We show analytically that the presence inside an optical cavity of a polarizer and a hard diffracting object, for example, a circular aperture or waveguide, reduces the symmetry of the system from cylindrical to rectangular. As a consequence, patterns with concentric rings of bright or dark spots made up by modes whose azimuthal indexes are not multiples of one another, appear when the zero-field solution becomes unstable. These types of bifurcations are anomalous if the symmetry is cylindrical and therefore indicate the presence of polarization effects induced by diffraction. As an example of this type of system, we investigate numerically the bifurcations of a ring laser with a metallic duct and a polarizer inside the optical cavity.

In this paper we show how to use the richness of the dynamic responses of a physical system to perform a nontrivial measurement. In particular, we have calculated the Cr:YAG (YAG denotes yttrium aluminum garnet) absorption cross section in an optical system, namely, a solid-state laser (Nd:YAG) with a saturable absorber $({\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}),$ via the parameters fitting from time series. The technique consists of minimizing a ${\chi }^2$ function which is constructed by transforming the original rate-equation system into its standard form. The value obtained for ${\sigma }_a,$ $(2.5\mathrm{}\pm 0.3)\times {10}^{-18}{\mathrm{cm}}^2,$ is consistent with previously reported results that had dispersion of more than one order of magnitude.

We present detailed statistical investigations of the irregular fast pulsing behavior present in the dynamics of semiconductor lasers with delayed optical feedback operating in the low-frequency fluctuation and coherence collapse regimes. We demonstrate that the probability density distributions of the laser intensity on a picosecond time scale are essentially independent of the number of optical modes involved in the laser emission, using two complementary high-resolution experimental measurement systems: a high-bandwidth sampling digitizer and a single-shot streak camera. The experimental results are supported by numerical studies using the single-mode Lang-Kobayashi equations, as well as a multimode extension of the model. Furthermore, we also demonstrate that gain saturation and coexisting attractors can cause substantial qualitative changes of the probability density distribution.

We report a direct measurement of the Wigner function characterizing the quantum state of a light mode. The experimental scheme is based on the representation of the Wigner function as an expectation value of a displaced photon number parity operator. This allowed us to scan the phase space point-by-point, and obtain the complete Wigner function without using any numerical reconstruction algorithms.

A three-level atom interacting with classical electromagnetic fields is coherently excited by a two-photon transition near resonance and subsequently makes a second transition driven at resonance by a weak ir field at the noise level. Our calculation predicts generation of an electromagnetic field at a third frequency in the uv from zero field. Calculations show a gain of the uv radiation with propagation through the medium, though the populations of the two levels involved are never inverted. Other calculations produce a pulsed amplifier, two-photon optical nutation, and free induction memory. An effective susceptibility is defined and its imaginary part is found to be a good indicator of mode specific absorption and emission by the atomic state, and its real part a good indicator of dispersion. These calculations exemplify the possibility of coherent control over an atomic vapor and the production of a superradient macroscopic ensemble of states in the retarded frame for realistic parameters.

Recently, the stochastic nonlinear wave equation describing the dynamics of an observed quantum system has been solved for a free particle [Phys. Rev. A 45, 1347 (1992)]. In this paper, transient effects that occur during a continuous observation of the particle position are discussed. It is shown that the dispersion of the Gaussian wave packet of the particle always decreases in the beginning of the observation, then takes the form of oscillations which, after a short time, decay rapidly to the asymptotic value.

We investigate the iteration of a sequence of local and pair unitary transformations, which can be interpreted to result from a Turing-head $\left(\mathrm{pseudospin}S\right)$ rotating along a closed Turing tape $(M$ additional pseudospins). The dynamical evolution of the Bloch vector of S, which can be decomposed into $2^M$ primitive pure state Turing-head trajectories, gives rise to fascinating geometrical patterns reflecting the entanglement between head and tape. These machines thus provide intuitive examples for quantum parallelism and, at the same time, means for local testing of quantum network dynamics.

We suggest a scheme for realizing a universal two-quantum-bit (qubit) operation. The scheme uses two laser beams with different intensities to illuminate two different ions in a harmonic trap. Both beams are tuned to the red motional sideband. We find that, under certain conditions, the interaction will realize a universal two-qubit operation, the controlled-rotation operation, which is to rotate the phase of the state by $\pi$ only when the two states are both in the $|1〉$ state. The scheme requires careful control of laser intensity and Lamb-Dicke parameters. But after we reach the required parameters, the logic operation is very simple.

