The nonlinear Jaynes-Cummings model is investigated for squeezing and higher-order squeezing produced from the interaction of the model with two coherent modes. Squeezing of the matter operators is also considered. Two-mode squeezing and higher-order two-mode squeezing are investigated for the present model. We found that squeezing produced using the concept of two-mode squeezing is more effective than squeezing produced using the single-mode-squeezing concept. It is shown that squeezing of the field can be enhanced for small n¯=0 and m¯=0 when the atom is initially in a coherent superposition state.

We study both experimentally and theoretically the intensity and frequency profile of the pulse that is generated by second-harmonic generation with phase mismatch of a pulse with a duration of 50 fs. Experimentally, we determine the shape and the frequency of the generated pulse by correlating it with a second fundamental pulse and by measuring the spectra of the generated pulse. Theoretically, we solve numerically the coupled differential equations that describe the nonlinear interaction. We show that for ultrashort pulses the effects of phase mismatch, depletion, and group-velocity differences between the fundamental and the second harmonic strongly influence the intensity profile and the frequency spectrum of the second-hamonic pulse. We find that in second-harmonic generation with phase mismatch the frequency of the generated pulse becomes modulated.

We calculate the quasienergies and steady states of a coupled two-level atom and quantized electromagnetic cavity mode with the cavity mode driven by a periodic classical field. The atom, the cavity mode, and the classical field are all on resonance. The quasienergies give shifted Jaynes-Cummings level splittings. These splittings are reduced by the interaction with the driving field and vanish at a threshold value of the driving field strength. Above the threshold, discrete quasienergies and normalizable steady states do not exist. Below the threshold, for weak driving fields, the steady states are squeezed and displaced Jaynes-Cummings eigenstates. We discuss the relevance of these results to work in cavity quantum electrodynamics.

The realization of the optical stochastic (or nonstationary) field interferometer (Sto-IF) is reported. By this device, whose properties are determined by those of the stochastic beam splitter (Sto-BS), relevant Bose-Einstein correlations are generated within the investigated particle field. A very general quantum theory of Sto-BS and Sto-IF is reported. Because it accounts for any distribution function of the Sto-BS driving field, this theory embodies the formal content and the results of previous interferometry theories. All theoretical results are substantiated by an experiment carried out with a Mach-Zehnder Sto-IF. Basic considerations on Bohr’s complementarity in stochastic interferometry are expressed on the basis of Shannon’s information theory applied to the particle welcher weg problem.

Resonantly enhanced second-harmonic generation in atomic hydrogen was investigated near 121.6 nm. With the application of a dc electric field, it is shown that coupling of the 2s and 2p states produces resonantly enhanced nonlinear susceptibility and reduced absorption at the second-harmonic wavelength, resulting in an increased net efficiency of the second-harmonic-generation process.

Intrinsic optical bistability due to dipole-dipole interactions among interacting two-level atoms shows strong phase dependence in the presence of a squeezed vacuum. We show that by varying the relative phase between the squeezed vacuum and the incident field, it is possible to excite the system of two-level atoms from the lower to upper branch of the bistable curve. On this basis, an optical switch that utilizes this phase dependence for intrinsic optical bistability is proposed.

The dynamics of a single-mode laser containing a saturable absorber in its cavity is investigated by means of the linear stability analysis of the rate equations of a recently proposed model. It is found that a single degree of freedom, which characterizes the saturation effect in the absorptive medium, well predicts whether the laser oscillation becomes chaotic or not.

We consider two modes of the electromagnetic field interacting via a three-level atom in a ladder configuration. We calculate the squeezing spectra of the sum and difference of the two output beams. The usefulness of this system as a quantum-nondemolition-measurement scheme is analyzed and a prediction is made using the parameters of a recent experiment by Grangier et al. [Phys. Rev. Lett. 66, 1418 (1991)]. We use a full three-level model in the most general case and in particular the influence of both the one-photon and the two-photon detunings are investigated.

