We have developed a simple and systematic method to calculate analytic perturbation corrections of large order to the vibrational-rotational energies and matrix elements between vibrational-rotational states of diatomic molecules. The method, which is based on a powerful combination of perturbation theory and the hypervirial and Hellmann-Feynman theorems, is suitable to derive analytic expressions for both expectation values of observables and transition moments. As an illustrative example we discuss the isotopic effect on the vibrational-rotational energies. We show that, according to the Kratzer potential-energy function, perturbation theory renders a good approximation to the vibrational-rotational energies of diatomic molecules.

A method is proposed to evaluate the energy levels and wave functions of atomic hydrogen in a uniform electric field. A self-consistent criterion is used and the method proves to be sufficiently accurate and easy to implement even for high electric-field strengths. We present the results obtained for the ground-state level and compare them with those obtained by other authors.

We study the statistical properties of the distortions of irregular energy spectra when a perturbation parameter is varied; for example, the strength of an external field acting on the bounded quantum system. Three kinds of generalized Calogero-Moser (GCM) classical Hamiltonians are shown to rule the parametric motion of the energy levels in orthogonal, unitary, and symplectic systems. Using these GCM Hamiltonians, we construct a Newtonian theory of ensembles where irregular spectra are correlated with the properties of infinite gases of GCM particles. In this dynamical approach, the results of random matrix theory are recovered. Furthermore, we are able to study parametric properties of irregular spectra such as the level curvature defined by the second derivative of a level energy with respect to the perturbation parameter. We prove that the level curvature density of the orthogonal, unitary, and symplectic systems decreases, respectively, as ‖K${\mathrm{\Vert }}^{\mathrm{-}3}$, ‖K${\mathrm{\Vert }}^{\mathrm{-}4}$, and ‖K${\mathrm{\Vert }}^{\mathrm{-}6}$ for large curvature ‖K‖. We present numerical results supporting our theoretical analysis and suggesting the universality of the curvature distribution. The relationship of the curvature distribution to the spacing distribution, as well as the possible experimental observation of the curvature distribution, is discussed.

The polarization of helium (2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$) metastable atoms saturates at 50% when the ensemble is optically pumped with the ${\mathit{D}}_0$ (2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_{1–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$) transition. We have obtained polarizations approaching 100% with a simple, straightforward modification to the conventional experimental arrangement. The addition of a small amount of π-polarized ${\mathit{D}}_0$ light incident on the cell perpendicular to the defining field direction doubles the polarization produced by circularly polarized ${\mathrm{\sigma }}^{+}$ light along the field direction. A simple rate-equation model illustrates the enhancement.

Using an atomic beam we have experimentally observed the one-dimensional motion of atoms in a standing-wave field. The dependence of the laser-cooling effect on the saturation parameter has been measured, and the velocity bunching of atoms has been observed. The results have been compared with the two-level theory of a light-pressure force.

Recent calculations on the bound states of atomic hydrogen in a laser field in the nonrelativistic dipole approximation have produced metastable states with decreasing binding energy as a function of ${\mathrm{\alpha }}_0$∼${\mathit{I}}^{1/2}$${\mathrm{\omega }}^{\mathrm{-}2}$ (where I is the laser intensity and ω is its frequency). We extend the calculations by removing these restrictions. We find the limit of validity of the previous calculations and find that beyond this limit of ${\mathrm{\alpha }}_0$ the lowest bound state persists but that its character is completely changed.

