A theoretical analysis is given for one-dimensional laser cooling below the Doppler limit of J=1/2 ground-state atoms. The laser field consists of a pair of counterpropagating, linearly polarized, low-power beams, whose polarization directions differ by an angle θ (0≤θ≤π/2). For θ≪1, the effective optical-pumping time is shown to increase strongly near the nodes of the standing wave, and the cooling force can be much larger than that for θ=π/2. Moreover, for θ≪1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for θ=π/2. As a consequence it is possible to achieve an equilibrium atomic distribution that, for θ≪1, is characterized by a mean kinetic energy that is lower than that predicted to occur for θ=π/2. The equilibrium velocity distribution is not necessarily Maxwellian, and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms may be trapped in the vicinity of the laser-field nodes.

We have investigated the spectral modification of the Raman Stokes line in the cavity version of Raman scattering where a three-level system in the Λ configuration interacts with an externally driven pump mode and a Stokes mode in a cavity. Anti-Stokes modes are eliminated by the cavity-resonance condition. At very low intensities the spectrum consists of a single-peak structure (Raman Stokes) that splits into a doublet when the external pump field is sufficiently intense so that the effective Rabi frequency exceeds the rate of spontaneous emission. At very high intensity, however, a triplet structure appears where the strong sidebands are symmetrically separated from the central weak band.

Multiphoton ionization of Ca and Sr was studied at a wavelength of 532 nm with optical pulses of 12-ns and 35-ps duration. Excess photon absorption followed by autoionizing decay leads to populations of excited states of singly charged ions that can be observed via their spontaneous emission. Relative measurements were performed on fluorescence from ${\mathrm{Ca}}^{+}$(4p), ${\mathrm{Ca}}^{+}$(5s), and ${\mathrm{Ca}}^{+}$(4d), and from ${\mathrm{Sr}}^{+}$(5p) and ${\mathrm{Sr}}^{+}$(6s). The contribution of the highly excited states was found to be favored under short-pulse (35-ps) irradiation.

A coupled set of equations for carrier distributions and stimulated emission in a semiconductor laser is presented, based on a nonequilibrium Green’s-function formulation. Carrier momentum-dependent dephasing caused by carrier-carrier scattering and frequency-dependent optical gain are shown to govern the interplay between carrier relaxation and stimulated recombination. Ignoring the interband Coulomb interaction, the coupled system of equations for the carrier distribution functions and the optical gain is solved self-consistently for a single-mode short-cavity semiconductor laser under steady-state operation conditions. Numerical results show spectral and kinetic hole burning as well as nonlinear gain saturation.

We examine the phase-insensitive amplification of three different kinds of higher-order squeezing. In particular, we consider fourth-order squeezing, intrinsic fourth-order squeezing, and amplitude-squared squeezing. It is found that for any input state both fourth-order squeezing and intrinsic fourth-order squeezing disappear at the output if the intensity gain is greater than 2. Amplitude-squared squeezing, on the other hand, can survive amplification at gains slightly greater than 2. Therefore the photon-cloning limit (intensity gain equals 2) is not a fundamental limit to nonclassical behavior.

The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.

We study the temporal evolution and the stationary regime of an electromagnetic-field mode interacting with three-level Λ-type atoms in a lossless microwave cavity. We find that under certain conditions the field evolves to the recently defined tangent or cotangent states [J. J. Slosser and P. Meystre, Phys. Rev. A 41, 3867 (1990)]. In particular, in this system number states can be generated for any value of the atomic-upper-level population. In addition, a strong squeezing in the quadrature fluctuations is found.

Based on the standard laser model of a large number N of model atoms resonantly coupled to a single lasing mode, we show that the nonlinear dynamics of the active atoms of the laser can lead to output-intensity fluctuations significantly reduced below the shot-noise level. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through the pumping as the key process leading to this dynamic-pump-noise reduction. This process has been neglected in most of the standard treatments of the laser so far. We find that the results are closely related to recent calculations based on the assumption of an external regular pump. For the widely used four-level model of the active atoms, the intensity noise can be reduced 50% below the shot-noise level. Generalizing the model to an m-level system, we find a quantum-noise reduction by a factor of 1/2m/(m-1)(m≥3), leading to perfect output-intensity noise reduction in the limit of a large number of intermediate steps in the recycling process of the active atoms. Finally, we demonstrate that the bandwidth of the noise reduction can be significantly enhanced using a nonlinear absorber in the cavity.

We investigate the occurrence of instabilities related to possible transitions to chaos in specific configurations based on semiconductor lasers. Various scenarios, such as period doubling, frequency locking, quasiperiodicity, and intermittency, are observed experimentally as functions of the control parameters. These are, respectively, the current modulation, external light injection, and delayed feedback. The experimental findings are described and discussed on the basis of semiconductor-laser rate equations.

The theory of a two-mode nondegenerate parametric amplifier in a cavity is reformulated in terms of quadrature-phase-amplitude variables. The corrrespondence with a genuine classical stochastic linear process is found (non-negative-definite diffusion matrices) for the case of a cavity device immersed in thermal or ordinary (nonsqueezed) vacuum sources. A special kind of squeezing, i.e., quadrature squeezing [B. L. Schumaker, Phys. Rep. 135, 318 (1986)], is found to be characteristic of the internal steady state for the case of a cavity model subjected to an additional phase-sensitive noise source coupled to one of the two internal modes. Finally, the usual squeezing spectrum of the output field is calculated in both cases by means of an input-output formalism based upon a symmetric ordering scheme of noncommuting operators, well adapted for the quadrature-phase description of the fields involved in the interaction.

