The Wigner-Weyl (WW) phase-space formulation of quantum mechanics is discussed within the Liouville-space formalism, where quantum operators A^ are viewed as vectors, represented by L kets ‖A^>>, on which act ‘‘superoperators’’; the scalar product is <<A^‖B^>>=TrA${\mathrm{^}}^{\mathrm{°}}$B^. With every operator A^, we associate commutation and anticommutation superoperators A${\mathrm{^}}^{\mathrm{-}}$ and A${\mathrm{^}}^{+}$, defined by their actions on any operator B^ as A${\mathrm{^}}^{\mathrm{-}}$B^=${\mathrm{ħ}}^{\mathrm{-}1}$[A^,B^], A${\mathrm{^}}^{+}$B^=1/2(A^B^+B^A^). The WW representation corresponds to the choice of a special basis in Liouville space, namely, the eigenbasis of the position and momentum anticommutation superoperators q${\mathrm{^}}^{+}$ and p${\mathrm{^}}^{+}$ (where [q^,p^]=iħ). These, together with the commutation superoperators q${\mathrm{^}}^{\mathrm{-}}$ and p${\mathrm{^}}^{\mathrm{-}}$, form a canonical set of superoperators, [q${\mathrm{^}}^{+}$,p${\mathrm{^}}^{\mathrm{-}}$]=[q${\mathrm{^}}^{\mathrm{-}}$,p${\mathrm{^}}^{+}$]=i (the other commutators vanishing), as functions of which all other super- operators can be expressed. Weyl ordering is expressed as f(q^,p^${)}_{\mathrm{Weyl}}$ ordering=f(q${\mathrm{^}}^{+}$,p${\mathrm{^}}^{+}$)1^. A generalization of Ehrenfest’s theorem is obtained.

We evaluate the emission into a dielectric induced by the dipole polarization of an atomic vapor, in the case where two light beams are incident on the dielectric-vapor interface. These beams are a weak signal beam and a pump beam. Effects of spatial dispersion, arising from deexcitation of the vapor particles at collisions with the interface, are accounted for. The reflected radiation contains sub-Doppler structures arising from combinations of the effects of velocity-dependent transient behavior and the nonlinear response of the vapor. We express the modification of the signal-field reflection due to the pump field in terms of an effective susceptibility of the signal field. This susceptibility explicitly depends on the incidence angles and the frequencies of both beams. We present explicit simplified expressions for this effective susceptibility, valid in special cases. We also give some numerical results.

Nuclear transitions induced by an optical laser coupled to atomic electrons are examined in the context of a soluble model obtained by replacing the Coulomb field of the electrons by a harmonic oscillator. The results indicate that present lasers are marginal for causing this effect, but reasonable extrapolations in intensity and frequency would lead to experimental tests. Choosing the oscillator constant to reproduce realistic atomic radii results in nuclear electric dipole transitions that are potentially observable but that higher electric moments will be too small.

We discuss the quantum fluctuations of the fields associated with a broad class of optical scattering and transmission problems by developing the quantum electrodynamics of an idealized linear, but nonuniform, dielectric medium. We present and compare two quantization schemes for this purpose. The first is based on the expansion of the field in terms of a set of single-frequency solutions of the Maxwell equations. The second involves expanding the field in the set of plane-wave solutions of the Maxwell equations in the vacuum. The relation between the two quantization schemes is discussed in the framework of the scattering theory that connects them. The methods presented are used to show that various field components within a dielectric medium may be either superfluctuant or subfluctuant relative to their fundamental uncertainties in the vacuum. These alterations of the fluctuation properties of the fields are shown to lead to changes in the spontaneous emission rates for both electric and magnetic dipole transitions of excited atoms within or near dielectric media. We also analyze the quantum properties of the transition radiation emitted by a fast charged particle in passing from one dielectric medium to another.

