In this paper we derive an expression for the lifetime of excited atomic states taking account of contributions due to nonresonant two-photon transitions. Explicit integration of the two-photon emission spectrum is not required. The results are applied to the case of the hydrogen atom.

The quantum-electrodynamical problem of N identical two-level atoms interacting with M field modes is considered, and an exact solution for the case of spontaneous emission from a single atom is obtained. The behavior of this system is shown to be quite different from the exponential decay of a single excited atom radiating into free space. A ‘‘ringing’’ behavior at the enigmatic frequency ∼ √N which occurs when only one mode is accessible to the field persists when many modes are present. When a continuum of modes is accessible, the long-time limit shows that the energy of the originally excited atom is equally likely to be shared by the N-1 originally unexcited atoms and the electromagnetic field when M/N→1. ‘‘Radiation suppression’’ occurs whenever N≫1 and M≪N, when the originally excited atom does not emit its energy. When M=N≫1, the single atom decays monotonically to zero (and approximately exponentially) but with a decay rate that is √N times the Rabi frequency. Such unexpected effects are presently within experimental range.

A rotating-wave approximation (RWA) for the single-photon and multiphoton resonance profiles for a two-level molecule interacting with both sinusoidal and static electric fields is derived. Included is a useful expression for the coupling between the molecule and the applied sinusoidal field which exhibits the effects of both diagonal dipole matrix elements (permanent dipole moments) and the applied static electric field. Comparisons of the RWA results with exact two-level calculations provide qualitative information concerning the validity of the RWA as a function of molecular and field parameters. These examples are also used to illustrate the interpretive nature of the RWA results for the resonance profiles and some of the effects of permanent dipoles and static fields on the profiles. Of particular interest are examples involving Boltzmann rotationally averaged spectra as a function of temperature where it is shown that minima in the spectra occurring for high temperatures can be reduced or removed completely if the temperature or applied static field is reduced.

Narrowing of magnetic-resonance lines in a dense optically pumped alkali-metal vapor ${(}^{87}$Rb) has been observed. This observation is shown to be a result of optical pumping with a monochromatic light source tuned such that the real part of the vapor polarizability, which is responsible for light shifts, is essentially zero. A model based on the Bloch equations is used to describe the observed narrowing effect, and results of numerical calculations based on this model are presented. The results agree qualitatively with observations, and show correctly the disappearance of the effect at low light levels. This narrowing effect is of importance to the development of precision frequency standards and magnetometers utilizing monochromatic light sources (such as semiconductor lasers).

Experimental observations of dissociative attachment in lithium are described. Using laser excitation of a supersonic lithium beam a population of metastable vibrationally excited lithium molecules has been created. A cold-electron population (0.13 eV) has been created by laser photoionization of lithium atoms, and the attachment of these electrons has been studied as a function of molecular state. The dissociative attachment rate constant does not vary significantly for ${\mathrm{Li}}_2$(X) between v∼10 and v∼13, states which lie above the attachment energy threshold, nor is there significant rotational variation between J∼0 and J∼20. The rate constant for dissociative attachment to these states for thermal electrons at ∼0.05 eV has been measured to be (2±1)×${10}^{\mathrm{-}8}$ ${\mathrm{cm}}^3$ sec ${}_{}{}^{\mathrm{-}1}{}_{}{}^{}$.

