The usual approach to calculating multiphoton collision and half-collision processes uses the interaction picture and introduces a classical time-dependent field into the Hamiltonian for the scattered particles, which is further simplified using the Floquet ansatz. In particular, the laser-induced decay of an initial bound state is derived from a half-collision loquet ansatz that utilizes a complex quasienergy, whose imaginary part is identified with the laser-induced decay constant of the bound state. This interpretation presupposes a pure exponential decay of the initial-state population and yields a Lorentzian distribution of product-state energies in the infinite-depletion limit. Here we demonstrate how a full-collision Floquet ansatz can be derived from a fully quantal wave packet constructed to represent scattering in the presence of a coherent state of the laser field. The wave packet utilizes the set of the time-independent close-coupled wave functions for scattering in the field generated by quantized radiation number states. The resultant Floquet scattering states are energy normalized and stationary, and the quasienergy is real. We show how to use these states to construct a coherent-state wave packet that describes the decay of an arbitrarily prepared bound state, and yields a half-collision Floquet ansatz without any commitment to a complex quasienergy. The product energy and quantum-state distribution in the infinite-depletion limit are obtained without approximation to exponential decay. Further we show how the Fourier transform of the infinite-depletion line shape gives the temporal behavior of the initial bound-state population, often with distinctly nonexponential behavior. Such results are demonstrated for the above-threshold ionization of H, and the above-threshold dissociation of ${\mathrm{H}}_2^{+}$. In the following paper [R. W. Heather and F. H. Mies, Phys. Rev. 44, XXXX (1991)], excellent agreement is found between the present fully quantal wave-packet approach, utilizing the time-independent scattering wave functions, and the comparable solutions to the time-dependent Schrödinger equation for a corresponding classical time-dependent laser field.

The decay of the initial bound-state population and the fragment kinetic-energy distribution produced by the intense-field photodissociation of ${\mathrm{H}}_2^{+}$ are calculated using both a time-dependent and a time-independent method. The time-dependent method calculates the time evolution of the wave function describing ${\mathrm{H}}_2^{+}$ interacting with a classical time-dependent laser field by repeated application of a short-time propagator. The time-independent method constructs a wave packet using the energy eigenstates of the total molecule-plus-field Hamiltonian with the field expressed as a superposition of quantized photon number states. Specifically, the wave packet represents an initial bound-state wave function of the field-free molecule subjected to a coherent photon state that simulates the classical radiation field at t=0. The subsequent decay of this nonstationary state can be viewed as a laser-induced predissociation of field-dressed bound states into field-dressed continuum states with various numbers of photons absorbed from the field. For very rapid dissociation, the decays of the initial bound-state population calculated by both methods are in good agreement if a square pulse shape is used and the initial phase of the time-dependent interaction is averaged over. The fragment kinetic-energy distributions calculated by the two methods are in good agreement if they are compared at times when there is unit probability for dissociation. For slow to moderately rapid dissociation, averaging over the initial phase of the field is unnecessary because there is no rapid decay component. However, this also implies that the wave function must be propagated over many time steps before complete dissociation is achieved. To avoid this, we describe a procedure for fitting a short-time line-shape function, which represents incomplete dissociation of the initial state, to the nondepletion-limit fragment kinetic-energy distribution. A parametric fit to the calculated distributions allows us to extract very accurate estimates of decay rates, ac Stark shifts, and branching ratios.

This paper analyzes a four-wave sum-difference-frequency generation scheme to convert coherent soft-x-ray radiation to shorter wavelengths, using a plasma medium. The governing equations are reviewed, and scaling laws are explored to show how the scheme would scale in the extreme ultraviolet and soft-x-ray regimes. Susceptibilities and conversion rates are evaluated numerically in the case of conversion from approximately 66 to 130 eV in a Na-like K plasma. Finally, phase-matching considerations are discussed.

We have observed and developed a theory for polarization-resolved two-beam coupling via nondegenerate two-wave mixing in water-glycerol suspensions of shaped polytetraflouroroethylene microparticles. Experiments detected energy transfer driven by two different classes of moving optical index gratings: density and orientational. These gratings arise from and reflect translation of the microparticle’s center of mass and rotation of its symmetry axis by laser-induced electrostrictive forces and torques. Each grating features its own response time, frequency response, and polarization characteristics. The steady-state and transient dynamics of moving shaped microparticle optical index gratings were studied by measuring the energy diffracted by these two gratings from one beam to the other. The dependence of the two-wave-mixing gain coefficient on beam polarization, laser frequency difference, pump intensity, and volume fraction was measured and found to be in accord with theory. Furthermore, the evolution to steady state was examined, with theory and experiment in good agreement. Finally, beam combination was also achieved using degenerate laser beams and moving the suspension relative to the laser interference pattern.

We show that a laser heterodyne technique permits one to measure in detail the phase and amplitude dynamics of a laser. For the regularly and chaotically pulsing ${\mathrm{NH}}_3$ laser, we find qualitative agreement with the dynamics of the complex Lorenz equations.

