Čerenkov radiation in the vicinity of atomic spectral lines in a gaseous medium was numerically calculated in an earlier paper of ours [J. H. You and F. H. Cheng, Acta Phys. Sinica 29, 927 (1980)]. The results showed that a new line-emission mechanism, the Čerenkov line mechanism, exists. The main characteristics are as follows: asymmetric profile, a small red shift of line, polarization (if the velocities of electrons are anisotropically distributed), and a large linewidth. The basic theory of Čerenkov line emission was then developed [J. H. You, T. Kiang, F. H. Cheng, and F. Z. Cheng, Mon. Not. R. Astron. Soc. 211, 667 (1984)]. In the present paper, the main formulas have been revised and simplified, and a systematic physical discussion is given. Furthermore, the causes of Čerenkov lines, and their basic characteristics are clarified.

Laser cooling af atoms in an atomic beam is studied theoretically by using a simulation approach derived from a pure-state analysis of resonant radiation pressure. Detailed numerical results are presented discussing the form of the atomic velocity distribution (and its minimum achievable width) and effects due to the spatial (focusing) and frequency variation of a Gaussian laser beam. A comparison of these results with recent experiments is given.

Hydrogen Lyman-α Stark broadening is calculated for a low-density plasma (N≤${10}^{14}$ ${\mathrm{cm}}^{\mathrm{-}3}$) for detunings smaller than 10 Å in the dipolar and no-quenching approximations. Semiclassical and quantal descriptions are alternatively used to describe the contribution of each collision. The results may be compared with the impact and static approximation limits, thus defining their range of validity and leading to analytical expressions for the relaxation rate in these cases. The effects of the trajectories curvatures and relative velocity variations are analyzed.

We extend the semiclassical two-photon two-level model to include upper-level ionization and upper-level decay via an intermediate level. We examine the effects of these relaxation mechanisms on multiwave interactions, finding the generalized one- and two-wave two-photon absorption coefficients and the three-wave coupling coefficient. These mechanisms cause asymmetries to appear in the absorption spectra in addition to those caused by Stark shifts. The Stark-shift term becomes more complicated and fails to vanish even when it does in the simpler model. For recombination rates and ionization decay rates comparable to the coherence decay rate, coherent dips fill in.

A kinetic formalism based on the Vlasov-Maxwell equations is used to investigate properties of the sideband instability for a tenuous, relativistic electron beam propagating through a constant-amplitude helical wiggler magnetic field (wavelength ${\lambda }_0$=2π/$k_0$ and normalized amplitude $a_w$=eB${^}_w$/${\mathrm{mc}}^2$$k_0$). The analysis is carried out for perturbations about an equilibrium Bernstein-Greene-Kruskal state in which the distribution of beam electrons $G_s$(γ’) and the wiggler magnetic field coexist in quasisteady equilibrium with a finite-amplitude, circularly polarized, primary electromagnetic wave (${\omega }_s$,$k_s$) with normalized amplitude $a_s$=eB${^}_s$/${\mathrm{mc}}^2$$k_s$ and constant equilibrium wave phase.

Particular emphasis is placed on calculating detailed properties of the sideband instability for the case where a uniform distribution of trapped electrons $G_s^T$(γ’) is localized near the bottom of the ponderomotive potential moving with velocity $v_p$=${\omega }_s$/($k_s$+$k_0$) relative to the laboratory frame. For harmonic numbers n≥2, it is found that stable (Imω=0) sideband oscillations exist for [ω-(k+$k_0$)$v_p$${]}^2$≊${\mathrm{n}}^2$${\mathrm{\Omega }}_{\mathrm{B}}$ ${}_{}{}^2{}_{}{}^{}$.

Here, (ω,k) are the perturbation frequency and wave number in the laboratory frame, ${\Omega }_B$ =[$a_w$$a_s$$c^2$($k_p^{\mathcal{’}}$${)}^2$/(γ ^ ${}_M{}^{\mathcal{’}}{}_{}{}^{}$${)}^2$${\gamma }_p^2$${]}^{1/2}$ is the bounce frequency, γ^ ${}_M{}^{\mathcal{’}}{}_{}{}^{}\mathrm{mc}_{}^2{}_{}{}^{}$ is the maximum energy of the trapped electrons in the ponderomotive frame, and $k_p^{\mathcal{’}}$ and ${\gamma }_p$ are defined by $k_p^{\mathrm{sprime}/emph>\mathrm{}=(k_s+k_0)/{\gamma }_p}$ and ${\gamma }_p$=(1-$v_p^2$/$c^2$${)}^{\mathrm{-}1/2}$. On the other hand, for the fundamental (n=1) mode, instability exists (Imω>0) over a wide range of system parameters ${\Omega }_B$/${\mathrm{ck}}_0$≪1 and ${\Gamma }_0$≪1, where ${\Gamma }_0^3$=($a_w^2$/4)(ω${^}_{\mathrm{pT}}$ ${}_{}{}^2{}_{}{}^{}$/${\gamma }_p^2$$c^2$$k_0^2$)(1+v ${}_{p/}{}^{}{}_{}{}^{}v_p^{}{}_{}{}^{}$(γ^ ${}_M{}^{\mathcal{’}}{}_{}{}^{}$${)}^3$] and ω${^}_{\mathrm{pT}}$=(4πn${^}_T$$e^2$/m${)}^{1/2}$ is the plasma frequency of the trapped electrons.

