The dynamics of coherences between sublevels of an electronic ground state is investigated under conditions of modulated optical pumping. It is shown that the modulation corresponds to an effective reduction of the apparent sublevel splitting, thereby allowing the excitation of coherences between atomic sublevels whose energy splitting would require very high laser intensities for dc excitation. In addition, the frequency and phase of the modulation introduce additional degrees of freedom that can be utilized for the design of new experiments. The theoretical evaluations are compared with experiments on the ground state of atomic sodium.

An alternative mechanism is demonstrated to bring about light-induced kinetic effects in gases without the necessity of a state-dependent collision cross section. This is achieved by velocity-selective optical excitation followed by collisional deexcitation in the subsequent collision. This process may be termed velocity-selective heating and gives rise to an enhanced transport coefficient for a selected velocity class. A mean-free-path description of this phenomenon is given for the case of momentum transport in a one-component gas. For nonuniform illumination, a shear stress is found to result, which gives rise to light-induced viscous flow. Experimentally this effect is demonstrated for ${\mathrm{CH}}_3$F, ${\mathrm{CD}}_3$F, ${\mathrm{CO}}_2$, and ${\mathrm{C}}_2$${\mathrm{H}}_4$, rovibrationally excited by a ${\mathrm{CO}}_2$ laser. It is shown that the magnitude of the effect is determined by the rotational energy transfer. It can be of either sign (velocity-selective heating or cooling), depending on R- or P-branch excitation, and it can easily overwhelm the contribution to light-induced viscous flow arising from a state-dependent collision cross section.

We report results of calculations on the Hanle effect in a J=0⇆J=1 atomic transition with three types of model fluctuating light fields: (a) the Brownian-motion phase-diffusion field, as produced in recent experiments by Arnett et al. [Phys. Rev. A 41, 2580 (1990)]; (b) Gaussian amplitude fluctuations; and (c) the chaotic field model, in which real and imaginary parts of the electric-field amplitude fluctuate. For the stochastic density-matrix equations, we use methods developed by Zoller and co-workers [e.g., Dixit, Zoller, and Lambropoulos, Phys. Rev. A 21, 1289 (1980)] employing the Fokker-Planck operator and leading to matrix continued-fraction expansions. The Hanle effect is of interest as a prototype for multisublevel atomic transitions. The width of the Hanle dip at zero magnetic field reflects the tendency of the light field to preserve the coherence between excited-state sublevels. For monochromatic light, the Hanle dip width increases as the square root of light intensity. When the laser bandwidth increases, power broadening of the coherence dip normally decreases. However, with the Brownian-motion phase-diffusion model, if the laser spectral profile is nearly Gaussian, broadening the laser up to several times the natural width of the atomic line does not diminish the Hanle dip width. With amplitude fluctuations, even in the limit of monochromatic light, power broadening of the Hanle dip with intensity is reduced by one-third to one-half depending on the particular model.

An expression for the emitted fluorescence radiation by an atom near a phase conjugator is derived from a plane-wave expansion of the electric-field operator and Heisenberg’s equation of motion for the annihilation operator. The result is compared to a solution that was found previously, based on the classical Maxwell equations. It is shown that both theories yield the same expression for the field in the radiation zone, in the limit of a transparent medium. This confirms the correctness of either approach to the problem of optical phase conjugation of atomic radiation.

Modulation instability in the region of the minimum group-velocity dispersion is analyzed by means of an extended nonlinear Schrödinger equation. It is shown that the critical modulation frequency saturates at a value determined by the fourth-order dispersion. Experimental results demonstrate the viability of generating a train of femtosecond pulses with repetition rates of a few terahertz in reasonable agreement with the theory.

High-power gyrotrons, including both cw and high-peak-power configurations, are increasingly designed to operate in high-mode-density regimes. It has been observed that operation is often single mode even for cavities with dense mode spectra, but the mode density does affect the gyrotron efficiency and the available operating modes. Multimode effects have been studied extensively for the quasioptical gyrotron, but there has been less progress on fully nonlinear formulations for conventional waveguide cavity gyrotrons that involve different transverse modes with irregularly spaced frequencies and unequal coupling impedances. A time-dependent, nonlinear, multimode theory of gyrotrons has been recently developed along with a computer code to carry out the numerical calculations. The code has been used to simulate the operation of a cw-relevant 140-GHz gyrotron experiment carried out at the Massachusetts Institute of Technology (MIT) by K. E. Kreischer et al. [Int. J. Electron. 57, 835 (1984)] and the 750-kV, 35-GHz intense-beam gyrotron experiment at the Naval Research Laboratory (NRL) by Gold et al. [Phys. Fluids 30, 2226 (1987)]. The MIT gyrotron involves competition between two transverse modes: the ${\mathrm{TE}}_{03}$ and ${\mathrm{TE}}_{23}$ modes. The NRL gyrotron involves competition between ${\mathrm{TE}}_{\mathit{m}2}$ modes and is an example of a three-mode interaction.

