The exact adiabatic representation scheme of Nguyen-Dang [J. Chem. Phys. 90, 2657 (1989)] is applied to time evolution of the general laser-driven two- and three-level systems. It leads to exact formal results that do not assume a specific shape of the pulse and do not invoke the rotating-wave approximation (RWA). These results are a generalization of the corresponding RWA results because the former depend on an effective pulse area that varies with the detuning and involves a Rabi frequency modulated by a phase cphi(t). In addition, the exact adiabatic representation scheme is applied to N-level systems exhibiting various dynamic symmetries and, as in the previous cases, leads to results that do not invoke the RWA and depend on an effective pulse area. Time-reversal analysis on two- and three-level systems leads to quantization of the effective pulse area for time-symmetric pulses. This quantization leads to localized asymptotic population distributions.

We treat the shot noise of a light source modulated in power as a nonstationary random process. The spectrum of such modulated shot noise, although it is still white, is shown to contain correlations between different frequency components. In addition, the noise is not equally distributed in phase. These effects can deteriorate the shot-noise-limited sensitivity of modulated interferometers. Maximizing the signal-to-noise ratio (SNR) introduces constraints on both the modulation and demodulation waveforms. The sensitivities obtained with several commonly used modulation schemes are calculated, and new modulation strategies are proposed to realize good SNR. We apply the results to the case of laser interferometer gravitational wave detectors where it is essential to reach a shot-noise-limited sensitivity. By taking into account the additional noise contribution from the modulated shot noise, we reduce the 3-dB discrepancy between the measured sensitivity of the Garching prototype detector and the theoretical shot-noise limit to about 1.5 dB.

In this paper, we shall report the investigation of the non-Markovian effects of the dynamical process on optical absorption. It will be shown that in steady-state experiments the non-Markovian effects cannot be probed. The non-Markovian effects on the transient pump-probe experiment are treated, and a couple of typical memory functions have been used to obtain the transient band-shape functions. Finally, probe-pulse duration effects on the absorption are considered.

We calculate the third-order nonlinear absorption and dispersion (self-phase-modulation and cross-phase modulation) of a homogeneously broadened two-level molecular system with permanent dipole moments interacting with (1) an optical field of frequency ω, and (2) two optical fields of frequency ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$, i.e., the susceptibilities ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$(-ω;ω,-ω,ω) and ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$(-${\mathrm{\omega }}_1$;${\mathrm{\omega }}_1$,-${\mathrm{\omega }}_2$,${\mathrm{\omega }}_2$). Sharp features in the nonlinear absorption and dispersion appear whenever one- or two-photon resonance conditions are met. Only features corresponding to one-photon resonance arise if the difference between the permanent dipole moments of the levels, Δμ, vanishes. The ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$(-ω;ω,-ω,ω) spectrum has two features, one at frequency ${\mathrm{\omega }}_{\mathit{b}\mathit{a}}$ dominated by contributions proportional to ${\mathrm{\mu }}_{\mathit{a}\mathit{b}}^4$, where ${\mathrm{\mu }}_{\mathit{a}\mathit{b}}$ is the transition dipole moment of the two levels with transition frequency ${\mathrm{\omega }}_{\mathit{b}\mathit{a}}$, and the other at frequency ${\mathrm{\omega }}_{\mathit{b}\mathit{a}}$/2 dominated by contributions proportional to (Δμ${)}^2$${\mathrm{\mu }}_{\mathit{a}\mathit{b}}^2$. Sharp features in ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$(-${\mathrm{\omega }}_1$;${\mathrm{\omega }}_2$,-${\mathrm{\omega }}_2$,${\mathrm{\omega }}_1$) appear when ${\mathrm{\omega }}_2$ is near ${\mathrm{\omega }}_{\mathit{b}\mathit{a}}$,${\mathrm{\omega }}_1$,${\mathrm{\omega }}_1$+${\mathrm{\omega }}_{\mathit{b}\mathit{a}}$, and ‖${\mathrm{\omega }}_1$-${\mathrm{\omega }}_{\mathit{b}\mathit{a}}$‖.

