The double photoionization of molecular hydrogen is theoretically investigated in the 40–100-eV photon energy range. The calculation is ab initio and rests first on the Born-Oppenheimer separation. The exact nuclear wave functions have been used for both (bound) initial and (dissociative) final two-proton states and the Franck-Condon approximation is not invoked. The electronic part of the initial ground state of ${\mathrm{H}}_2$ is highly correlated while the final one is simply a symmetrized product of uncorrelated Coulomb wave functions. Within this framework, the total cross sections obtained in the dipole-velocity formulation agree well with very recent experimental results. In addition, the method is able to provide the kinetic-energy distributions of the fragments (electrons and protons) as functions of the photon energy. The energy distributions of the ejected protons, produced by 60–100-eV impacting photons, are similar in shape to those resulting from electron or proton impact on ${\mathrm{H}}_2$. In contrast, it is found that the most probable two-proton kinetic energy is significantly lowered in the threshold region. On the other hand, the differential electron spectrum gives some insights into the sharing of energy between the s, p, and d ejected electrons. Within the δ approximation, which is shown to be very accurate over the whole photon energy range, the threshold law for the double photoionization of diatomic molecules is derived. It is found that the cross section can be represented, up to 10 eV above threshold, as the convolution of the density probability in the initial vibrational ground state with a series of linear thresholds, similar to those derived in the Wannier-Rau-Peterkop theory for atoms.

We present a proof that nonrelativistic Coulomb dipole matrix elements are monotonically decreasing functions of transition energy, for transitions from any given bound state to states of greater energy, including bounded and unbounded negative-energy states and positive-energy continuum states. (By an unbounded negative-energy state we mean a solution of the Schrödinger equation, regular at the origin, which is unbounded and therefore is not an eigenstate.) The proof applies both to reduced matrix elements (normalization constants factored out so that for small distances wave functions behave as ${\mathrm{Cr}}^2$ with C≃1) and to full analytic matrix elements (including bound-state normalizations and their analytic continuations). It also applies to the full bound-free matrix element (including the complete continuum normalization) and to the bound-free cross section. The method of proof is related to our recent demonstration that there are no zeros in nonrelativistic Coulomb dipole matrix elements. Our result follows from a new recursion relation, simply related to the Infeld-Hull recursion relation utilized in our previous demonstration.

Observations are reported of complete sequences of N-photon resonant microwave transitions, in potassium, from the (n+2)s state to the lowest energy state of the linear Stark manifold of principal quantum number n. The number N of photons absorbed ranges from 1 to as high as 30, and n is in the range from 16 to 19. A sequence is observed by scanning the static electric field, starting at the field at which the levels undergo an avoided crossing, until zero field is reached. The maximum number of photons absorbed is observed to be proportional to the microwave field amplitude, with an offset of two photons at zero field. Dynamic Stark shifts of the levels are observed to be proportional to the microwave power. The n dependence and absolute size of the shift are in agreement with Floquet calculations. The relation between the N-photon resonances and microwave ionization is discussed. In particular, resonances in microwave ionization spectra are seen to be due to dynamic-Stark-shifted multiphoton transitions.

We formulate a semiclassical model for the collective response of an atom to a strong laser pulse and use it to study the behavior of the valence shell of xenon. We find that, in a monochromatic wave, a fraction of the shell ionizes rapidly and the rest is driven coherently. The energy distributions of the emitted electrons show reasonable agreement with experimental distributions that are generated via single-particle ionization, indicating that the spectra are independent of the ionization dynamics. The remaining part of the shell is driven coherently and expands with time, thus exerting minimal effect on the core. We also analyze the effects of pulse shape, pulse duration, and the ponderomotive potential. In particular, we present results for femtosecond pulses.

By including rotations in a previously developed generic vibrational model of ir multiple-photon excitation (MPE) [Phys. Rev. Lett. 51, 1259 (1983) and Phys. Rev. A 34, 1211 (1986)] it is found that the combination of chaotic dynamics and rotational averaging leads to fluence-dependent absorption and removes the sensitivity of the results to model-dependent parameters. Therefore, a complete propagation calculation through a molecular medium of this type would show a Beer’s law absorption of photons consistent with the vast majority of MPE experiments performed to date, a result which previously was attributed to rate-equation dynamics in the molecular quasicontinuum. In addition, the classical rotation-vibration dynamics observed in this model correlate very well with one’s quantum intuition based on a molecule’s P-, Q-, and R-branch structure and on the red shift of the vibrational absorption feature with excitation.