A quantum nondemolition measurement based on a three-mode interaction mediated by a second-order nonlinear susceptibility is discussed. All three modes are treated quantum mechanically. The signal field is taken as one of the three modes and the probe field is the combined field in the other two modes. If the probe system is initially in a number state, the interaction between the signal and probe is equivalent to that between a harmonic oscillator and an angular momentum system. Photon counting on the probe field realizes a quantum nondemolition measurement of the square of a quadrature phase amplitude of the signal, and thus provides a direct measurement of second-order squeezing.

We study the adiabatic evolution of the fundamental nonlinear Schrödinger soliton under a general integro-differential perturbation. This perturbation is shown to model a saturable bandwidth-limited amplification of an optical soliton with a nonresonant carrier wave. We use the soliton perturbation theory to calculate the evolution of the amplitude, frequency, group velocity, and phase of the pulse. The perturbative analytical steady-state solution is obtained and its stability is studied using the phase-plane formalism.

We present dynamical calculations for the quantum parametric oscillator using both number-state and coherent-state bases. The coherent-state methods use the positive-P representation, which has a nonclassical phase space—an essential requirement in obtaining an exact stochastic representation of this nonlinear problem. This also provides a way to directly simulate quantum tunneling between the two above-threshold stable states of the oscillator. The coherent-state methods provide both analytic results at large photon numbers, and numerical results for any photon number, while our number-state calculations are restricted to numerical results in the low-photon-number regime. The number-state and coherent-state methods give precise agreement within the accuracy of the numerical calculations. We also compare our results with methods based on a truncated Wigner representation equivalent to stochastic electrodynamics, and find that these are unable to correctly predict the tunneling rate given by the other methods. An interesting feature of the results is the much faster tunneling predicted by the exact quantum-theory methods compared with earlier semiclassical calculations using an approximate potential barrier. This is similar to the faster tunneling found when comparing quantum penetration of a barrier to classical thermal activation. The quantum parametric oscillator, which has an exact steady-state solution, therefore provides a useful and accessible system in which nonlinear quantum effects can be studied far from thermal equilibrium.

We analyze the effects of pump statistics on degenerate and nondegenerate two-photon lasers. We find that, although the steady-state mean photon numbers are not affected by pump statistics, there is an interesting reduction in the photon-number fluctuations, both in degenerate and nondegenerate two-photon lasers when the pump statistics is regular (p=1), as compared to the Poissonian case (p=0).

A general technique for modeling the behavior of an atom in the presence of a laser field is described. This involves the integration of the time-dependent Schrödinger equation in the Kramers-Henneberger frame. Results are presented for a one-dimensional calculation for a model hydrogen atom across a range of frequencies and intensities. The resultant peaks in the photoelectron spectra produced are shown to be partly the result of Stark-shifted bound-state multiphoton resonances. The spectra also contain rainbow features due to interference between the electron amplitude generated on the rising and falling edge of the pulse. These rainbow features are a purely time-dependent effect that can only be easily reproduced in time-dependent calculations.

In this paper we derive analytic expressions of the field on the mirror surfaces of a pendular and misaligned Fabry-Pérot resonator by taking into account longitudinal and transverse optical modes. In particular, we obtain analytic expressions of the spectral components of the power reflected by these devices for oscillating mirrors and modulated laser beams. In addition, we discuss the equations of motion of the mirror holders and analyze the onset of instabilities induced by the radiation pressure, by accounting for transverse optical modes and torsional oscillations of the multiple pendula to which the mirrors are suspended.

The simple intuitive picture of phase diffusion in a traveling wave is introduced to calculate the fundamental (Schawlow-Townes) limit to the laser linewidth. Contrary to the usual phase-diffusion model, our variety is not limited to the regime of low outcoupling; it predicts an enhancement of the linewidth for large outcoupling. It is demonstrated that the results of the traveling-wave phase-diffusion model are identical to those of the theory of nonorthogonal eigenmodes. Finally, the effects of saturation on the linewidth are estimated.

A complete treatment of a three-level ladder system interacting with a broadband squeezed vacuum field is presented. It is assumed that the ground state and the second excited state are decoupled in the electric-dipole approximation, and are tuned close to the sum frequency of the incident squeezed vacuum field. Using Zwanzig’s projection-operator techniques, we derive the master equation, assuming that the system interacts with a broadband squeezed vacuum field in one or more dimensions. It is shown that, in the first case, the squeezed vacuum introduces new decay constants and frequency-shift parameters. These have the same dependence on the atom-radiation coupling parameter as the ordinary vacuum decay rate and frequency shift, the only major difference being that they are multiplied by the squeezing parameters M and N. In more dimensions, the decay constants and frequency-shift parameters depend on the solid angle Ω over which the squeezing is propagated. For Ω=0 these correspond to the usual Einstein A coefficients and Lamb shifts of the atomic levels, while for large Ω they are similar to those for the one-dimensional squeezed vacuum.