The system we analyze has the structure of a planar optical waveguide containing a multiple quantum well, with the planes of the wells parallel to the direction of propagation. We consider the two different configurations of a Fabry-Pérot cavity and distributed-feedback device. The optical nonlinearities are described by means of the first-principles theory developed by Haug, Koch, Schmitt-Rink, and co-workers, generalized to include the finite width of the wells. The dynamics of the system is described by the equations that govern the evolution of the two counterpropagating fields, coupled with the carrier-density equation, and accompanied by the appropriate boundary conditions. The steady-state behavior is analyzed as a function of the control parameters of the system for the case of a GaAs/${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/AlAs structure. The system develops bistability even when the input field is in resonance with the excitonic peak, but the phenomenon becomes more pronounced in the detuned configuration. The hysteresis cycles obtained in the case of distributed-feedback device turn out to be competitive with those displayed by the Fabry-Pérot system.

A quantum-nondemolition method to measure the number of photons stored in a high-Q cavity, introduced by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)], is described in detail. It is based on the detection of the dispersive phase shift produced by the field on the wave function of nonresonant atoms crossing the cavity. This shift can be measured by atomic interferometry, using the Ramsey separated-oscillatory-field method. The information acquired by detecting a sequence of atoms modifies the field step by step, until it eventually collapses into a Fock state. At the same time, the field phase undergoes a diffusive process as a result of the back action of the measurement on the photon-number conjugate variable. Once a Fock state has been generated, its evolution under weak perturbation can be continuously monitored, revealing quantum jumps between various photon numbers. When applied to an initial coherent field, the intermediate steps of the measuring sequence produce quantum superpositions of classical fields, known as ‘‘Schrödinger cat states.’’ Ways to prepare and detect these states in a cavity subjected to a weak relaxation process are discussed. The effects analyzed in this article could realistically be observed by using circular Rydberg atoms and very high-Q superconducting microwave cavities. The possibility of photon ‘‘manipulation’’ through nonresonant atom-field interactions opens a domain in cavity QED studies.

Two-dimensional light trapping of TM and TE patterns in saturable self-defocusing nonlinear media is examined. The vector dark spatial soliton of TM type is found to exist only within a certain range of the beam effective index, which can be wider or narrower compared with the corresponding one in the Kerr-law nonlinearity, depending on the nonlinear saturation index. This contrasts with the scalar dark spatial soliton of TE type, the guidable region of which in saturable nonlinear media is equal to or narrower than that in the Kerr-law nonlinear medium. The physical origin leading to such a distinct contrast is also explored.

The dynamics of the two counterpropagating modes of a dye ring laser with backscattering have been studied experimentally. By varying the power of the pump laser, we have observed the dye-laser intensities change from random switching to anticorrelated oscillations. When the magnitude of the backscattering coefficient R is close to the critical value ${\mathit{R}}_{\mathit{c}}$, the laser exhibits noise-induced transition between the switching region and the oscillation region. This noise-induced effect can be attributed to pump fluctuations. A frequency lock-in effect has been observed in the oscillation region when ‖R‖ is near ${\mathit{R}}_{\mathit{c}}$. The experimental results are compared with solutions obtained both from the analysis of the third-order equations of motion and from the Monte Carlo simulations of these equations with additive and multiplicative noise.

Measurements performed on a system will alter the dynamics of that system, and in the strong-measurement limit, can theoretically freeze the free evolution completely. This is the quantum Zeno effect. We utilize quantum-nondemolition photon-counting techniques to realize the Zeno effect on the evolution of either a two-level Jaynes-Cummings atom interacting with a resonant cavity mode, or on two electromagnetic modes configured as a multilevel parametric frequency converter. These systems interact with another electromagnetic cavity mode via a quadratic coupling system based on four-wave mixing and constructed so as to be a nondemolition measurement of the photon number. This mode is then coupled to the environment through the cavity mirrors. This measurement is shown to be a measurement of system populations, which generates the desired Zeno effect and in the strong-measurement limit will freeze the free dynamics of the system.