We introduce states defined by ‖α,m〉=${\mathit{a}}^{\mathrm{°}\mathit{m}}$‖α〉 up to a normalization constant, where ‖α〉 is a coherent state and m an integer. We study the mathematical and physical properties of such states. We demonstrate phase squeezing and the sub-Poissonian character of the fields in such states. We study in detail the quasiprobability distributions and the distribution of the field quadrature. We also show how such states can be produced in nonlinear processes in cavities.

For a gain-switched semiconductor laser we study the statistics of the time at which the laser intensity first reaches a threshold level and also the laser intensity fluctuations in the nonlinear regime. The dispersion in the maximum value of the laser intensity at the first peak of the relaxation oscillations is calculated. A simple relation between this maximum value and the passage time for each individual switch-on event is found.

We calculate the electric-field-induced second-harmonic-generation (EFISH) susceptibility of a homogeneously broadened two-level system with permanent dipole moments. This susceptibility has contributions from the second-harmonic-generation (SHG) susceptibility of the same system without the presence of a dc field and the four-wave-mixing (FWM) component of the susceptibility ${\gamma }_{\mathit{e}}$(-2ω;ω,ω,0). The magnitude and phase of the various contributions to EFISH arising from SHG and from FWM depend on the frequency of the fundamental optical field, the transition dipole moment ${\mathrm{\mu }}_{\mathit{a}\mathit{b}}$, the permanent dipole moment of the ground-state level ${\mathrm{\mu }}_{\mathit{a}\mathit{a}}$, and the difference of the ground- and excited-state dipole moments Δμ. We present non-rotating-wave-approximation results for both the quasi-steady-state in systems where the dephasing time ${\mathit{T}}_2$ is much shorter than the population decay time ${\mathit{T}}_1$, so the polarization is in a steady state but the population is not, and for the complete steady state. Extraction of the SHG susceptibility from EFISH measurements is considered.

The real and imaginary parts of the square of the field amplitude are the variables that describe amplitude-squared squeezing. These quantities obey an uncertainty relation. Here we find a particularly simple subset of the states that satisfy the uncertainty relation as an equality. These states are constructed by applying a squeeze operator to a state that consists of a Hermite polynomial, whose argument is the mode creation operator multiplied by a constant, acting on the vacuum. The squeezed vacuum is such a state. These states may or may not be squeezed in the normal sense, and may or may not have sub-Poissonian photon statistics.

We calculate the Lamb shift in the hydrogen atom in a thermal vacuum containing a squeezed mode using thermofield dynamics. We find finite corrections that depend on the temperature and the intensity of the squeezed mode.

We present results of a numerical simulation of photodetachment of ${\mathrm{H}}^{\mathrm{-}}$ ions by an intense laser. We perform a direct integration of the one-dimensional Schrödinger equation, where a model potential is selected to provide the electron with a single bound state and short-range attraction. The numerical integration employs the Crank-Nicholson algorithm, and a variable space grid greatly reduces the computation time. In order to obtain the energy spectrum of the detached electrons, the final wave function is projected onto the discrete, but closely spaced, positive eigenstates of the model potential. The photodetachment rate is computed for wide ranges of laser intensity and frequency. Plots of detachment rate versus intensity display sharp variability with minima that correlate with suppression, at threshold, of peaks in the electron energy spectrum.

We study fluorescence from a three-level atom in a cascade configuration driven by two coherent fields and damped by a broadband squeezed vacuum. Under the conditions that one or both of these fields are intense, a secular approximation is invoked to derive an analytical solution of the relevant master equation. When the two fields are in exact resonance with their respective transitions, expressions for the fluorescent spectra show a narrowing of the central peak for some specific values of the parameters of the squeezed vacuum and the phases between the driving fields and the squeezed vacuum. We also present analytical expressions for second-order intensity correlations. The inhibition of fluorescence in a squeezed vacuum is reflected in the quantum-jump-like behavior shown by these correlations.

Input-output relations in resonators are studied on the basis of a recently developed field-theoretical approach to the action of passive systems in quantum optics [Knöll, Vogel, and Welsch, Phys. Rev. A 36, 3803 (1987)]. This method allows the rigorous proof of recently adopted quantum stochastic approaches, including the presence of sources that form the active medium in the cavity. Quantum Langevin equations are obtained in a coarse-graining approximation. Moreover, we derive all required commutation relations that have been postulated so far. Correlation functions of the field quantities measured outside the cavity are related to correlation functions of field operators of the intracavity field and the incoming field.