We calculate the sum- and difference-frequency-generation (SFG and DFG) susceptibilities, ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$(-(${\mathrm{\omega }}_1$+${\mathrm{\omega }}_2$);${\mathrm{\omega }}_1$,${\mathrm{\omega }}_2$) and ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$(-(${\mathrm{\omega }}_1$-${\mathrm{\omega }}_2$);${\mathrm{\omega }}_1$,-${\mathrm{\omega }}_2$), of a homogeneously broadened two-level system with permanent dipole moments in the presence of pump fields at frequencies ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$. Both SFG and DFG susceptibilities have two maxima at frequencies corresponding to the one- and two-photon resonances of the two-level system. Knowledge of the magnitude of one of the maxima of either SFG or DFG is sufficient for determining the magnitude of the second peak of that process and also the two peaks of the other process. In both processes the peak at the two-photon resonance has dominant contributions arising from off-diagonal elements of the density matrix. The interference between these contributions is constructive in SFG and destructive in DFG. Therefore, SFG is more efficient at the two-photon resonance than DFG. An expression for the ratio between these peaks is obtained. The peak of the spectrum of each process corresponding to the one-photon resonance has two main contributions, one of which is diagonal and the other off diagonal. In DFG the interference between the two contributions is constructive and in SFG the interference is destructive. Hence, DFG is more efficient in the vicinity of the one-photon resonance. However, since the off-diagonal contributions to SFG and DFG on the one-photon resonance are equal in magnitude (and differ by a phase difference of ∼π) the efficiencies of the two processes are equal when the duration of the pulses is comparable to or shorter than ${\mathit{T}}_1$.

An ideal nondegenerate parametric oscillator is known to give perfect squeezing in the difference of the intensities of the signal and idler modes. In this paper, we look at a frequency down-conversion system comprising three-level atoms in a cavity. The squeezing in the intensity difference is calculated and found, in general, to be degraded by spontaneous emission. In the limit of large detunings, the system is found to behave as a nondegenerate parametric oscillator.

Semiclassical models for laser-dynamics studies typically incorporate a derivative approximation that reduces the second-order wave equation for the electric field to a first-order equation. It is shown here that this approximation and further frequency approximations are not necessary and may lead to significant errors for some high-gain laser systems. A more exact analysis also reveals a partial decoupling of the electric and magnetic fields that occurs with fast transient phenomena. These ideas are illustrated in terms of well-known dynamical effects.

The input-output theory, originally developed for a linear coupling between cavity mode a and a bath, is extended to a coupling that is quadratic in the cavity mode operator a. We then apply this to second-harmonic generation, in a cavity that is resonant at the fundamental frequency and has an active laser medium working at the fundamental frequency. We find intensity squeezing of 50% below the shot-noise level in the output light at the second-harmonic frequency, whether or not the cavity is resonant at the second-harmonic frequency. To compare the singly resonant cavity to the doubly resonant cavity, we develop in an appendix a general technique for extracting a single mode from a continuum.

We present the theory of a microscopic maser operating on a nondegenerate two-photon transition between two states of same parity. We start from a three-level Hamiltonian, and discuss both the one-photon resonant cascade and the two-photon regime, when the intermediate state is far off resonance. In the semiclassical limit, we derive rate equations for the field intensities and get the corresponding steady-state values. The vacuum is stable in the two-photon regime but becomes unstable for zero detuning (a clear signature of a one-photon process). Solutions displaying true two-photon operation (intermediate state unpopulated) even with zero detuning are displayed. Using the full quantum density-matrix approach, we derive a master equation for the field and discuss both operating regimes, showing that the spontaneous emission may turn the vacuum unstable in the two-photon case. In the off-resonance two-photon regime, there is a strong correlation between the fluctuations of the intensities of the two modes. We find a squeezing factor of 50% for the fluctuations in the difference of intensities.

We analyze the interaction and the competition of a set of transverse cavity modes, which belong to a frequency-degenerate family. The laser turns out to be able to realize several different stationary spatial patterns, which differ in the transverse configuration of the intensity or of the field and are met by varying the values of the control parameters. A striking feature that emerges in almost all steady-state patterns is the presence of dark points, in which both the real and the imaginary part of the electric field vanish and such that, if one covers a closed loop around one of these points, the field phase changes by a multiple of 2π, which corresponds to the topological charge of the point. We show in detail the analogy of these phase singularities to the vortex structures well known in such fields as, for example, hydrodynamics, superconductivity, and superfluidity. In our case, at steady state, these singularities are arranged in the form of regular crystals, nd the equiphase lines of the field exhibit a notable similarity to the field lines of the electrostatic field generated by a corresponding set of point charges. We analyze in detail the patterns that emerge in the cases 2p+l=2 and 2p+l=3, where p and l are the radial and angular modal indices, respectively, and we compare the results with the experimental observations obtained from a ${\mathrm{Na}}_2$ laser. The observed patterns agree in detail with those found by theory; in particular, they exhibit the predicted phase singularities in each pattern. The transitions from one pattern to another, that one observes under variation of the control parameters, basically agree with those predicted by theory.

We show that the stationary transverse patterns, formed by the interaction of the modes of a frequency-degenerate family, are selected by the laser according to a specific variational principle. We discuss the phenomenon of spatial multistability, which consists in the coexistence of two or more different configurations for the same values of the control parameters. We establish a general connection between laser physics and hydrodynamics, by reformulating the dynamical equations of the laser in the form of hydrodynamical equations for a compressible fluid, similar to the law of mass conservation and to the Bernoulli equation. This result provides a general framework for the discussion of the relations between optical and hydrodynamical turbulence.

