Recent developments in quantum optics have led to new proposals to generate number states of the electromagnetic field using conditioned measurement techniques or the properties of atom-field interactions in microwave cavities in the micromaser. The number-state field prepared in such a way may be transformed by the action of a displacement operator; for the microwave micromaser state this could be implemented by the action of a classical current that drives the cavity field. We evaluate some properties of such displaced number states, especially their description in phase space. The photon number distribution is shown to display unusual oscillations, which are interpreted as interference in phase space, analogous to Franck-Condon oscillations in molecular spectra. The possibility of detecting these oscillations is discussed, through the photodetection counting statistics of the displaced number states. We show that the displaced-number-state quantum features are relatively robust when dissipation of the field energy is included.

Variances and power spectra of the resonance fluorescence intensity induced by laser noise in two-level systems are studied theoretically. The effects of amplitude and phase noise fluctuations of a single-mode laser are investigated. Correlations of amplitude and phase fluctuations, as is relevant for excitation with diode lasers, are shown to lead to pronounced asymmetries in variance spectra.

A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ‘‘vacuum’’ Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).

We present three examples of pressure-induced extra resonances that can be observed in nonlinear spectroscopy: fluorescence of a ‘‘three-level atom’’ driven by two laser fields, two-photon ionization of a ‘‘three-level atom’’ (plus continuum) driven by two laser fields, and excitation of a ‘‘four-level atom’’ driven by four laser fields. We show that all these extra resonances can be interpreted in terms of quantum pathways, each pathway involving a collisionally aided excitation. We also demonstrate that the two first extra resonances can be obtained with incoherent fields, while relatively coherent fields are required in the last example.

A Stokes shifted superbroadening stimulated scattering has been studied in a ${\mathrm{CS}}_2$ liquid-core hollow fiber system with a long gain length (2.5 m) by using ≊10-ns laser pulses with a pump intensity range of (${10}^6$–5×${10}^8$ W/${\mathrm{cm}}^2$). The salient features of this stimulated scattering are that the spectral broadening range is very large (≥700 ${\mathrm{cm}}^{\mathrm{-}1}$) and no detectable shift of the spectral maximum or periodical modulation structure is observed. In order to interpret our experimental results, various possible mechanisms and processes are discussed. A model based on stimulated Kerr scattering of anisotropic molecules in liquid is suggested to explain the observation. This model assumes a single-step reorientation of anisotropic molecules induced by an intense optical field.

Two manifestations of the quantum nature of coherent, resonant light scattering from atoms are photon antibunching and sub-Poissonian statistics. The existence of both effects has been demonstrated previously; in the present work, using individual barium atoms, measurements of the dependence of the latter effect on the frequency of the radiation field are presented. The distinction between the two phenomena is demonstrated by data that exhibit antibunching, yet have a photon counting distribution with variance equal to the Poisson value.

The codimension-two bifurcation set of single-mode optical bistable systems is investigated. The entire set is classified into three classes, a cusp bifurcation set, a degenerate Hopf bifurcation set, and the intersection of a Hopf bifurcation and a saddle-node bifurcation. Based on the specification of degenerate Hopf bifurcation, super- and subcritical Hopf bifurcations can be identified. It is found that, in the subcritical Hopf bifurcation region, an attractor of time-dependent motion may coexist with the stable stationary solution when the cavity is filled by a passive medium. Moreover, the coexistence of three attractors is observed for certain parameter combinations.

A method developed in terms of the su(2) Lie algebra for the treatment of many-level atoms is now modified to treat the system of many two-level atoms interacting with a cavity field. Special attention is given to field squeezing up to fourth order. The effects of the number of atoms and detuning on the squeezing are investigated numerically for various initial-field intensities. It is found that the atomic cooperation effect on the squeezing is closely related to the initial-field excitation. When the initial excitation is strong, the cooperation enhances the squeezing, while in the case of weak excitation, it weakens the squeezing. The possibility of constructing many-atom micromasers is suggested.

We present a theory of time-resolved emission spectroscopy in the femtosecond region. It is shown that a femtosecond time-resolved emission spectrum consists of the contributions from the population and coherence of the system. Theoretical expressions for describing femtosecond time-resolved emission molecular spectra based on the use of the adiabatic approximation are derived. Detailed numerical calculations have been carried out to show the effect of the time evolution of the population and coherence on the time-resolved emission spectra.

We present here a fully quantum-mechanical treatment of the laser using a three-level atom model. The phase-space method employed is identical to that in a previous publication of ours [Phys. Rev. A 38, 4073 (1988)] and again results in a Fokker-Planck description of the laser without any approximations. The third level only provides extra deterministic terms and, if it is regarded as a further reservoir to the lasing levels, then the resultant stochastic equations have much improved stability. These equations are suitable for extensive theoretical analysis of both the laser and optical bistability, although in this paper we have concentrated on the adiabatically eliminated limit and calculated the leading noise terms in various regimes. However, we do use the technique of direct numerical simulation to solve exactly the full system of laser equations. The results display clearly many of the known laser characteristics.

The dynamical behavior of an atom interacting with a coherent field and a chaotic field is studied. Monte Carlo methods are used to integrate the equations describing the dipole moment, population inversion, and two-time correlation functions. The chaotic field can have a finite correlation time. Numerical results for a wide range of the parameters are given. The results depend sensitively on the ratio of the Rabi frequency and the bandwidth of the chaotic field. It is shown how an intense coherent field can suppress the effects of incoherence. The intensity of fluorescence as a function of detuning exhibits narrowing as the strength of the coherent field increases.

