Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak-field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. Heisenberg equations of motion are solved in the steady-state and analytic expressions for the fluorescent-light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed, and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation, the second-order intensity correlation function does not factorize. This and other differences are discussed, and curves are presented to illustrate the behavior of various quantities. We also present results for thermal excitation of the atom.

Numerical simulations of mode locking in synchronously pumped KCl:${\mathrm{Tl}}^0$(1) and LiF:${\mathrm{F}}_2^{+}$ color-center lasers in Fabry-Pérot and ring configurations are presented. The presence of spontaneous-emission noise leads to large-scale fluctuations in the resulting pulses, and conditions for pulse optimization and stabilization are described. There exists a close correspondence between regimes of quasistationary and fluctuating pulses in the Fabry-Pérot and unidirectional ring lasers, with regimes of quasistationary, spontaneously unidirectional and stochastically driven, competitive, bidirectional pulsing in the bidirectional lasers.

A nondegenerate two-photon Jaynes-Cummings model is analyzed for its atomic-dipole squeezing and emission spectra. The input fields are assumed to be coherent or squeezed. The atomic dipole squeezes both for the on- and off-resonance excitations, showing a greater amount of squeezing for the former. The emission spectrum shows a central-two-peak structure for a variety of field inputs. When the fields are initially in coherent or squeezed states, sidebands appear whose widths are governed by the input-field statistics.

The space-time behavior of a wide-gain-section, single-longitudinal-mode laser is investigated. Analysis of the full Maxwell-Bloch model in one transverse spatial dimension identifies a traveling-wave solution beyond the first laser threshold, for positive detuning from resonance, which appears to be a globally attracting state of the laser. On the negative-detuning side we observe an initial bifurcation to a homogeneous plane-wave state. A second instability threshold can be identified by linearizing about the respective solutions for both positive and negative detuning. We also find that the standard approach to adiabatic elimination, whereby the polarization equation is adiabatically eliminated, can lead to a spurious high-transverse-wave-number instability in the reduced equations. The derivation of an adiabatically reduced set of equations to remove the instability on the positive-detuning side is a nontrivial matter.

Models of a two-photon interference experiment proposed by Franson to study the Einstein-Podolsky-Rosen (EPR) effect are presented. The experiment considers a pair of photons correlated in time and in frequency, each of which is passed through an interferometer. When the path difference through the two interferometers is set so there is no first-order interference, Franson showed that second-order interference between the two photons could occur with 100% visibility. In this paper both quantum and classical models are considered and the importance of the coincidence time window and the effect of the frequency correlation are shown. Calculations are presented for all settings of the interferometers. The EPR effect arises from entangled states; a brief discussion is given of the nature of the entangled state for this type of experiment.

The steady-state fluctuations of an inhomogeneously broadened two-mode laser with both additive and multiplicative white noise are investigated theoretically. A Fokker-Planck equation of the intensity-distribution function is presented. Analytic expressions of the autocorrelation and cross correlation of the steady-state two-mode intensities are derived for equal pump parameters of the two modes. Large intensity fluctuations occur when the laser is operated below threshold. However, when the laser is operated far above threshold, there is almost no difference between the laser models with and without multiplicative noise.

We present a comprehensive quantum theory of correlated-emission lasers (CEL’s) in a combination-mode approach, which is valid for both the quantum-beat laser and the CEL with injected atomic coherence. We first show that, under certain conditions, the linear master equation of the CEL’s breaks down into two uncoupled equations in the combination modes, which are linear combinations of two CEL modes. One combination mode that is above threshold represents the average phase and the average amplitude of two CEL modes (called the sum mode), whereas the other that is below threshold represents the relative phase and the relative amplitude of the two CEL modes (called the relative mode). When the relative mode is in its vacuum state, the normally ordered variances of two Hermitian operators corresponding, respectively, to the relative phase and the relative amplitude vanish. Through deriving a nonlinear master equation for the CEL with injected atomic coherence in the combination modes, we show how a set of proper initial atomic conditions can keep the relative mode in its vacuum state. We obtain the Glauber P functions, the mean photon numbers, and the photon-number variances in both the combination modes and the CEL modes, and find the mode pullings of the CEL’s and the natural linewidth of the sum mode. We also show a correspondence between the vacuum state of the relative mode and the vanishing of the relative-phase diffusion coefficient.