The relationship, recently derived by Krieger, Li, and Iafrate [Phys. Lett. A 148, 470 (1990)], that ${\mathrm{\epsilon }}_{\mathit{m}\mathrm{\sigma }}$, the exchange-only Kohn-Sham (KS) single-particle energy eigenvalue corresponding to the highest occupied orbital, exactly equals ε${\mathrm{¯}}_{\mathit{m}\mathrm{\sigma }}^{\mathrm{HF}}$, the expectation value of the Hartree-Fock (HF) single-particle Hamiltonian averaged over this Kohn-Sham orbital, is employed to test the accuracy of the local-spin-density (LSD) exchange-only potential as well as the recent results of Wang et al. [Phys. Rev. A 41, 78 (1990)]. For the eleven atoms with closed subshells from He to Xe we find that in the LSD approximation ${\mathrm{\epsilon }}_{\mathit{m}\mathrm{\sigma }}$ is only approximately equal to 60% of ε¯ ${}_{\mathit{m}\mathrm{\sigma }}{}^{\mathrm{HF}}{}_{}{}^{}$, whereas the potential of Wang et al. yields ${\mathrm{\epsilon }}_{\mathit{m}\mathrm{\sigma }}$≃ε¯ ${}_{\mathit{m}\mathrm{\sigma }}{}^{\mathrm{HF}}{}_{}{}^{}$ to within 0.5%, providing further evidence that it closely approximates the exact KS exchange-only potential.

We present in this Brief Report the results of the distorted-wave Born approximation calculations of the electron-pair-creation cross section by 7.5-MeV photons on Sn and U. The results are compared with the cross sections obtained by using semiempirical formulas of Overbo [Phys. Lett. 71B, 412 (1977)] and of Maximon and Gimm [Natl. Bur. Stand. (U.S.). Internal Report No. 78-1456 (1978)] and the interpolated experimental data.

A variational study of the linear E-e Jahn-Teller effect, in which an electronic doublet interacts with a doubly degenerate vibration, has been performed using a simple correlated trial ground-state wave function–a correlated squeezed state. Our calculated variational ground-state energies are not only in good agreement with the exact diagonalization results, but they are also better than those from earlier analytical studies. This seems to suggest that the linear E-e Jahn-Teller system favors a strongly correlated squeezed ground state.

Recoil ions from very small impact-parameter collisions of 20–70-keV protons with xenon atoms were selected by viewing only those ejected at 50° and 70° from the beam direction. These ions were charge-state analyzed and the cross sections determined for the production of charge states up to 6+. In such collisions, multiple ionization accounts for 60–80 % of the ionizing collisions and 80–90 % of the total ionization.

A theoretical calculation, based on the first-order Born and boundary-corrected first-order Born approximation, is presented that includes simultaneous electron capture to the continuum of the projectile and target excitation or ionization processes in the ${\mathrm{He}}^{2+}$+He collision system. The results show that the cross sections are dominated by the continuum capture and that the influence of the accompanying target excitation or ionization is negligible. A comparison with the recent measurement of Kövér et al. [J. Phys. B 19, 1187 (1986)] shows better agreement than do those of the ordinary first-order Born approximation.

Numerous studies of one-dimensional scattering systems have failed to provide a satisfactory theory for tunneling times. Although there is some support for the idea that such interaction times should be complex, the physical meaning of complex interaction times has defied explanation. Here we demonstrate an explicit relation between several proposed complex times and a Hermitian sojourn-time operator. We have previously shown that this operator describes the effect of a perturbation of the scattering system on observable quantities.

Dynamic resonance in atom-diatomic molecule collisions has been relatively well studied compared to orbiting resonance. We discuss orbiting resonance on reactive scattering involving proton (charge) transfer. Resonance structure is predicted to exist at forward-scattering angles in both the state-to-state angular distribution and the Argand diagram for the proton-transfer collision system of He+${\mathrm{H}}_2^{+}$→${\mathrm{HeH}}^{+}$+H. The present study demonstrates the possibility of orbiting resonance particularly in proton (charge) -transfer reaction involving atom-diatomic molecule systems.

Using a general Green’s-function formalism for time-periodic Hamiltonians, it is shown that the above-threshold ionization spectra can be generated from time-independent calculations. Taking only the leading-order term of the corresponding Born-series expansion leads to a simple closed analytical expression that accounts for the essential features of the ionization spectrum and their connection to the time-independent quantities in question.

An approximation scheme is proposed to incorporate the influence of the Coulomb potential on the photoelectron in a nonperturbative treatment of multiphoton ionization rates. The method involves an approximation to an exact rate expression; when the latter is expanded in powers of the binding potential, the zeroth-order term is the commonly used Keldysh rate. The approach is applied to hydrogenlike atoms. Photoelectron angular distributions are calculated; these compare favorably with experimental measurements and with results of some other theoretical approaches.