When two pump waves propagate through a single-mode optical fiber, sidebands are generated due to third-order (${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$) nonlinear interactions in the fiber. The transfer of energy from the pumps to the sidebands can be periodic or chaotic, depending on the detuning and power of the input waves. We experimentally examine the statistical distributions of sideband power at the output of the fiber for input power and detuning regimes that correspond to periodic and chaotic energy exchange. Fluctuations of the input pump waves are accounted for in the comparison of experimental measurements with predictions of the theoretical model. Good agreement is obtained between experimental observations and numerical computations of the statistical distributions of sideband power. Limitations of the theoretical model and the experimental procedure for testing its predictions are discussed.

Light can induce thermodynamic and hydrodynamic fluxes in a gas, which reflect the light-induced modifications of the velocity distribution of the gas particles. The common condition for these effects to occur is the combination of velocity-selective radiative excitation with state-dependent gas-kinetic cross sections. It has recently been suggested that gas-kinetic effects of light in a molecular gas can also arise without state-dependent total cross sections, due to rotational inelastic collisions. Standard gas-kinetic techniques are not directly applicable in this case, since the rapid processes do not drive the system to a steady state. We give a generalization of the standard formalism so as to encompass this case. We apply this generalized formalism in the simplest model case of three-state particles.

A microscopic model for the origin of the source correlations responsible for Wolf shifts is proposed. To illustrate the main features of the phenomenon of these correlation-induced frequency shifts, a simple atomic system consisting of a pair of identical two-level atoms interacting with each other via the dipole-dipole interaction is considered. Effects of the finite temperature of the source are also included. For this microscopic model, the far-zone spectrum for two different experimental situations is calculated. The red and blue frequency shifts of the spectrum can be understood in terms of the dipole-dipole interaction. The magnitude of the shifts depends on the strength of the dipole-dipole interaction. The dependence of the frequency shifts on the temperature of the radiating source is also given.

We report an experiment on the observation of Hanle resonances in weakly sinusoidally amplitude modulated, nonsaturating, phase-diffusing optical fields. The ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ to ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ transition (J=0 to 1) in an atomic beam of ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ was probed with a frequency stabilized dye laser, whose bandwidth and band shape were precisely controlled with an extra-cavity noise modulation system. Phase-sensitive detection of the Hanle fluorescence signal at the amplitude modulation frequency revealed resonances in the in-phase and in-quadrature parts, whose position, shape, and strength were sensitive to the laser bandwidth. These resonances, which were Lorentzian or dispersion shaped or a combination of the two, occurred when the Zeeman splitting (ΔE) of the excited ${\mathit{m}}_{\mathit{j}}$=±1 sublevels equaled the modulation frequency (Ω) for monochromatic light, and at a ΔE of Ω/2 for broadband light. The results are in good agreement with the theoretical predictions of Saxena and Agarwal [Phys. Rev. A 25, 2123 (1982)].

We use the field-strength eigenstates, that is, the quadrature eigenstates rotated by an angle ccphi, to define a phase distribution of a single mode of the radiation field. A measurement procedure lies at the heart of this operational phase distribution: A balanced homodyne-detection scheme measures, in principle, the field-strength probability curve in its dependence on ccphi. The probability of finding a zero electric field plotted versus ccphi constitutes the proposed distribution. For a wide class of quantum states, this curve is in good agreement with the abstract phase probability curve obtained from phase states, but it is free of the familiar problems accompanying the notion of a Hermitian phase operator. The phase distribution of a quantum state has been achieved without using phase states; this can be summarized as ‘‘phase without phase.’’

We study the statistical and phase properties of the output states of a Mach-Zehnder interferometer with a nonlinear Kerr medium in one of its arms. The combination of nonlinearity and displacement produced by the interferometer generates output states (displaced Kerr states) that, unlike those derived from a Kerr medium alone (Kerr states), do not necessarily retain the photon statistics of the initially coherent field. As the parameter characterizing the nonlinear medium is varied, the statistics of the output field vary from sub-Poissonian to super-Poissonian. The photon-number distributions of these states are rationalized by examining their quasiprobability distributions, which vary from banana-shaped for sub-Poissonian statistics to complicated interference structures for highly super-Poissonian statistics. The number-phase properties of the Kerr and displaced Kerr states are studied for the case of small photon numbers (relevant to cavity quantum electrodynamics) using a methodology based on the Pegg-Barnett formalism. In particular, we determine the range of parameters for which the states are minimum-uncertainty states and whether they are squeezed with respect to photon number and phase, drawing a distinction between a sub-Poissonian nature and number squeezing. Finally, we find that sub-Poissonian statistics can coexist with quadrature squeezing for a range of parameters.