We consider the dynamics of the suspended mirror of a pendular Fabry-Pérot cavity, taking into account the delays due to the finiteness of the velocity of light. We obtain an approximate equation for the asymptotic motion which allows a simple analysis of the behavior of the mirror and in particular of the instabilities that cavities with a large enough finesse or length can develop. The results, which are of relevance in cases of actual interest, can in principle be tested using presently available cavities. A pendular Fabry-Pérot cavity then appears as a perhaps ideal example of a delay system where theory, numerical, and laboratory experiments can be compared.

We use the harmonic-oscillator realization of the SU(1,1) group to study the time evolution of a quantum state undergoing an anharmonic interaction. The result is then applied to the propagation of an initially Gaussian beam through an optical fiber with a quartic aberration.

A study is presented for the time-dependent resonance-fluorescence spectrum of two-level atoms irradiated by hyperbolic-secant pulsed lasers, allowing for an arbitrary spontaneous-emission rate from the excited level to the ground level. Novel features of the temporally transient spectrum have been observed. The spectrum is dominated by a central peak which oscillates in time and is accompanied by multiple side peaks. Asymptotically (i.e., after the pulse has passed) the side peaks disappear, leaving a tail at the line center which displays a Lorentzian shape of width equal to the sum of the spontaneous-emission rate and the width of the spectrometer considered and of magnitude proportional to the instantaneous intensity of the pulse. The exact behavior of the spectrum is dictated by the area of the engaged pulse and by how the atom is prepared initially. In particular, it is found that the spectrum can be asymmetric even when the laser is tuned to exact resonance if the atoms are initially prepared in a certain class of proper coherent states, irrespective of how the field amplitude may vary in time. An analysis of the spectral symmetry without resorting to any explicit evaluation of the spectrum itself is also presented. Furthermore, the associated optical Bloch equations are solved analytically in terms of hypergeometric functions in a similar manner to that done previously for the undamped two-level Schrödinger equation. Specific numerical results are presented for pulses of area equal to π, 2π, 3π, 4π, and 5π for both symmetric and asymmetric cases.

We present a detailed derivation of a new, rotationally invariant formalism for the theory of stimulated Raman scattering. The formalism is applied to Raman transitions of well-defined rotational symmetry, e.g., rotational Raman (S) transitions, yielding the explicit dependence of gain on light polarization, phase mismatch, and frequency offset. For a linearly polarized laser, the Stokes fields parallel and perpendicular to the laser field are decoupled. Far from Stokes–anti-Stokes phase matching, their gain coefficients are in the ratio of 4:3; at phase matching, both are suppressed and have zero exponential gain. For a circularly polarized laser, the circularly polarized Stokes fields circulating in the same and opposite senses as the laser field are decoupled. The gain of the opposite-sense field, which is decoupled from the anti-Stokes field, is independent of phase mismatch. Far from phase matching, the gain of the same-sense Stokes field is (1/6 that of the opposite-sense field; at phase matching, the same-sense field has zero exponential gain. An unpolarized laser is shown to have the lowest Raman gain; far from phase matching, its Stokes fields decouple into two incoherent, oppositely circularly polarized fields, but at phase matching all Stokes polarizations have zero exponential gain. The gradual transition away from phase matching is also treated explicitly, and it is shown that when the gain is suppressed the maximum Stokes growth occurs when the Stokes-laser beat is a fraction of a Raman linewidth off resonance.

The spontaneous electromagnetic decay of a two-level atom coupled to a narrow cavity resonance is investigated rigorously in terms of the (Hermitian) modes of the ‘‘universe’’ rather than the (dissipative) quasimodes of the cavity. Special attention is paid to the strong-coupling regime (atomic linewidth Γ≳ cavity resonance width γ), in which there are significant corrections to the golden rule. In particular, spontaneous decay is most rapid for intermediate values of the quality factor Q of the cavity resonance. The photon line shape, the effect of several cavity resonances, and the competition of several transitions are also investigated. The additivity of partial rates does not hold, and in some circumstances, the addition of an extra decay channel may reduce the total decay rate. These results are relevant to optical processes observed in dielectric microspheres, and also to usual laser cavities.