Moreover, the maximum growth rate and bandwidth of the sideband instability for the fundamental (n=1) mode exhibit a sensitive dependence on the normalized pump strength ${\Omega }_B$/${\Gamma }_0$$k_0$c. .AE

We present the theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity. Both a microscopic theory and a heuristic Fokker-Planck approach are presented. We show that the micromaser exhibits a number of novel features that are averaged out in usual masers and lasers. First, the field is in general sub-Poissonian, which reflects the quantization of both the field and its sources. Second, the onset of maser oscillations may be followed by a succession of abrupt transitions in the state of the field. Finally, as the atomic flux through the resonator is increased, the maser threshold acquires characteristics of a continuous phase transition, whereas the subsequent changes in the field distribution become analogous to first-order phase transitions.

We discuss a phenomenological one-dimensional, self-consistent, multimode (longitudinal) theory for a free-electron-laser oscillator. A strong fundamental mode and a weak sideband mode are followed through many passes in the optical cavity as the energy of the electron beam decreases monotonically. The time evolution of the laser power exhibits oscillations produced by the sequential growth to saturation and subsequent decay of longitudinal modes evenly distributed in frequency.

We perform an exact linear stability analysis of the Maxwell-Bloch equations for a unidirectional ring laser. The model analyzed in this paper is based on the plane-wave assumption for the cavity field, but it allows arbitrary values of all the other parameters for the cavity and for the active medium. This problem had been solved previously only under exact resonance conditions, or in the uniform-field (mean-field) limit, or after adiabatic elimination of the atomic polarization.

A quantum theory of formation and propagation of superfluorescence and Stokes pulses in samples of small Fresnel numbers is presented. Linearized Maxwell-Heisenberg equations for the system of two-level atoms and a quantized electromagnetic field are solved analytically in the second-order Debye approximation. Under this approximation paths of rays which undergo one reflection from the sides of the sample and those which propagate without reflections are studied. We point out that due to guiding effects, if the Fresnel number is smaller than unity, the contribution from totally reflected rays is not negligible with respect to that from nonreflected rays. This leads to the interference between reflected and nonreflected rays which affects spatial properties of superfluorescence and Stokes pulses. Moreover, as a consequence of guiding effects, the spectral density of light becomes asymmetric and shifted from the atomic resonance frequency.

We study a Fabry-Perot system with a homogeneously broadened medium of active two-level atoms when monochromatic waves are incident on it from both sides. It is found that the ratio of output intensities at both sides depends on the relative phase between the bilateral incident waves and there are the cases when the output intensities are equal even if the bilateral inputs are different from each other. It is shown that completely absorbed states or emission states are attained for the light of special modes with proper intensity and for suitable population.

A single-atom optical clock proposed over ten years ago utilizes an amplification scheme which only recently was recognized as a novel problem in quantum statistics. The atom, a three-state system, has two coupled transitions that are driven continuously by two external fields, one being an allowed transition (1⇆3) and the other a forbidden transition (2⇆3) where ‖3〉 is the lowest state. It has been argued that the weak transition, which is difficult to detect, could be monitored by the presence or absence of spontaneous emission of the strong transition. Thus, when the atom is shelved in the metastable state ‖2〉, the strong transition is extinguished, but when the atom executes a single quantum jump (2→3), it triggers a succession of perhaps a million quantum jumps (macroscopic quantum jumps) in the strong transition, an amplification that can be detected easily. This intuitive argument for alternating bright and dark intervals assumes, however, that the atom is always in an eigenstate. Should the atom be in a superposition state, because of coherent excitation, one could imagine that the weak transition would merely reduce the intensity of the strong transition slightly. This issue is resolved, in favor of the first intuitive argument, by calculating the photon-counting statistics, the probability W(n,T) of observing precisely n photon-counting events in a collection T in a quantum-mechanically consistent way. The results cannot be described by classical statistics. A compact analytic form is obtained for W(n,T) by considering the entire hierarchy of correlation functions where the emission interval peaks sharply about a particular n with a Poisson distribution and can be comparable in length to the darkness interval (n=0) while the other values of n display vanishingly small probabilities.

The signal and idler photons generated by a parametric down converter are highly correlated. We show that the information obtained from a photodetector monitoring the idler port can be used to open and close a shutter in the signal port in such a manner that an antibunched photon beam is produced.