Multiphoton dissociation or ionization partial widths ${\mathrm{\Gamma }}_{\mathit{n}}$ and branching ratios for time-periodic Hamiltonians H(r,t)=${\mathit{H}}_0$(r)+λV(r,t) are obtained from the asymptotic analysis of the complex scaled metastable Floquet states and for V(r,t)=${\mathit{H}}_1$(r)cos(ωt) also from the leading term in the Born-series expansion of the T matrix (LTB). It is shown here that within the framework of the LTB approximation the branching ratios are given by ${\mathrm{\sigma }}_{\mathit{n}+1\mathrm{}}$/${\mathrm{\sigma }}_{\mathit{n}}$ =(λπ/2${)}^2$‖〈${\mathrm{\phi }}_{\mathit{E}+\mathrm{ħ}\mathrm{\omega }\mathit{n}}^{\mathrm{}\left(0\right)\mathrm{}}$‖H${\mathrm{^}}_1$(x)‖φ ${}_{\mathit{E}+\mathrm{ħ}\mathrm{\omega }(\mathit{n}+1)}{}^{\mathrm{}\left(0\right)\mathrm{}}{}_{}{}^{}\mathrm{\Vert }_{}^2{}_{}{}^{}$, where {${\mathrm{\phi }}^{\mathrm{}\left(0\right)\mathrm{}}$} are the continuum eigenfunctions of the field-free Hamiltonian ${\mathit{H}}_0$. Therefore for strong enough laser intensity the ratio ${\mathrm{\sigma }}_{\mathit{n}+1\mathrm{}}$/${\mathrm{\sigma }}_{\mathit{n}}$ may become larger than 1 and multiphoton dissociation or ionization processes will be more efficient than the single-photon process. When the partial widths ${\mathrm{\Gamma }}_{\mathit{n}}$ (defined to be a factor of the residue of the S matrix at a pole) are small, then ${\mathrm{\Gamma }}_{\mathit{n}+1\mathrm{}}$/${\mathrm{\Gamma }}_{\mathit{n}}$≊${\mathrm{\sigma }}_{\mathit{n}+1\mathrm{}}$/${\mathrm{\sigma }}_{\mathit{n}}$.

A recently proposed definition of the angular-momentum transfer ${\mathbf{j}}_{\mathit{t}}$=${\mathrm{l}}_{\mathit{r}}$-j (=l+s) is used to derive a formula for the distribution of spin-polarized E1 electrons ejected by photoionization in unpolarized atoms. The final expression is identical to one obtained earlier for the angular distribution of spin-resolved photoelectrons from freely rotating, unpolarized polyatomic molecules, except for the absence of an incoherent sum over the projection of ${\mathit{j}}_{\mathit{t}}$ due to the spherical nature of an atomic field and, of course, for a different set of reduced amplitudes. This, consequently, means that the same set of formulas (with these two minimal changes) can be used for the ionization of atomic as well as molecular targets. The present paper thus puts the theories for angle- and spin-resolved photoelectron spectroscopy of both atoms and molecules on the same footing. This approach has been used to analyze the currently observed spin-resolved photoionization in atomic ytterbium.

In a crossed-beam experiment the total ionization cross section for the title systems has been investigated in the range 0.1⩽E (eV) ⩽4 of collision energies. The population of the short-lived Ne**[(3p);J=3] state is produced by saturated optical pumping of the Ne*[(3s);J=2]↔Ne**[(3p);J=3] two-level system with a polarized laser beam, resulting in a well-determined distribution of the magnetic substrates |J,M〉 with respect to the relative velocity g. By measuring the ion yield in the scattering center at five different orientations of the laser polarization (linear and circular) with respect to g, the data can be analyzed in terms of pure-state total ionization cross sections Q3|M| corresponding to a single asymptotic state |J,M〉. The observed polarization effect at E=0.1 eV is Q3|M|=0,1/Q3|M|=3=2.5, which is in good agreement with the data of Bussert, T. Bregel, R. J. Allan, M. W. Ruf, and H. Hotop [Z. Phys. A 320, 105 (1985)] in the thermal energy range as obtained by analyzing the Penning electrons. This polarization effect decreases to a value of 1.4 for E>2 eV. The results are discussed in terms of semiclassical scattering calculations with an optical potential as input, using a model-potential approach for calculating both the real and the imaginary parts. For the autoionization width this results in a two-state Γσ′ and Γπ′ basis for the σ′ and π′ orientations of the (2p)-1 hole, calculated in a one-electron orbital overlap approximation. The preference for the Ω=0,1 states at E=0.1 eV indicates the correct relative scaling of these two ionization widths, leading to Γσ′=79Γπ′ at R=4.5a0. The observed energy dependence is due to the decrease of “locking” of the total angular momentum J to the internuclear axis R with increasing angular velocity φ̇, leading to the dynamical criterion ωprec=4φ̇ for the transition of a space-fixed to a body-fixed description of J. The semiclassical precession frequency ωprec of J around R is related to the average Ω splitting of the real part of the optical potential by ωprec=〈ΔVΩ,Ω±1〉/ħ. With these assumptions we observe a good agreement between the experimental results and the semiclassical calculations. Finally, we discuss the validity of a semiclassical locking picture, with emphasis on the difference between locking of the angular momentum versus locking of the electron orbitals involved.