The photoelectron spectra obtained following two-photon resonant, three-photon ionization of atomic iodine via a number of Rydberg states are presented. Photoelectron spectra obtained via the ${(}^3$${\mathrm{P}}_2$)np${\left[1\right]}_{1/2}$ levels and via the ${(\mathrm{}}^3$$P_0$)4f${\left[3\right]}_{5/2}$ level demonstrate the production of state-selected ${\mathrm{I}}^{+}$ ${\mathrm{}}^3$${\mathrm{P}}_2$ and ${}_{}{}^3{}_{}{}^{}\mathrm{P}_0^{}{}_{}{}^{}$ ions, respectively, with ∼85% efficiency. Photoelectron spectra obtained via the ${(}^3$${\mathrm{P}}_2$)nf${\left[3\right]}_{5/2}$ levels show the effect of a perturbation by the ${(}^3$${\mathrm{P}}_0$)4f${\left[3\right]}_{5/2}$ level, as both ${\mathrm{I}}^{+}$ ${\mathrm{}}^3$${\mathrm{P}}_2$ and ${}_{}{}^3{}_{}{}^{}\mathrm{P}_0^{}{}_{}{}^{}$ are observed. The relative magnitudes of the ${}_{}{}^3{}_{}{}^{}\mathrm{P}_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{P}_0^{}{}_{}{}^{}$ photoelectron peaks are shown to be strongly dependent on the relative magnitudes of the ${(}^3$${\mathrm{P}}_2$)nf${\left[3\right]}_{5/2}$ and ${(\mathrm{}}^3$$P_0$)4f${\left[3\right]}_{5/2}$ photoionization matrix elements. Two additional processes are observed in the photoelectron spectra. These correspond to fluorescence of the resonant intermediate level to lower-lying levels, followed by ionization of those levels, and to energy transfer from ${\mathrm{I}}^{\mathrm{*}}$ ${\mathrm{}}^2$${\mathrm{P}}_{1/2}$ atoms to Rydberg atoms, resulting in ionization of the latter.

We have measured the position of the Zeeman level crossing between the (J,M)=(0,0) and (1,1) sublevels of the 3 ${}_{}{}^3{}_{}{}^{}$P state of helium. The result, 15.756 195(22) MHz (NMR frequency in water), is in good agreement with earlier, less precise measurements. This value, together with our previous measurement of the (2,2)-(0,0) level crossing, is used to calculate the zero-field fine-structure splitting. We find $E_{02}$=8772.517(16) MHz between the J=0 and 2 states, $E_{12}$=658.548(69) MHz between the J=1 and 2 states, and $E_{01}$=8113.969(80) MHz between the J=1 and 0 states.

Collision-enhanced Hanle resonances in the 3 ${}_{}{}^2{}_{}{}^{}S_{1/2}^{}{}_{}{}^{}$ electronic ground state of Na atoms have been studied in a phase-conjugate four-wave light-mixing geometry. Narrow resonances in zero magnetic field have been observed at very high inert-buffer-gas pressures, with a width of 21 mG, or less than 10 kHz, full width at half-maximum. The intensity and the width of these resonances has been studied as a function of buffer-gas pressure, of alkali-metal vapor pressure, of detuning from the $D_1$ and $D_2$ Na resonances, and of the intensity of the incident light beams. Saturation phenomena and power broadening are observed. The results are explained theoretically in terms of transversely pumped optical gratings. The equivalence of this description with collision-induced coherence gratings in the limit of low light intensities is demonstrated.

A search was made for photons from the two-photon deexcitation of the 2S state of muonic He by measuring the time and energy distributions of delayed photons emitted when negative muons were stopped in gaseous He at room temperature. An upper limit of 46±1 ns was obtained for the lifetime of this state at 40 atm, in disagreement with earlier measurements. Prompt K-series muonic x rays were also measured at pressures between 0.5 and 40 atm, and the x-ray intensity ratios were used to deduce initial 2S-state populations.

A method to obtain an effective single-particle potential for the photoabsorption of open-shell atoms is discussed and applied to the calculation of the photoionization cross section of neutral chlorine. The potential includes, in an approximate way, the effects of interaction among many final channels. For chlorine, the results are in very good agreement with elaborate many-body calculations except for the failure to describe resonance structure.

Effect of cavity leakage on the emission and absorption of radiation from an atom in a cavity, with the cavity mode in vacuum, is studied exactly by solving density-matrix equations and by evaluating the relevant two-time quantum-mechanical correlation functions. Analytic expressions for the widths and position of various spectral lines are given. Widths are found to depend on detuning. Manifestation of the vacuum-field Rabi oscillations on different types of spectra are discussed. Vacuum-field Rabi oscillations are also apparent in the coherent scattering of external radiation from the cavity.