Using the formalism developed earlier, we treat spontaneous emission from a three-level atom (ladder system) interacting with a broadband squeezed vacuum field. We obtain expressions for the transient and steady-state populations of the atomic levels with the conditions that the atom interacts with either a multimode perfect squeezed vacuum field, or a three-dimensional vacuum field in which the squeezed modes lie within a solid angle over which squeezing is propagated. The results are compared with those obtained for the atom interacting with a thermal field. We show that in the perfect case the first excited state is not populated when the squeezed vacuum field is in a minimum-uncertainty squeezed state. Moreover, the second excited state can have a steady-state population larger than 1/2. These features are completely absent when the atom interacts with the thermal field. In addition, for a low-intensity squeezed vacuum field the population in the second excited state exhibits a linear rather than quadratic dependence on the intensity of the squeezed vacuum field. In the three-dimensional case the presence of unsqueezed modes considerably reduces the effect of squeezing on spontaneous emission. However, a significant reduction in a population of the first excited state and a population larger than 1/2 in the second excited state can be achieved provided the squeezing is propagated over a large solid angle. We also discuss the effect of the two-photon detuning between the double carrier frequency of the squeezing and atomic transition frequency ${\mathrm{\omega }}_3$ on the steady-state atomic population.

We have calculated the high-order ac Stark effect for the ground state of atomic hydrogen by applying Rayleigh-Schrödinger perturbation theory to a complex-rotated Hamiltonian. We present results for the level-shift and multiphoton-ionization rate, which include effects of above-threshold ionization. Our results indicate that the field intensities at which high-order contributions become dominant can be as low as ${10}^{11}$ W/${\mathrm{cm}}^2$, much lower than is commonly expected. A systematic treatment of the frequency dependence of the perturbation coefficients in the vicinity of multiphoton resonances and ionization thresholds is provided by reference to the analytical properties of the Coulomb Green’s function.

Absolute quantitative comparisons between experiment and theory are reported for the steady-state characteristics of optical bistability with two-state atoms in ring and in standing-wave resonators. The case treated here is the absorptive one, with both atoms and cavity resonant with the field. The experiment is designed to realize as closely as possible a standard theoretical model of two-state atoms interacting with a single mode of the electromagnetic field in a resonator and is described in detail. A detailed explanation is also given of the extensions to the standard theory that are needed to account for unavoidable experimental limitations such as transit broadening and the nonideal nature of the resonator. The good agreement observed between experiment and theory provides a foundation for quantitative investigation of nonlinear dynamics and quantum phenomena in this nonequilibrium optical system.

We present a theoretical investigation of the potential for squeezing of a doubly resonant cavity that contains a laser medium as well as a ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ nonlinearity. If the lasing mode is coupled to its second harmonic, i.e., for a self-frequency-doubling laser, we find more than 60% squeezing in the up-converted mode outside the cavity. In the opposite case of a ‘‘self-down-converting laser,’’ i.e., when the lasing mode is coupled to its subharmonic, a perfectly squeezed vacuum in the down-converted mode develops into a less squeezed state with a nonvanishing coherent amplitude as the pump rate is increased. Our analysis extends beyond the first stable regime of the classical dynamics and compares results for different laser models.

We study the statistical properties of fluorescence from a coherently driven two-level atom placed in a broadband squeezed vacuum. The photon statistics are studied in terms of waiting time distribution or the delay function that describes the probability of emission of the very next photon following an emission of a photon initially. In an intense field limit, we analytically obtain the delay function for total emission and examine its phase-dependent behavior in a squeezed vacuum. We further analytically calculate the delay functions for the Mollow sidebands and use them to discuss the time correlation and successive emission of photons belonging to the left and right sidebands.

In the present paper, we discuss the photon statistics of nonclassical fields in a linear directional coupler. We study the photon distributions at the output ports of the coupler for number-state inputs, as well as for arbitrary-state inputs. In particular, we show that when a number state enters one port of the coupler and the vacuum enters the other port, an SU(2) coherent state is generated at the output ports. If the same number state enters both ports of the coupler, the probability of finding an odd number of photons at either of the output ports vanishes for a particular choice of the coupler length. We show that if a number state enters port 1 and a strong coherent field enters port 2, the coupler can serve as a generator of displaced number states (in fact, in this case the coupler behaves essentially as a homodyne detector). We show that the coupler is equivalent to an imperfect photon detector with efficiency governed by the coupler parameters. We study the effect of dissipative losses within the coupler as well as the effect of scattering coupling in the coupler. The latter leads to equalization of the energy in each guide. We show that in the presence of scattering coupling, the coupler behaves neither like an imperfect photon detector nor a homodyne detector.