method for obtaining exact solutions of the nonlinear Schrödinger equation for describing pulse propagation in optical fibers in the normal-group-velocity-dispersion regime. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system whose solutions determine the exact solutions of the nonlinear Schrödinger equation.