The propagation of optical pulses is considered at the zero-dispersion wavelength of nonlinear dispersive fibers. Even in the absence of group-velocity (first-order) dispersion, higher-order dispersive effects in single-mode silica fibers are found to be strong enough to cause significant broadening and distortion of picosecond optical pulses for fiber lengths of 10–100 km. Using the parameters appropriate for a 1.55-μm dispersion-shifted single-mode fiber, we have studied the evolution of pulse shapes and pulse spectra along the fiber length for a wide range of initial pulse widths. For peak powers ∼10 mW, the dispersive and nonlinear effects are comparable for pulse widths ∼1 ps and their mutual interplay leads to new qualitative features in the pulse shape and spectrum that are largely independent of the input profile. The theoretical results are useful for an understanding of the higher-order dispersion and, at the same time, have implications for high-capacity, long-haul, optical communication systems.

We study the semiclassical mean-field theory of single-mode dispersive optical bistability in the limit of a fully developed hysteresis cycle (i.e., in the limit of large values of the bistability parameter C) and when all decay rates have comparable magnitude. We locate (i) on the upper branch instabilities leading to time periodic regimes, (ii) on the lower branch instabilities leading to a switching before the limit point is reached. None of these instabilities are observed in the case of purely absorptive optical bistability.

Collisionless extraresonances (ER) in degenerate four-wave mixing (DFWM) are predicted when the upper state ‖b〉 of the ‖a〉→‖b〉 transition, excited by near-resonant incident laser beams, decays to the lower state ‖a〉 both directly (‖b〉→‖a〉) and via one or two intermediate states: ‖b〉⇄‖d〉→‖a〉 or ‖b〉→‖c〉→‖d〉→‖a〉. The width of the new ER, which depends on the relative decay rates in the cascade process, may be very narrow leading to very strong DFWM signals. Dephasing collisions affect the intensity of the new ER and also produce the usual, pressure-induced ER.

A theory is presented to describe the propagation of a laser pulse with several frequency components ${\omega }_j$=${\omega }_O$+j${\omega }_R$ through a Raman medium, where ${\omega }_0$ is the initial laser frequency and ${\omega }_R$ is the frequency of the Raman transition. We consider primarily the transient regime, where the pulse width is comparable to or less than the relaxation times of the medium. We formulate the Maxwell-Bloch equations in terms of a two-photon Rabi frequency Ω and an overall phase theta. The resulting equations are similar in form to those describing self-induced transparency, and exhibit solutions corresponding to slowly traveling, but ultimately decaying, pulses. Numerical solutions to the equations are presented that include pump depletion, the ac Stark shift, and finite relaxation times. Significant frequency conversion to high-order (j∼8) anti-Stokes modes is observed in the numerical results.

A Floquet-Liouville supermatrix (FLSM) approach is presented for nonperturbative treatment of the time development of the density-matrix operator of atoms and molecules exposed to intense polychromatic fields. By extending the many-mode Floquet theory (MMFT) recently developed, the time-dependent Liouville equation for the density matrix of quantum systems undergoing relaxations (due to radiative decays and collisional dampings, etc.) can be transformed into an equivalent time-independent non-Hermitian FLSM eigenvalue problem. This yields a numerically stable and computationally efficient approach for the unified treatment of nonresonant and resonant, one- and multiple-photon, steady-state and transient phenomena in nonlinear optical processes, much beyond the conventional rotating-wave-approximation (RWA) method. Connections of the FLSM approach to the MMFT in the limit of zero relaxations are also made, providing the understanding of the physical significance of FLSM supereigenvalues and eigenvectors. In addition to the exact FLSM formalism, we have also presented higher-order perturbative results, based on the extension of the generalized Van Vleck (GVV) nearly degenerate perturbation theory, appropriate for somewhat weaker fields and near-resonant processes, but beyond the RWA limit. The implementation of the GVV method in the time-independent Floquet-Liouvillian allows the reduction of the infinite-dimensional FLSM into a finite-dimensional GVV-Liouville matrix, from which essential analytical results are readily obtained. As an illustration of the usefulness of the new formalism, we extend both the FLSM and the GVV methods to a formal study of the multiphoton-induced resonance fluorescence spectra of two-level systems subject to purely radiation relaxations. Both the time-averaged power spectrum and the time-dependent physical spectrum are exploited in details, and novel new features in intense fields are pointed out.