The correlations of the fluctuations of the electric field are studied for a simple model of the buildup from spontaneous-emission noise of the output of a single mode of a laser cavity. Results for when the laser cavity is detuned with respect to the center frequency of the gain medium are compared with the case in which the cavity is resonantly tuned. Resonantly tuned lasers display transient phase and amplitude correlations with a peak at the time that the evolving amplitude departs from the neighborhood of the origin in the complex plane of the amplitude where phase diffusion dominates. Deterministic frequency chirps during the switch-on of a detuned laser delay and significantly strengthen the transient correlation of phase and intensity fluctuations when the detuning is sufficiently large compared with the strength of the noise. In this case the peak in the correlations is related to the anomalous intensity fluctuations characteristic of transient switching.

Both the junction voltage fluctuations and the frequency fluctuations of a semiconductor laser are highly correlated with its intensity noise. We analyze three schemes where the correlation information is used to reduce the intensity noise. In conventional semiconductor lasers, starting with intensity noise at the standard quantum limit, ideally 3-dB amplitude squeezing is possible. The influence of nonideal factors such as parasitics for junction voltage feedforward and the linewidth floor for frequency noise feedforward are discussed. It is shown that under certain conditions the number-phase uncertainty can reach the ultimate limit set by Heisenberg’s uncertainty principle. These conditions are clarified, and examples are given for both conventional semiconductor lasers and microcavity lasers.

We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and ‖Δ${\mathit{k}}_{\mathit{r}}$L‖≫1, where Δ${\mathit{k}}_{\mathit{r}}$ is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when ‖Δ${\mathit{k}}_{\mathit{r}}$b‖≫1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.

The quantum correlation between photon number and junction-voltage fluctuations in a constant-current-driven semiconductor laser is theoretically predicted and experimentally demonstrated. An external electrical circuit has the two functions of pumping to compensate for cavity loss and measuring the photon number. The photon-number noise can be reduced to below the standard quantum limit and even to near that of a number state by referring to the junction-voltage measurements. Phase diffusion incorporates the inherent back action noise of such a measurement process. The number-phase uncertainty principle is conserved between the measurement-induced sub-Poissonian photon-number noise and the Schawlow-Townes phase-diffusion noise.

We present a detailed theory of dressed-state lasers, i.e., the lasers that operate due to the gain on an inverted transition between dressed states of a coupled atom-field system. We derive effective Hamiltonians that describe such lasers for the case of one- and two-photon resonances. We argue that, due to the presence of nearly resonant intermediate states, the use of gain media consisting of strongly driven two-level atoms provides an unorthodox yet promising means for achieving cw optical two-photon laser oscillation. We disscuss the stability properties of radiation generated by such media.

We present a detailed theory of the quantum-statistical properties of dressed-state lasers, i.e., lasers that operate due to the gain on an inverted transition between dressed states of a coupled atom-field system. With the help of quantum Langevin equations, we calculate squeezing spectra of such lasers. One-photon dressed-state lasers exhibit large squeezing due to antiresonant transitions between dressed states that lead to Bloch-Siegert-type shift effects. Two-photon dressed-state lasers may also generate squeezed light.

We present further developments in the theory of dressed-state lasers, i.e., lasers that operate on inverted transitions between the dressed states of a coupled atom-field system. We take into account the quantum character of the driving field, and consider the effect of its depletion. We derive effective Hamiltonians appropriate for the analysis of both one- and two-photon dressed-state lasers, and then discuss the stability and statistics of such lasers. We show that pump-depletion effects tend to reduce the degree of squeezing found in dressed-state-laser output while simultaneously introducing small squeezing effects into the depleted pump field.

We analyze the pairwise atomic states that are produced when a system of two atoms is irradiated by a squeezed vacuum field. Included in the analysis is the three-dimensional squeezed vacuum field propagated over a solid angle Ω, the interatomic separation ${\mathit{r}}_{12}$, the microscopic Fabry-Pérot cavity, and the role played by an imperfect coupling between the cavity modes and squeezed input modes. It is shown that the steady state of the system in free space is the pairwise atomic state when the atoms interact with a perfect squeezed dipole wave and the interatomic separations are much smaller than the resonant wavelength (Dicke model). With the interatomic separations comparable to the resonant wavelength or with an imperfect squeezed dipole wave, the system decays to a state that is not the pairwise atomic state. The effect of squeezed vacuum field on the system is now manifested by the selective population of the collective atomic states. For atoms inside a microscopic Fabry-Pérot cavity the pairwise atomic states are produced with an imperfect squeezed dipole wave. This can occur even for small solid angles Ω. However, this effect is sensitive to mode matching between internal and external fields. It is shown that with a Gaussian profile for the input squeezed modes the steady state is not the pairwise atomic states, but a significant reduction of the population in the symmetric state still can be observed.

In this paper, the use of squeezed light in laser cooling is investigated. We find that in a traveling-wave laser field, a two-level atom in a squeezed vacuum cannot be cooled to a lower temperature than in normal vacuum. For a two-level atom in a standing-wave laser field, if it is tuned from the resonant region, the conclusion is the same as in the traveling-wave case. However, near the resonant region, the atom in a standing-wave field can achieve a lower temperature than Doppler limit.