We analyze an intensity feedforward scheme to produce a sub-Poissonian (amplitude-squeezed) light beam from the intensity-correlated twin beams generated by a nondegenerate parametric amplifier. Photon-number measurement of the idler beam at the output of the parametric amplifier is linearly fed forward onto the output signal beam using an amplitude modulator. The minimum available Fano factor is shown to be 1/(2g-1), where g is the parametric amplifier gain, and is equal to the nonclassical intensity-noise-reduction factor of the twin beams at the output of the parametric amplifier. By changing the frequency of the input-signal beam, tunable sub-Poissonian light can be generated with this scheme for application in precision absorption spectroscopy.

We study the statistical properties of the intensity of a good-cavity laser driven across the threshold by a linear variation in time of the cavity losses. This study is performed by using the quasideterministic theory (QDT) for two cases: In the first one, case I, the control parameter a(t) changes without bound, and in the second, case II, a(t) reaches a fixed value. The validity of QDT is then analyzed for both cases. We characterize the anomalous fluctuations by the time ${\mathit{t}}_{\mathit{m}}$ at which the maximum appears and by the value of this maximum ${\mathrm{\sigma }}_{\mathit{m}}$. Our results show that ${\mathit{t}}_{\mathit{m}}$ coincides with the average of the time of maximum rate of growth of the intensity T. We show that in case I, ${\mathit{t}}_{\mathit{m}}^{\mathrm{-}1}$ and ${\mathrm{\sigma }}_{\mathit{m}}$ scale with √v and that the relative fluctuations are given by a universal scaling function. The scaling of ${\mathit{t}}_{\mathit{m}}$ is in agreement with experimental studies. In case II we calculate analytically T, ${\mathit{t}}_{\mathit{m}}$, and ${\mathrm{\sigma }}_{\mathit{m}}$, and we show that the moments of the intensity are given through a scaling variable. All the results are checked with numerical simulations.

We report magnetic dipole hyperfine-structure constants, obtained by doing nonrelativistic configuration-interaction calculations, for ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ti}$ i 3${\mathit{d}}^2$4${\mathit{s}}^2$ ${}_{}{}^3{}_{}{}^{}$P, which are in excellent agreement with experiment [theory (experiment) ${\mathit{A}}_2$=-23.150 (-25.215) MHz, ${\mathit{A}}_1$=2.202 (2.665) MHz] in contrast with Hartree-Fock and some semiempirical values. Second-order electrostatic effects, arising mainly from the 3${\mathit{d}}^3$4s configuration, are crucial to understanding this system. The nuclear quadrupole coupling constant is -138.4 MHz and 69.2 MHz×Q (in b) (J=1,2). By combining with measurement, we predict Q=0.346 b. Hyperfine-structure constants are also given for the 3${\mathit{d}}^3$4s and 3${\mathit{d}}^4$ ${}_{}{}^3{}_{}{}^{}$P terms.

The time-dependent Schrödinger equation for a particle in general rotating systems is solved analytically, and the exact solutions are used to study the nonadiabatic Berry phase. It is shown that the nonadiabatic Berry topological phase appears in general rotating systems for purely mechanical reasons and is observable. An alternative expression for the nonadiabatic Berry phase is given and discussed.

For the Dirac equation in one dimension, a transparent potential is constructed such that the transmission probability is unity at all energies. The potential is related to a soliton-type solution of the nonlinear Dirac equation with a specific type of nonlinearity that exhibits ‘‘supersymmetry.’’

In this paper we investigate the time evolution of a charged oscillator with a time-dependent mass and frequency in a time-dependent electromagnetic field using the Lie algebraic technique. We obtain an exact form of the time evolution operator which, in turn, enables us to find the exact wave functions and coherent states of the system at any time t. Our analyses indicate that the wave function of the system starts as a coherent state at t=0 and evolves as a squeezed state at a later time.

By the use of the local-scaling density-functional method, simple yet accurate isotropic Compton profiles are variationally determined for the helium atom within the Hartree-Fock framework.