A nonlinear response theory of a quantum-mechanical system undergoing arbitrary relaxation and interacting with fields, some of which may be strong enough to saturate optical transitions, is developed. Explicit expressions for second-order and third-order susceptibilities are obtained. If the fields are weak, then these expressions show the existence of additional resonant contributions to ${\chi }^{\left(n\right)}$ which arise due to inelastic collisions. Various applications of these ${\chi }^{\left(n\right)}$’s to modulation spectroscopy, four-wave mixing, and pump-probe experiments are discussed. The general structure suggests how the additional resonances can be used to determine inelastic rates in a Doppler-broadened medium. For saturating fields, ${\chi }^{\left(n\right)}$’s become dependent on the intensity of such fields and can be formally obtained from weak-field ${\chi }^{\left(n\right)}$’s, provided proper identification of unperturbed eigenfunctions, eigenvalues, and relaxation times is made. Such intensity-dependent ${\chi }^{\left(n\right)}$’s have resonant denominators which lead to resonances at Rabi frequencies and submultiples of these frequencies, the widths of which are also dependent on the strength of the field. In the special cases intensity-dependent ${\chi }^{\mathrm{}\left(1\right)\mathrm{}}$ agrees with the work of Cohen-Tannoudji and co-workers.

A laser-electron-acceleration scheme based on self-sustained cyclotron resonance is discussed. Nonlinear electron dynamics in combined axisymmetric magnetic and transverse laser radiation fields is investigated. Analytic solutions are given for a circularly polarized luminous (ω/ck=1) radiation case, which allows time unlimited phase locking between the electrons and the accelerating electromagnetic wave. An appropriate tapering of the magnetic field in the superluminous case (ω/ck>1) can also lead to significant accelerations, restricted by the maximum available strength of the guide magnetic field. We discuss the entrance conditions for the accelerated beam as well as its launching into the desirable autoresonance regime through a transition region. It is shown that the radiation losses in a 1-TeV accelerator are negligible. Also, high-current-beam acceleration seems to be feasible. Nd-glass lasers with intensity of ${10}^{18}$ W/${\mathrm{cm}}^2$ are capable of accelerating high-current electron beams from 0.25 to 2.5 GeV over 1 m by using a 100-kG guide magnetic field.

A novel type of optical bistable configuration, namely the so-called double-ring (DR) device, is presented. The stationary solutions in the purely absorptive case for a homogeneously broadened atomic system are derived. In the mean-field limit it has been pointed out that use of a DR arrangement enables us to reduce both the length of the sample of the nonlinear medium and the response time of the device. Linear stability analyses have shown that the position and the length of the unstable regions of a given hysteresis cycle can be controlled, to a great extent, by means of the two new parameters of our DR scheme. Finally, it has been remarked that, in order to observe self-pulsing, the purely absorptive DR system may present a similar behavior to that offered in the dispersive single-ring case.

We present theoretical and experimental evidence for a new type of multimode instability in a homogeneously broadened ring-laser system. The unstable behavior discussed in this paper is the result of multimode competition and can manifest itself either through self-pulsing or hysteretic behavior of the bistable type in the laser output intensity and operating frequency. We have verified some of our predictions with the help of a ${\mathrm{CO}}_2$ laser whose observed bistable behavior is in good qualitative agreement with the theoretical predictions.