Diagrammatic methods for the calculation of the nonlinear response of a system that is dressed by resonant external fields are developed. The double-sided diagrams used earlier by Prior [IEEE J. Quantum Electron. QE-20, 37 (1984)] for the calculation of nonlinear susceptibilities in the presence of weak fields are generalized. Additional types of double-sided diagrams are given that incorporate explicitly (a) the relaxation-induced population transfers among the dressed levels and (b) the effects of the nonvanishing of the diagonal elements of the dipole operator in the dressed-state basis. The rules for the diagrams are worked out from the analytical structure of the nonlinear response. Applications of the diagrammatic techniques to several intense-field phenomena are discussed.

Laser light with a Laguerre-Gaussian amplitude distribution is found to have a well-defined orbital angular momentum. An astigmatic optical system may be used to transform a high-order Laguerre-Gaussian mode into a high-order Hermite-Gaussian mode reversibly. An experiment is proposed to measure the mechanical torque induced by the transfer of orbital angular momentum associated with such a transformation.

The Jaynes-Cummings model of optical resonance describes the simplest fully quantized interaction between two quantum systems of different nature: a two-level atom (fermionic system) and a quantized field mode (bosonic system). This interaction leads to extreme quantum entanglement of the atom and field. However, the model also predicts that, at precisely half of the revival time, the atom and field become asymptotically disentangled. This disentanglement becomes more exact as the coherent-state amplitude increases. In this paper we investigate the nature of the pure-field-state superposition generated at such times. We show that this superposition is of distinguishable states of the field with the same amplitude but opposite phase. Interference between these components leads to nonclassical oscillations in photon-number distributions and squeezing in quadratures of the field. The Schrödinger-cat states of the field are highly transient, and depend very sensitively on the interaction time, the initial intensity of the field, and the atom-field detuning.

It is predicted theoretically and registered experimentally that the speckle pattern of a laser beam transmitted through a multimode fiber undergoes an angular shift from the switching of the chirality of the polarization. The effect may be considered as the result of the spin-orbit interaction for the photon in the inhomogeneous medium.

We perform nonperturbative calculations of resonant multiwave mixing of two high-intensity laser beams of different frequencies both for a general three-level system and for the 3 ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$–3 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ electronic resonance of the sodium atom. Our calculations proceed by direct numerical integration of the density-matrix equations and subsequent Fourier analysis of the calculated time-dependent density-matrix elements. We examine the case where two nearly degenerate input beams are each detuned many collisional linewidths from electronic resonance, and the frequency difference between the input beams is tuned through a ground-state resonance. Unlike previous high-intensity analyses, each input beam can be resonant with numerous transitions simultaneously; for a three-level system, we refer to this as an ‘‘M-type’’ system, in analogy with Λ- and V-type systems. Calculated four-, six-, and eight-wave-mixing spectra exhibit subharmonic resonances of the type observed experimentally by Trebino and Rahn [Opt. Lett. 12, 912 (1987)]. The three-level system is studied to gain insight into the physics of these subharmonic resonances. For more quantitative comparison with experiment, we use a model that includes the 16 Zeeman and hyperfine states in the 3 ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$ and the 3 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ levels, and accounts for arbitrary linear polarization of the input laser radiation. The relative intensities of the resonance features in the calculated multiwave-mixing spectra show good agreement with experiment. These resonance features broaden and shift as laser intensity increases, as predicted for four-wave-mixing processes in previous, less general high-intensity analyses. Both theory and experiment also show additional resonant features in the eight-wave-mixing spectra that appear at very high intensity.

A multimode quantum analysis of noise reduction in interferometric measurements is presented. A unitary transformation relating the output modes with the input ones for a Michelson interferometer with moving mirrors is given. The evaluation of the noise spectrum shows that with a proper choice of the input states, the sensitivity of the interferometer can be pushed beyond the standard quantum limit. The results are compared with a semiclassical analysis.