This paper presents a scheme for simulating and observing the Wigner angle using an optical parametric amplifier. The scheme is based on the observation that the dynamical symmetry group of the amplifier, which is SU(1,1), is locally isomorphic to the group SO(2,1) of Lorentz transformations in two space and one time dimension(s). It is shown how boosts and rotations in relativity can be realized as suitable operations on the amplifier, and a quantum-optical analog of the Wigner angle is identified. Using recently developed techniques for the generation and detection of squeezed states, a scheme is proposed for observing the optical analog of the Wigner angle. The feasibility of the scheme is evaluated, and its significance is discussed.

If three light pulses interact in a second-order nonlinear-optical process with a phase mismatch, the pulses may acquire a significant phase modulation. This phase modulation leads to a modification of the spectrum of the pulses and may offer the possibility of compressing the pulses. In this paper we discuss the effects of the ratio of intensities of the interacting pulses and the amount of phase mismatch on the phase modulation using analytical and numerical results. When the phase mismatch is small, it turns out that the modulation is also strongly influenced by the initial phase difference between the fields. Finally, we study the combined effects of a phase mismatch and a difference in group velocity on the spectrum and intensity profile of the interacting pulses.

We formulate the quantum theory of optical wave propagation without recourse to cavity quantization. This approach avoids the introduction of a box-related mode spacing and enables us to use a continuum frequency space description. We introduce a complete orthonormal set of operators that can describe states of finite energy. The set is countable and the operators have all the usual properties of the single-mode frequency operators. With use of these operators a generalization of the single-mode normal-ordering theorem is proved. We discuss the inclusion of material dispersion and pulse propagation in an optical fiber. Finally, we consider the process of photodetection in free space, concluding with a discussion of homodyne detection with both local oscillator and signal fields pulsed.

We study the statistics of direct, heterodyne, and homodyne detection for some generalized squeezed states. The heterodyne statistics yield ‘‘classical’’ phase statistics, which give a clear picture of the phase-sensitive noise of these generalized squeezed states. The homodyne statistics display quantum-mechanical interference effects that are not present for ordinary squeezed states.

This study is motivated by the analytical solutions of superradiance in a high-gain free-electron laser obtained by Bonifacio, Maroli, and Piovella, using the technique of Laplace transforms [Opt. Commun. 68, 369 (1988)]. An error in these analytical solutions is remedied by a correct treatment of the boundary conditions on the electron beam, and the earlier theory is extended to allow for both electron shot noise and an optical pulse in the initial state. It is shown that, when the optical pulse is shorter than the electron pulse, superradiant behavior can also occur at the leading edge of the optical pulse.

We examine the fourth-order interference properties of two photons at a lossless four-port optical device. The photon pair is represented by a joint single-photon wave-packet state with arbitrary spectral composition. We explicitly determine the coincidence probabilities at the output ports of a beam splitter and a Mach-Zehnder interferometer when the incident wave packet is described by a joint Gaussian spectral distribution and the two photons are incident one at each port of the device. For uncorrelated and distinguishable input photons, the fourth-order interference is readily understood in terms of the particle or wave behavior of each photon acting separately. On the other hand, highly correlated photon pairs, such as those generated from spontaneous parametric down-conversion, exhibit fourth-order interference effects at the output of the interferometer that depend expressly on the joint nature of the photon-pair wave packet, and cannot be described by the particle or wave behavior of either photon.

