The influence of injected atomic coherence on a laser’s operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.

An experimental study was made on the effect of multiphoton ionization on high-order harmonic generation and propagation in rare gases with subpicosecond dye-laser (λ∼616 nm) pulses at the intensity up to ∼2×${10}^{14}$ W/${\mathrm{cm}}^2$. Both high-order harmonic intensity and the ion signal were measured as a function of the position of the laser focus. The harmonic signal in Ar, Kr, and Xe shows a remarkable decrease near the peak position of the ion signal. We have observed the asymmetry in the shape of the harmonic signal and the change of the asymmetry with harmonic order. Furthermore, the dependence of harmonic signals on fundamental intensity were found to be quite different at the specific positions of the laser focus. These experimental results are consistently explained by the medium ionization and the resulting self-defocusing of the laser beam. The results obtained with the XeCl laser (λ∼308 nm) pulses back up our interpretations for those obtained with the dye-laser pulses.

A classically pumped, two-quantized-mode micromaser model operating in a two-channel Raman configuration is proposed. In this model, three-level (Λ-type) atoms are injected through the cavity. The field-atom interaction is governed by Raman transitions in which both the pump-Stokes channel and the pump-anti-Stokes channel are involved. Under the trapping state conditions, we find that the Stokes and the anti-Stokes fields are strongly correlated and squeezed.

We analyze the Risken-Nummendal–Graham-Haken instability occurring in a homogeneously broadened two-level unidirectional ring laser modeled by the Maxwell-Bloch equations. We investigate the class-B limit of these equations and derive partial differential equations describing the evolution of traveling waves. In particular, we obtain a degenerate Ginzburg-Landau equation with higher-order nonlinearities. We then investigate this equation and determine periodic traveling wave solutions. We discuss their stability in terms of the laser parameters and predict unusual properties for the long-time behavior of the laser.

Phase-coherent states associated with the Pegg-Barnett (PB) phase operator formalism are introduced in terms of the algebraic properties of the PB phase theory. The phase-coherent-state representation of the PB phase states and the PB phase operators is obtained. Squeezing properties of these coherent states with respect to the phase quadrature operators are studied. The number-phase squeezing and number-phase uncertainty relations are also investigated in detail for a two-state system. Some new number-phase minimum uncertainty states are found.

We study the statistics of photons reflected by a harmonically suspended mirror. The noise modification can be interpreted in terms of temporal redistribution of the photon flux. Due to radiation pressure, the mirror is displaced and a variable delay is applied to the photons. The statistical properties of the reflected light are studied by Monte Carlo simulation with a corpuscular photon model and by analytic derivation. In the latter derivation, the effect of thermal fluctuations is included. The results indicate that a movable mirror appears as a passive quantum-noise eater at frequencies about the mechanical eigenfrequency of the mirror suspension.

We develop a first-order theory of the unified colored-noise approximation. It can be applied to general multidimensional systems driven by colored noise (the Ornstein-Uhlenbeck noise). A general formula for the first-order correction is derived, which is used for investigating the transient process of a dye laser. For the colored cubic model and colored gain-noise model of a dye laser, the Fokker-Planck equations are derived based on the general formula of first-order theory. The first-order corrections of the mean first-passage times for the models are obtained. We compare the results with numerical simulations, and show that the present results have greatly improved the results obtained by the original unified colored-noise approximation.

We show how a squeezed environment can be obtained by means of a suitable feedback of the output signal corresponding to a quantum-nondemolition (QND) measurement of an observable. As an example we show how the variance of a field quadrature of a cavity mode subject to QND-mediated feedback can be squeezed below the standard quantum limit and that this actually means that applying feedback is equivalent to coupling the mode to a squeezed environment.

Squeezed coherent states associated with the SU(1,1) group defined by (μ${\mathit{a}}^2$+ν${\mathit{a}}^{\mathrm{°}2}$)‖ψ〉=λ‖ψ〉, ‖μ${\mathrm{\Vert }}^2$-‖ν${\mathrm{\Vert }}^2$=1 are studied in detail. An explicit expression for the quasidistribution Q(α,${\mathrm{\alpha }}^{\mathrm{*}}$) in terms of the parabolic cylindrical functions is derived. The nonclassical properties of these states are discussed. The possibility of producing SU(1,1) squeezed coherent states using the down-conversion process is also demonstrated.

Forced light scattering using broad-bandwidth incoherent pump light (${\lambda }_{\mathit{B}}$=508 nm, full width at half maximum Δ${\lambda }_{\mathit{B}}$=13.8 nm), and narrow-bandwidth probe light is investigated experimentally and compared with self-diffraction. Forced light scattering improves the dynamic range of measurement by an order of magnitude compared to self-diffraction. A theoretical analysis of this scheme is presented. The technique is used to measure the dephasing kinetics of solutions of crystal violet and bis-(dimethylamino)heptamethine. Resulting from the relatively large autocorrelation time of 40 fs, the experimental signals show no influence from inhomogeneous broadening of the absorption bands; the dephasing kinetics can be characterized by a dephasing time ${\mathit{T}}_2$≊10 fs and an intrinsic correlation time ${\mathrm{\tau }}_{\mathit{C}}$≊30 fs with a weak modulation (center frequencies ranging from 800 to 1200 ${\mathrm{cm}}^{\mathrm{-}1}$), which is attributed to a coherent motion of the molecule (vibration). The dephasing kinetics of crystal violet shows a close agreement with the dephasing kinetics of malachite green previously reported for two-pulse photon echoes with ultrashort pulses [P. C. Becker et al., Phys. Rev. Lett. 63, 505 (1989)].