The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell’s inequalities in interference experiments is investigated.

Harmonic-generation processes at high laser intensity are strongly affected by resonant multiphoton ionization. In this paper coexistence of these phenomena at low pressure and high intensity is taken into account with use of a mean-field theory. New consequences of this model are derived, especially for resonances strongly damped by ionization. Available experimental data on mercury agree qualitatively with this model. A second approach, called the quasistatic approximation, is used to get analytical solutions for mean-field equations, in good agreement with numerical results. Furthermore, possible applications of the quasistatic approximation to the study of harmonic generation at both high pressure and high laser intensity are mentioned.

We use the path-integral technique to solve the quantum-mechanical problem of interaction of a single two-level atom with a single-mode quantized field without the rotating-wave approximation (RWA). We calculate the full spin-Bose propagator in the form of a matrix as an expansion around a path corresponding to the RWA. The effect of energy-nonconserving terms on the atomic population inversion is studied, and we show that even under the conditions in which the RWA is considered to be valid there is a significant effect on the atomic inversion due to these terms.

The effect of cooperative atomic interactions on laser linewidth is investigated by suitably generalizing the Scully-Lamb theory of the laser. In particular, the single- and two-atom interactions with the field are included. It is shown that, under certain conditions, the cooperative interactions tend to reduce the natural linewidth.

The dynamics of a one-dimensional hard-core fluid is examined subsequent to a sudden increase in the size of its bounding container; attention is focused upon the standard hydrodynamical variables: density, current density, local temperature, and local pressure. The rather complicated equilibrating density pattern is found explicitly, and all other relevant quantities expressed in terms of this pattern. In particular, the local bulk diffusion constant retains an anomalous ideal-gas form, whereas the local pressure decomposes into a local-equilibrium part and a specific wall-reflection contribution.

In this paper a nonequilibrium description of the dynamics of electrons in a background gas under the influence of space-time varying fields is presented. It is obtained by interpolating between a kinetic and a moment formulation. To achieve this, the moment equations have been ordered by using characteristic scales. The ordering is then used to derive, from the kinetic equation, a new equation valid only in the scale of the moment equations. This equation and a finite set of moment equations form a closed system which can be used to describe the dynamics of electrons under various nonequilibrium conditions. Comparisons are presented between results obtained with this formulation and those obtained from a kinetic model.

A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.

We reformulate the theory of the acceleration of charged particles in the recently proposed plasma-wake-field acceleration scheme. Our treatment makes manifest the transient effects. To illustrate, we consider a point-charge driving beam traversing a semi-infinite plasma. We show that it takes a few plasma wavelengths for transient effects to dissipate and give the wake-field solutions currently discussed in the literature. Thus our treatment provides needed justification for the existing theoretical discussions since they neglect transient effects.

A method for extending finite-range Monte Carlo simulation data obtained for the classical one-component plasma (OCP) at Γ=100 is presented. It enforces continuity at the simulation range in the Ornstein-Zernike direct correlation function by adding a single Yukawa correction term to an assumed long-range mean-spherical form. In addition, 1/N corrections to the Monte Carlo data are accounted for in order to obtain a satisfactory value for the OCP isothermal compressibility, as compared to the value directly obtained from the Monte Carlo equation of state. The bridge function E(r) is then extracted, and it is found to follow the hard-sphere bridge function at short range, in agreement with the universality hypothesis of Rosenfeld and Ashcroft. However, at long range there are small but nonuniversal corrections whose form is also discussed.

The spatial and temporal bifurcations to chaos and dimensionality of strange attractors in Rayleigh-Benard convection are studied in an extended rectangular container with aspect ratios 15.0 and 1.0. With increasing Rayleigh number, oscillatory states, quasiperiodic states, and chaotic states are observed where the amplitudes of various modes strongly depend on the spatial position. The chaotic states just above the onset are characterized by low-dimensional attractors and the correlation dimension of the attractor is investigated as a function of Rayleigh number.