We compare the results of theoretical and experimental studies of a unidirectional, single-mode, inhomogeneously broadened ring laser. We find reasonable qualitative agreement between the calculated and observed output pulsations under resonant and detuned operating conditions, and over a fairly wide range of the pump parameter. With the help of homodyne and heterodyne power spectra, we find that the periodic output field oscillations are usually asymmetric in the phase plane. Over restricted regions of the control parameter space, on the other hand, both symmetric and asymmetric pulsations are found, sometimes coexisting for the same parameter values. The power spectra and temporal oscillations often resemble results from the Lorenz model for a single-mode homogeneously broadened laser.

Elastic scattering of electrons from hydrogen atoms in a chaotic laser field is considered. The necessary ensemble averages are evaluated assuming a field correlation function with an associated Lorentz spectrum. For nonzero bandwidths, the double differential cross sections exhibit peaks around the incident energy as well as around the atomic transition energies, all sidebands having a spacing of the mean laser energy. For zero bandwidth, the (single) differential cross sections reduce to those due to a coherent field, averaged over a Gaussian probability distribution. Some representative numerical results are presented and discussed.

Stochastic differential equations for absorptive optical bistability derived using the positive P representation are solved numerically. The stochastic model is formulated in ten dimensions, twice the dimensions of the space of physical observables. Extra dimensions are needed to include the quantum character of the noise. Ensemble averages are computed for the field amplitude, the incoherent intensity, and the second-order correlation function of the transmitted light. Comparisons with linearized theory are made and detailed results are given in the vicinity of the critical point where nonlinear effects are paramount. The scaling of fluctuations with system size at the critical point is investigated. Transitions between deterministic steady states are studied in a system just beyond the threshold for bistability. A potential difficulty with the use of the positive P representation for modeling nonlinear quantum-statistical systems is identified.

The resonance fluorescence spectrum of a laser-cooled trapped ion is theoretically studied in the Lamb-Dicke limit. Angular averaged spectrum around the elastic peak and the motional sidebands is calculated. The widths of the sidebands are shown to be given by the cooling rate of the ion in the trap. In the limit when the trapping force is strong a possibility of dispersive line shapes is predicted. The spectrum derived is also shown to reproduce in the low-intensity limit the earlier perturbative results.

In a single-atom double-resonance experiment involving a strong and a weak transition, quantum jumps on the weak transition cause the resonance fluorescence of the strong transition to turn on and off randomly in time when observed over intervals long compared to the lifetime of the strong transition but short compared to that of the weak transition. Here we present a theory of this intermittent atomic fluorescence for the case of coherent excitation.

We performed molecular dynamics simulations on a system of 864 particles interacting through a repulsive Lennard-Jones potential at a reduced temperature $k_B$T/ɛ=0.97 and at 11 different densities to determine the sound dispersion as a function of wave number and density. As the density increases a propagation gap appears in the sound-dispersion curve, as predicted by the revised Enskog theory for hard spheres. The gap disappears again at densities well before the undercooled fluid phase, similar as in the Lennard-Jones systems and in liquid argon.

The generalized hypernetted-chain free-energy formulas derived earlier are used for an accurate analysis of the phase properties in the binary ionic mixtures with dielectric screening of the electrons. The miscibility of iron atoms in the hydrogenic solar plasmas has been treated as a specific example. It is found that while the extent of the electronic screening effect is substantial, the resulting change in the phase diagram is not sufficiently large as to be able to account for the solar-neutrino problem.

Observations of the heliumlike titanium spectra with 20-ms temporal resolution during electron cyclotron heating (ECH) of Doublet III tokamak plasma have been made. Several prominent lines in the heliumlike spectra are observed: 1$s^2$ ${}^1$$S_0$←1s2p ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ (labeled w), 1$s^2$ ${}^1$$S_0$←1s2p ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$,2 (y,x), and 1$s^2$ ${}^1$$S_0$←1s2s ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ (z). In addition, the dielectronic satellite lines from the autoionizing lithiumlike ionization states are also observed, e.g., 1$s^2$2p ${}_{}{}^2{}_{}{}^{}°_{3/2}^{}{}_{}{}^{}$←1s2$p^2$ ${}_{}{}^2{}_{}{}^{}D_{5/2}^{}{}_{}{}^{}$ (j), 1$s^2$2s ${}_{}{}^2{}_{}{}^{}S_{1/2}^{}{}_{}{}^{}$←1s2p2s ${}_{}{}^2{}_{}{}^{}°_{3/2}^{}{}_{}{}^{}$ (q), etc. The intensity of the resonance line w (i.e., 1$s^2$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$←1s2p ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$) is found to be extremely sensitive to the ECH power. Ion temperatures rise from the Ohmic phase to steady-state ECH phase in 20–40 ms at an electron density of 6×${10}^{13}$ ${\mathrm{cm}}^{\mathrm{-}3}$. Time-resolved line ratios G=(x+y+z)/w, R=z/(x+y), and j/w are also presented. Detailed analysis of the observed spectra is carried out, based on the relevant atomic and plasma effects, and it is concluded that there exists a significant departure from a Maxwellian distribution of electrons in the present ECH plasmas, which are also dominated by nonequilibrium ionization.