We study in detail the influence of pumping statistics on the laser dynamics. We apply the technique of quantum Langevin operators and generalize the corresponding noise operators to incorporate the statistical properties of the pump mechanism. These equations are then used to derive expressions for the phase and intensity fluctuations of lasers with various pump statistics. We find that a reduction of pump noise can lead to a significant squeezing of the photon number noise below the shot-noise limit. This is in complete agreement with our previous analysis, which used a density-operator approach.

We employ recently published data on the dc Kerr effect and electric-field-induced second-harmonic generation in ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, and Ar gases to calculate the nonlinear-optical indices governing self-focusing, self-induced changes in the state of polarization, and third-harmonic generation, over a wide range of wavelengths in these gases. We construct a new, one-parameter, dispersion formula that not only fits all existing data on the above gases, but also fits recent quantum calculations of each tensor component of the third-order optical susceptibility of helium, over a wide range of frequency arguments. We compare the difference between the predictions of this formula and the predictions of a previously used formula based only on linear refractive-index dispersion. The difference is negligible at 1053 nm but becomes significant at blue or shorter wavelengths (<350 nm), where it indicates the uncertainty in our dispersion calculations. We find the coefficient for self-induced polarization changes in one atmosphere of air to be $c_{1221}$(-ω,ω,ω,-ω) =(24±2)×${10}^{\mathrm{-}19}$ esu, at 1053 nm and 20 °C. This is consistent with one of two reported measurements of this coefficient.

We describe the nonlinear dynamics of intracavity doubled multimode lasers. Baer [J. Opt. Soc. Am. B 3, 1175 (1986)] observed irregular amplitude fluctuations in a multimode yttrium aluminum garnet laser with an intracavity potassium titanyl phosphate frequency-doubling crystal; we identify type-III intermittency as the route to chaos. Subsequently, Oka and Kubota [Opt. Lett. 13, 805 (1988)] demonstrated the stabilization of such a laser by the introduction of a quarter wave plate into the cavity. A generalized model of rate equations for this case is introduced. It is shown that a second route to chaos through a Hopf bifurcation, synchronization, and period-doubling sequence occurs on rotation of the quarter wave plate within the cavity. In addition, we predict that the laser output may be stable for particular lengths of the doubling crystal.

It has been observed that fairly accurate estimates for two-photon bound-bound amplitudes in hydrogen can be obtained from a simple partial summation restricted to the discrete spectrum contribution, provided one uses the E⋅r form of the interaction Hamiltonian. We show that this conclusion does not hold when considering higher-order multiphoton processes. In fact, the corresponding multiple sums can be shown to be divergent and, consequently, no reliable estimates can be obtained from such an approximation. Using the (1/c)A⋅p form of the interaction does not lead to reliable estimates either. Those conclusions are based on a comparison with exact results for the second- and fourth-order contributions to the ac Stark shift of the ground state, computed with the help of a Sturmian basis.

Recent pump-probe experiments in the femtosecond time scale exhibit features that cannot be understood in terms of conventional frequency-dependent susceptibilities either in linear or nonlinear regimes. Here duration of the pulses becomes comparable to typical vibrational periods and the linear-response theory cannot be used because the system never reaches a steady-state regime. To this end, we develop an approach to handle these problems. It requires the introduction of a time- and frequency-dependent susceptibility based on the mode-mode frequency conversion. Then, we focus on second-order processes with a particular application to second-harmonic generation.

By intermittently and periodically pumping N atoms and observing time-scale separation for pumping, emission, and photon leakage from the cavity a laser with up to 50%, sub-Poissonian photon statistics can be realized. We present a stroboscopic period-to-period description of such a laser and clarify how pumping and spontaneous emission can be eliminated and cavity damping be minimized as sources of photon noise.

The time-dependent fluorescence spectrum from a strongly driven two-level atom damped by a broadband-squeezed vacuum is obtained analytically using the counting-rate definition of Eberly and Wodkiewicz [J. Opt. Soc. Am. 67, 1252 (1977)] and employing the high-field approximation. The spectrum shows considerable modifications compared to the corresponding time-dependent spectrum in a normal vacuum. It is now dependent on the relative phase between the squeezed vacuum field and the coherent driving field. In particular, the time development of the central peak of the Mollow triplet (which is known to show a phase-dependent linewidth in the steady state) is discussed. The effects of detuning on the spectrum are also presented.

This paper gives a detailed analysis of collective free-electron lasers with a linearly polarized electromagnetic-wave wiggler and axial guide field, where the pump wave (wiggler) is either a fast wave propagating counter to the electron beam or a slow wave propagating parallel to the electron beam. The linear dispersion and nonlinear growth are derived in the laboratory frame for the process of three-wave interaction (the scattered wave, pump wave, and space-charge wave). It is found that the critical condition of the nonlinear growth of the scattered wave for the former wiggler is ${\omega }_c$<$k_p$$v_{z0}$+${\omega }_p$, whereas for the latter wiggler the critical condition is ${\omega }_c$>‖$k_p$$v_{z0}$-${\omega }_p$‖, where ${\omega }_c$ and $v_{z0}$ are the electron’s initial cyclotron frequency and axial velocity, and ${\omega }_p$ and $k_p$ are the frequency and wave number of the pump, respectively. The cases of ${\omega }_c$≊$k_p$$v_{z0}$+${\omega }_p$ and ${\omega }_c$>$k_p$$v_{z0}$+${\omega }_p$ are discussed for a counterpropagating wave pump.

An exact solution of the time-dependent Schrödinger equation is obtained for a simple model with only two quantum states. The calculated transition probability involves only exponential and hyperbolic functions.