We consider two copropagating fields in a nonlinear Kerr medium, each with a particular phase and intensity. The Kerr medium possesses an intensity-dependent refractive index and the phase shift of each field thus depends on the intensities of the fields. Classically it is possible to induce an arbitrary phase shift of one field (the signal field) by either increasing the intensity of the other field (the control field) or by increasing the interaction legnth. We show that if the intensity of the control field is low, the phase shift on the signal is limited by the discrete nature of the photon-number distribution in the control field and cannot be increased simply by increasing the interaction length. In general the maximum phase shift of the signal field is φ if the control field possesses φ photons. This limit arises as a consequence of quantum recurrence effects.

Squeezing of classical (or quantum) fluctations is studied in a driven one-dimensional oscillator coupled to an environment in thermal equilibrium. The problem is reduced to a quasiclassical Langevin equation. A theory based on an iterative mapping is formulated, and analytical results are obtained from it. Squeezing spectra as a function of damping and frequency are found. The theory gives a finite limit to squeezing of 75% (in power) for systems operating in a steady state. The theory is compared with numerical calculations on the Josephson-junction resistively shunted junction model. The theory is in excellent agreement with numerical results, indicating a possibility of universality of the squeezing spectrum in certain limits of damping and frequency.

We have measured the quantum noise added to a signal by a Raman amplifier. This was done using a modified Mach-Zender interferometer with an amplifier placed in each leg. Quantum noise added by the amplifiers manifests itself by degrading the visibility of the ensemble-average output fringe patterns. The amount of noise added by the amplifiers is deduced from the degradation of the visibility. The experimental results are compared with both ideal, single-mode amplifier theory and Raman theory. We find that the Raman amplifier operates near the quantum limit with only a few input photons per mode required to dominate the noise added by the amplifiers.

The phase states of a harmonic oscillator are considered and used to define an analytic representation in the unit disk. The Weyl semigroup in the number-angle phase space is studied. More general states called negative binomial states are introduced, and the corresponding analytic representations in the unit disk are defined. Möbius conformal mappings are used for the study of SU(1,1) transformations. They define alternative types of one-mode squeezing based on the discrete series of SU(1,1) representations.

Transient stimulated hyper-Raman scattering has been observed in an ultrathin organic crystal (-)2-(α-methylbenzylamino)-5-nitropyridine (MBA-NP) pumped by picosecond laser pulses. Results were modeled by an instability theory.

The variations of the optical frequency during the switch-on of a single-mode semiconductor laser diode have been studied. Our model relies on stochastic rate equations, and therefore a meaningful description of the laser frequency in the presence of both noise and transient evolution is difficult. The relation between an approximately instantaneous frequency that we calculate numerically and experimentally measured frequencies is discussed. We analyze the frequency variations during switch-on processes and the statistical properties of the nearly instantaneous frequency that we chose as the most reasonable to calculate. The range of the frequency chirp during the first pulse of the intensity is stochastic, but it is correlated with the switch-on time, and therefore its statistical properties can be deduced from those of the first-passage-time distribution. The correlations permit a single discriminator to select a subset of pulses with similar peak intensities, delay times, and chirp ranges. In addition, there are significant differences between the averaged quantities and results for a single switch-on.

The problem of the evolution of a two-level quantum system in a radiation field of Gaussian shape with detuning is addressed by seeking an approximate expression for the transformation function governing the interaction. The transformation operator requires the evaluation of two independent matrix elements: the former is obtained by the Rosen-Zener conjecture; the latter is based on an expansion using the main parameters involved in the first one. The expressions obtained, which are supposed to hold in the case of small detunings, have been tested by comparison with a numerical integration. Then the solutions are modified to take into account decay phenomena to other levels. As a final example, the expressions dealing with the transition probability in the case of two separated oscillatory fields are given.

Some striking analogies are exhibited between the lossless quantum-mechanical beam splitter and the following two elementary quantum systems: (1) the two-dimensional isotropic oscillator and (2) the two-dimensional hydrogen atom. For example, we show that the unitary transformation connecting the input and output photon statistics at a lossless 50-50 beam splitter is identical to the transformation connecting the polar and parabolic eigenstates of the two-dimensional (2D) hydrogen atom. A similar connection between (Gaussian) laser beams and the eigenstates of the 2D oscillator is pointed out. These analogies are established by identifying the underlying symmetries of these systems and exploiting them by means of group theory.

We study the role of classical resonances in quantum systems subjected to a periodic external force. It is demonstrated that classical invariant vortex tubes determine the structure of Floquet states ‘‘captured’’ by resonances in the classical phase space. In addition, resonance quantum numbers are introduced. The analysis of simple model calculations leads to a qualitative description of nonperturbative phenomena relevant for the interaction of atoms or molecules with strong, short laser pulses.

We calculate the first-order interference-fringe visibilities for Mach-Zehnder interferometers in which the input beam splitting has time-varying reflection and transmission coefficients. Particular attention is given to single-photon input states, and it is shown that fringes persist in appropriate conditions even for a beam splitter that alternates between complete transmission and complete reflection. The similar behavior found for input coherent and chaotic light confirms the single-photon nature of first-order interference. The states of excitation of the internal arms of the interferometer are derived and discussed in the context of delayed-choice experiments.