Stochastic ionization of a highly excited relativistic hydrogenlike atom in the monochromatic field is investigated. A theoretical analysis of chaotic dynamics of the relativistic electron based on the Chirikov criterion is given for the cases of one- and three-dimensional atoms. The critical value of the external field is evaluated analytically. The diffusion coefficient and ionization time are calculated.

A method to cool particles in a Paul trap without a laser is presented and simulated numerically. By adjusting the electric potential applied to electrodes as the feedback, an effect similar to that of laser cooling can be achieved. Results show that feedback control, with or without delay, continuously or discretely, and with or without noise, can effectively reduce kinetic energy and lead the system to a low periodic orbit over a wide range of control intensity. The final orbit of the controlled system is near to an elliptic orbit of the uncontrolled system and the system maintains regular motion when control is withdrawn.

The effect of quantum efficiencies of detectors on the phase sensitivity of a Mach-Zehnder is analyzed for the Fock state input. The phase uncertainty of two different interference experiments, the second order and the fourth order, are compared with two practical detectors with less than unit quantum efficiencies. It is found out that in the second-order interference experiment we cannot beat the classical limit in the phase sensitivity, even with ideal detectors. We show that almost ideal detectors are required to get the Heisenberg limit in the phase sensitivity of the fourth-order interference for two Fock state light inputs. There exists an optimum angle given by the efficiency of the detectors.

A nonlinear propagation of electromagnetic waves has been investigated in a heterostructure formed by spatially modulated density of ladder-type $\left(\Xi \right)$ three-level atoms. The appearance of a forbidden band gap for an electromagnetic field induced by another electromagnetic field has been found. An alternative concept of an optical transistorlike device based on this effect has been proposed.

A crossed laser-ion beam apparatus has been used to spectroscopically analyze electrons detached from an 80-keV beam of ${\mathrm{Ca}}^{-}$ ions at a photon energy of 1.903 eV. At this energy only the ${}^{1}Sks,d$ photodetachment channel is open. The photon flux dependence and the angular dependence of the measured electron yield were used to determine the photodetachment cross section $\sigma =48\mathrm{}\left(11\right)\mathrm{}$ Mb and the asymmetry parameter $\beta =0.90\mathrm{}\left(3\right)\mathrm{}$, respectively. The measured cross section is in significant disagreement with a recent R-matrix calculation. The present measurement has been used to establish an absolute scale for previous relative total cross-section data over a photon energy range 1.1–3.1 eV.

The development of an accurate method for solving systems of differential equations and the prediction of an unusual nonadiabatic regime of neutral atoms in magnetic traps as claimed by Yukalov [Phys. Rev. A 56, 5004 (1997)] are questioned. A defect arises from his method for the exact solution of differential equations, claiming generality at the basis of all his calculations. As shown in this Comment, the method is exact only for a very narrow class of equations. This class is determined and found to be quite inadequate for the physical conditions of the nonadiabatic dynamics in question.

Nonadiabatic dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, has been considered in my earlier paper [V. I. Yukalov, Phys. Rev. A 56, 5004 (1997)]. The main result of this paper is that an unusual semiconfining regime of motion was found, when atoms are confined from one side of an axis, but are not confined from another side. The author of the Comment [V. E. Shapiro, Phys. Rev. A 60, 719 (1999)] expressed doubts on the validity of this result, advancing several concrete questions. In the present reply I answer all of these questions and show that they do not invalidate the possibility of realizing the semiconfining regime of motion.

It is shown that the outcomes of measurements on systems in separable mixed states can be partitioned, via subsequent measurements on a disentangled extraneous system, into subensembles that display the statistics of entangled states. This motivates the introduction of the concept of “counterfactual” entanglement, which can be associated with all separable mixed states, including those that are factorable. This type of entanglement gives rise to a kind of postselection-induced Bell inequality violation. The significance of counterfactual entanglement, and its physical implications, are assessed.

We solve the relativistic equation for a hydrogenlike ion located at the center of a spherical cavity. Relativistic effects are determined as a function of atomic number. A few interesting properties such as level crossing and energy plateaus are discussed.