We calculate phase fluctuations of the phase operator defined by Pegg and Barnett [Europhys. Lett. 6, 483 (1988); J. Mod. Opt. 36, 7 (1989); Phys. Rev. A 39, 1665 (1989)] in a laser with atomic memory effects. First, we compute the phase fluctuations of a laser, using the Scully-Lamb theory. In a single curve of 〈(Δφ${)}^2$〉 versus time, we obtain the expected behavior: namely, for Dt∼1 the Schawlow-Townes linewidth and for t≫${\mathit{D}}^{\mathrm{-}1}$ the phase fluctuations corresponding to a random phase. As we include the atomic memory effects, we obtain a noise reduction for times of the order of the atomic decay time.

We study the question of recoil corrections to Rydberg energy levels in helium, making use of a formalism in which the He-ion core is treated as an elementary particle of spin 1/2 and the Rydberg atom is regarded as a relativistic two-body bound state, described by a ‘‘no-pair’’ wave equation. We show that when recoil effects are correctly included, the agreement with experiment for the n=10 levels of He is improved.

The behavior of slow, fully stripped ${\mathrm{Ar}}^{18+}$ ions near metallic surfaces has been studied. These ions capture, while touching the surface, a large number of electrons in outermost shells, leading to the formation of ‘‘hollow’’ atoms. The timing of the hypersatellite-satellite cascade filling the double K-vacancy states is studied in this paper by using the internal clock constituted by the ‘‘tops’’ of the temporal sequence filling stepwise the L shell of the ion.

A recent paper by Drake and Swainson [Phys. Rev. A 42, 1123 (1990)] presents a recursion relation that generates a set of coefficients needed to obtain general closed-form expressions for hydrogenic expectation values for ${\mathit{r}}^{\mathit{P}}$. By combining this recursion relation with an earlier semiclassical formulation of this calculation [J. Phys. B 14, 1373 (1981)], it is shown that the correct expectation values can also be obtained by a simple substitution of prescribed angular momentum operators into the classical Kepler formula, which provides a transparent connection to the correspondence limit.

We develop a nonrelativistic formulation for the quantum dynamics of an electron coupled to its own radiation field. For this purpose, we have applied the Feynman-Vernon approach to the composite system in order to obtain the reduced density operator of the electron. In the classical limit, some well-known results, such as the Abraham-Lorentz equation of motion, are reproduced. We have applied the resulting formalism to the problem of interference in order to investigate the possible effects of the incoherent modes of the electromagnetic radiation on the interference fringes. The results allow us to conclude that the coupling to the radiation field is not enough for one to observe a strong influence of those modes on the interference phenomenon.

We have calculated dielectronic recombination (DR) cross sections for Δn=0 transitions in Li-like Bi using the semirelativistic version of the autostructure code. We present results for the full Rydberg series associated with the 2s→2p¯ (j=1/2) core excitation, which opens up at n=20 and spans only 16 Ry, compared to the series associated with the 2s→2p (j=3/2) excitation, which opens up at n=6 and spans 200 Ry. We have also calculated fully relativistic and semirelativistic KLL DR cross sections for H-like Bi and find the effect of the Breit interaction to be important.

The alignment of excited ${\mathrm{Ne}}^{7+}$ ions produced in collisions of low-energy ${\mathrm{Ne}}^{8+}$ ions in a sodium beam target was studied. The linear polarization of both the 434-nm (n=9→8) and the 298-nm (n=8→7) emission lines was measured for beam energies from 4.8 to 32.8 keV/amu.

Cross sections and rate coefficients are reported for the process ${\mathrm{He}}^{\mathrm{*}}$(2 ${}_{}{}^1{}_{}{}^{}$S)+He→He+He+hν, for collision energies corresponding to gas temperatures in the range from 100 to 32000 K.