We report results of calculations of photodetachment rates and photoelectron energy spectra for the negative hydrogen ion irradiated by a low-frequency field. We have carried out calculations in both one-electron and two-electron models (with electron-electron correlation included in the initial channel in the two-electron model). Our main focus is on exploring the differences between various approximations that arise from different treatments of the electron-field interaction, rather than from different treatments of the electron-electron interaction. Thus, for the most part, we describe the active electron by the one-electron model. Within this framework, the Keldysh theory yields results in remarkably good agreement with those obtained using Floquet theory. Furthermore Keldysh theory reproduces well the minima and ‘‘discontinuous’’ slopes of the rate at thresholds. The accuracy of the Keldysh approximation can be understood by examining the parameters that characterize the strength of the electron-field interaction. The Faisal-Reiss theory also gives good agreement with Floquet theory (unless the intensity is very high); the reason for this is more technical, having to do with the short range of the one-electron atomic potential. We have generalized the Keldysh and Faisal-Reiss theories to include electron-electron correlation by representing the ground-state ion with an accurate two-electron wave function. Correlation leads to a long-range interaction of the active electron with the atomic core, and thereby to more significant discrepancies between the Keldysh and Faisal-Reiss theories. We compare results obtained using the two-electron Keldysh theory with results, obtained by others, using two-electron perturbation theory and two-electron Floquet theory.

We study the self-pulsing stemming from the Risken-Nummedal-Graham-Haken-type multimode instability in the dye laser described by a band model. Analytical self-pulsing solutions for arbitrary pumping are presented. A distinct feature of the pulsation is that it corresponds to a very low pumping threshold and the required cavity-mode condition can be satisfied in a conventional ring dye laser. Another distinct feature is that the phase velocity of the pulsation may be smaller than the light velocity in the medium. The simple rule, which tells us whether the pulsation is a super- or subcritical one and was found for the two-level model in a previous paper, has been extended to the band model. The results are relevant for experimental investigation of the Risken-Nummedal-Graham-Haken-type multimode instabilities, which are intrinsic to multimode lasers, but have not yet been identified in experiment.

We present a detailed analysis of a laser model with a squeezed reservoir. The steady-state behavior is described by means of the moments and the variance of the field intensity as a function of the pump parameter and the amount of squeezing. The dynamic properties are contained in the eigenfunctions and eigenvalues of the corresponding Fokker-Planck equation. Because of a loss of phase symmetry, the model exhibits interesting features concerning its stationary as well as its dynamic behavior.

The steady-state wave equation, used in the literature for the description of amplified spontaneous emission (ASE) in a refractive medium with inverted atoms, focuses on a narrow frequency band at the atomic line center. In the present work, the effect of this approximation was studied by comparison to an alternative procedure that accounts for the full line shape. The three-dimensional time-dependent Maxwell-Bloch equations for ASE in a refraction guided system were solved as an initial-value problem by using transverse-mode expansion. The steady-state limit was approached only for quantities that are bilinear in the field (autorcorrelation function, complex degree of coherence, and radiation intensity). It was found that, except for a gain narrowing factor, the inclusion of the full line shape (or equivalently the detailed dynamics of atomic polarization) does not change the theoretical prediction for the amplification of mode intensities. However, it drastically changes the prediction for the behavior of cross correlations of mode amplitudes. In the high-gain limit the steady-state wave equation predicts that these cross correlations, normalized to the intensity of the involved modes, are independent of the system length and of the excitation strength of the modes. The solution of the Maxwell-Bloch equations predicts that the normalized cross correlations are exponentially decreasing functions of the system length and of the difference between the excitation strengths of the modes. It is therefore argued that the inclusion of the detailed atomic line shape is essential to the analysis of spatial coherence in ASE systems.

Displaced and squeezed Fock states have recently been thoroughly investigated. Application of these states as the input of a Kerr nonlinear medium reveals many nonclassical effects. We solve this problem analytically and demonstrate results by numerical examples. We introduce a phase distribution for the antinormal quasidistribution ${\mathrm{\phi }}_{\mathit{s}\mathit{c}\mathit{r}\mathit{A}}$ and show that the ‘‘phase’’ of the new states can be sharply localized at some values. This happens when revivals appear in the field. If the states are shifted by a reference wave, photon-number distributions clearly detect the structure of ${\mathrm{\phi }}_{\mathrm{scrA}}$. Damping of the new states is briefly discussed.