Excitation of a quantum ladder system by frequency-swept (-chirped) laser pulses has been investigated by studying an atomic model system, the 5s-5p-5d ladder of rubidium. The population transfer is significantly enhanced when the frequency is swept such that it follows the spacing of the ladder. At intermediate intensities we observe oscillations in the population transfer to the upper level (5d), which can be attributed to interference between two routes of excitation: sequential transfer and direct two-photon excitation via a virtual intermediate state. We determine simultaneously the population transfer to the upper level (5d) and the direct three-photon ionization, the latter corresponding to a three-step ladder with the final state being in the continuum: 5s-5p-5d-ɛp/ɛf. Experiments were performed, using 100 fs pulses at ∼780 nm from a self-mode-locked Ti:${\mathrm{Al}}_2$${\mathrm{O}}_3$ oscillator amplified at 10 Hz.

The two-level atom in an external field of arbitrary time dependence is solved formally using projection techniques. As a particular result of the general solution, an exact expression is presented for the density matrix of a two-level atom in a sinusoidal field.

The representation of the states of a single electromagnetic field mode by coherent states of an identical mean number of photons, i.e., the representation on a circle in phase space, is presented. The connection between the circle representation and the analytic representation is given.

We propose an alternative method for detecting the density matrix of a radiation field via optical homodyne tomography. The method needs no assumption on the state, and the density matrix is recovered directly from averages on data. The tomographic reconstruction is very fast and provides very reliable statistics on line with detection. As a test of the method we present numericla results for a set of computer-simulated experiments, corresponding to different quantum states of the radiation source. Then a tomographic reconstruction is given for experimental data provided by Smithey etal. [Phys. Rev. Lett. 70, 1244 (1993)].

We have investigated theoretically the applicability of phase-fluctuating laser fields in saturated absorption spectroscopy. The fluctuations of pump and probe fields are fully correlated if they are derived from the same laser source. Inside the saturable medium, phase fluctuations are converted into intensity noise. This nonlinear mixing modifies the statistics of the transmitted fields. By measuring higher-order correlations one can deduce additional spectroscopic information. Apart from the mean intensity, we have examined the intensity noise and intensity power spectrum of the weak probe field. The resonances of these correlation functions are also unaffected by large inhomogeneous broadening since they are inherently related to the usual saturated absorption dip. We find qualitative agreement with results of a recent experiment employing this technique [D. H. McIntyre et al., Opt. Lett. 18, 1816 (1993)], which demonstrates the advantages of noise spectroscopy using spectrum analyzers.

We study theoretically the effect of transverse boundary conditions on the traveling waves found in infinitely extended and positively detuned laser systems. We find that for large-aspect-ratio systems, well above threshold and away from the boundaries, the traveling waves persist. Source and sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defects can also exist away from the boundaries. The transverse size of the sink defect, relative to the size of the transverse domain, is important in determining the final pattern observed, and so, close to threshold, standing waves are always observed.

We develop a birth-death model for a cavity QED laser and analyze the dependence of the lasing threshold on the fraction, β, of spontaneous emission directed into the laser mode. We define threshold in terms of the Fano factor for the intracavity phonon number. We emphasize the role of β as a parameter characterizing the ‘‘system size’’ and show that the concept of laser threshold is well-defined in the ‘‘thermodynamic’’ limit, ${\mathrm{\beta }}^{\mathrm{-}1}$→∞. An ideal cavity-QED laser operates far outside this limit and therefore, in contrast to a conventional laser, is not a threshold device. We present numerical results showing how this difference affects the noise properties of the device.

Recent work by Wolinsky and Carmichael $[—OSA Annual Meeting, 1989 Technical Digest Series Vol. 18 (Optical Society of America, Washington, DC, 1989)] suggests that a superposition of two macroscopically distinct coherent states (a ‘‘Schrödinger-cat’’ state) may be produced in degenerate parametric oscillation in a transient regime. We investigate this possibility by performing numerical simulations of quantum stochastic equations derived using the positive P representation. The equations allow for finite signal cavity loss. Interference fringes which indicate the existence of the macroscopic superposition states are indeed predicted in regimes where the parametric nonlinearity is sufficiently large compared to the signal cavity losses. Experimental criteria needed for the generation of macroscopic quantum superposition states using parametric oscillation are thus established.

We present theory and observation to show that in resonant sum-frequency mixing the two pathways to the excitation of the coherence driving the output may be controlled in relative strength, and combine in antiphase on resonance. These two pathways are, first, a two-step route resulting in the creation of a real intermediate population, and second, a direct two-photon excitation resonantly enhanced by, but not populating, the intermediate level. The former route is shown to be raised over the latter by use of a stronger lower laser field. Experimental observation uses the 3S-3${\mathit{P}}_{1/2}$-3D level scheme in sodium vapor and single-frequency continuous-wave lasers for steady-state conditions and high resolution. A cancellation ratio of 94% is reported. Further, noninterfering incoherent fluorescence and an anti-Stokes Raman process are observed and contrasted.

A harmonic oscillator interacting with the electromagnetic field in the vicinity of the planar dielectric-vacuum interface has been analyzed. The electromagnetic field is described in terms of Carniglia-Mandel modes (triple-wave modes) which take into account proper boundary conditions at the interface. Exact resolvent functions, which determine the solution of the initial-value problem for the oscillator and the electromagnetic field, have been obtained. These functions give frequency shifts and decay times for oscillator excitations. In most cases, when the oscillator approaches the interface, its excitation decay time decreases. Radiative frequency shifts have been calculated and interpreted in terms of the coupling with the Carniglia-Mandel photons. Outgoing photons, i.e., photons characterized by the outgoing waves and the outgoing wave vectors, have been used for a description of angular radiation intensity patterns. Some results for the radiative damping and the radiation angular distribution are equivalent to the classical ones, however, they get a new quantum interpretation.