The ac quasienergy for an atom irradiated by a strong field of low frequency ω can be expressed as an asymptotic expansion in powers of ${\mathrm{\omega }}^2$, with coefficients that depend on the field strength F. In this paper we give a prescription for calculating these coefficients for arbitrary polarization, and we show explicitly that the leading term of the expansion is the cycle-averaged dc quasienergy. We have calculated the first four coefficients in the case of ground-state atomic hydrogen in a linearly polarized field, and we present a table of these coefficients for various values of F. As an application, we compare the estimate of the ac width obtained from the first four terms of the expansion with the exact value when the (linearly polarized) light has the wavelength 616 nm and an intensity in the range 3×${10}^{13}$ to 3×${10}^{14}$ W/${\mathrm{cm}}^2$; the sum of the first four terms give an excellent interpolation through the exact results (though does not reproduce the resonance structure). When the F-dependent coefficients are expanded in powers of ${\mathit{F}}^2$ to yield a double series ${\mathit{tsum}}_{\mathit{m}}$${\mathit{tsum}}_{\mathit{n}}$${\mathrm{\beta }}_{2\mathit{n}}^{2\mathit{m}}$F 2n${\mathrm{\omega }}^{2\mathit{m}}$, the constant coefficients ${\mathrm{\beta }}_{2\mathit{n}}^{2\mathit{m}}$ are real and (in the case of atomic hydrogen) are rational numbers that can be evaluated exactly. We verify, for m=1 and for linearly or circularly polarized light, that in the large-n limit the ${\mathrm{\beta }}_{2\mathit{n}}^{\left(2\mathrm{}\mathit{m}\right)}$ satisfy an asymptotic formula of the Bender-Wu type. We show that just 19 coefficients ${\mathrm{\beta }}_2^{\left(2\mathrm{}\mathit{m}\right)}$ are needed to accurately reproduce the second-order (order ${\mathit{F}}^2$) ac shift and width over a remarkably large range of frequencies.

While the analysis of the stationary solutions of nonlinear periodic media suggests the existence of gap-soliton-induced bistability, numerical simulations show that some of the states involved are unstable. To investigate the instability, a linear stability analysis is presented showing the stable and unstable regions as a function of both the intensity of the incoming radiation and the frequency.

The low-frequency intensity noise of high-quantum-efficiency lasers or light-emitting diodes (LED’s) is dominated by the pump noise. By coupling two or more semiconductor lasers (or LED’s) in series with a current source, the pump noise of the two lasers will be equal, and the intensity noise of the lasers will be highly correlated. It is shown that one may generate sub-Poissonian light by measuring the intensity fluctuations of one of the beams and feeding back (or forward) the information to regulate the other photon beam. The generation scheme is shown to have much in common with intensity-correlated twin beam generation from nondegenerate optical parametric oscillators.

Nonlinear propagation of incoherent waves in single-mode optical fibers is presented both theoretically and experimentally. Spectral broadening and simultaneous coherent time narrowing occur owing to the Kerr nonlinearity, when two incoherent pulses copropagate in a single-mode optical fiber. Correlation time compression by a factor of 2 on a weak incoherent signal, induced by a strong noisy pump, was observed. Experimental data and theoretical analysis indicate that self-phase-modulation and induced phase modulation are the mechanisms responsible for the effects.

The diamagnetic Kepler problem, or quadratic Zeeman effect in hydrogen, is converted into an asymmetric top via a transformation to Lissajous action-angle variables. These variables are especially suitable for uniform semiclassical quantization of the system for arbitrary values of the azimuthal quantum number m.

We investigate the quantum survival-probability function (SPF) in regular and chaotic systems coupled to a reservoir via a particular quantum-nondemolition coupling. We show that for certain initial conditions the averaged SPF is markedly different in these two kinds of systems. We also relate this SPF to the averaged off-diagonal elements of the density matrix in the pointer basis.

We study classically the microwave ionization of hydrogen atoms using the standard one-dimensional model. We find that the survival probability of an electron decays algebraically for long exposure times. Furthermore, as the microwave field strength increases, we find that the asymptotic algebraic decay exponent can decrease due to phase-space metamorphoses in which new layers of Kolmogorov-Arnold-Moser (KAM) islands are exposed when KAM surfaces are destroyed. We also find that after such phase-space metamorphoses, the survival probability of an electron as a function of time can have a crossover region with different decay exponents. We argue that this phenomenon is typical for open Hamiltonian systems that exhibit nonhyperbolic chaotic scattering.