We consider a two-level atom interacting simultaneously with a classically described cw laser field and a quantized cavity field. The classical field is assumed strong, and the cavity field is regarded as a quantum probe of its dressed states. The two fields have different frequencies and amplitudes, but we show that an effective time-independent Hamiltonian can be obtained via two rotating-frame transformations. There is a different effective Hamiltonian in each of an infinite sequence of ‘‘probe resonance zones’’ associated with the subharmonic Rabi sidebands of the dressed states. In the mth zone, the Hamiltonian has the same form as the m-photon Jaynes-Cummings Hamiltonian. We consider both time-dependent and time-averaged atomic response and make comparisons with recent findings in the case that both fields are fully classical.

The threshold characteristics of the static and periodic instability of the single feedback mirror device are investigated for a homogeneously broadened two-level medium as a function of the input intensity, the detuning, the buffer-gas pressure, the atomic concentration, and the round-trip time d, and compared with experimental results. For a large range of parameters that agrees with the experiment, the self-oscillation process is shown to be mainly induced by the longitudinal grating, which ensures a large instability domain, and controlled by the buffer-gas pressure, which must be low enough in order that the threshold period of the oscillation is constant on a doughnutlike transverse profile and nearly equal to 2d. This oscillation, called the 2d oscillation, is neither a result of pure phase-conjugate-mirror operation of the atomic medium nor a result of a Rabi sideband gain process. It is shown to take place through a mixture of phase-conjugate-mirror and ordinary mirror operations, which are both allowed by the specific optical arrangement of the device.

Detailed analysis of the steady-state and dynamical unstable behavior of single-mode, homogeneously broadened Raman lasers is presented. Bistable features of the Raman emission and its operating conditions are determined from steady-state analysis. Parametrization of the dynamical behavior shows instabilities to exist over a broad range of operation conditions and for broad cavity detuning to the low-frequency side of the gain center where the bistable emission also prevails. Notably, period-doubling routes to chaos and sustained oscillatory behavior in both intensity and phase are found to occur for both good and bad cavity conditions, the dynamics of the phase revealing additional temporal features to that of intensity.

A quantum-mechanical treatment is developed, by using the Lie Group methods, for the properties of the detuned degenerate, vacuum, and excited squeezed-states photon number distribution. For a vacuum squeezed state, the detuning decreases the average photon number without changing the semichaotic distribution. In addition, an oscillatory behavior of the photon pair probability as a function of the detuning parameter appears below threshold. For an excited squeezed state, the photon number distribution, including its oscillatory characteristic at resonance, is strongly affected by the detuning. In addition to a continuous relaxation of the oscillations toward a Poissonian-like shape, there is also a very sensitive movement of the oscillations’ peaks, depending on a detuning produced phase.

The nonrelativistic N-body problem can be solved in the hyperspherical formalism by the hyperspherical adiabatic approach (HAA). The ground-state energy ɛ is compared with three other eigenenergies obtained from the HAA: the coupled and uncoupled adiabatic approximations (CAA and UAA), and the extreme adiabatic approximation (EAA). The first two provide an upper bound and the last provides a lower bound to the ground-state energy, or ${\mathrm{\varepsilon }}_{\mathrm{EAA}}$≤ɛ≤${\mathrm{\varepsilon }}_{\mathrm{CAA}}$≤${\mathrm{\varepsilon }}_{\mathrm{UAA}}$. A main point of the article lies in extending to hyperspherical formalism an inequality familiar for the Born-Oppenheimer approximation (BOA), namely, ɛ≥${\mathrm{\varepsilon }}_{\mathrm{BOA}}$.

We show that the Tomonaga-Schwinger formalism in quantum field theory provides a manifestly Lorentz covariant description of an Einstein-Podolsky-Rosen (EPR) correlated state defined on a curved-space-like surface. This avoids the notion of a universal time and clearly demarcates between the completion of the measuring process on a member of an EPR pair and its nonlocal effect on the state of its partner. Being reciprocal and restricted to a spacelike surface, the latter is deterministic but not causal and is consistent with Lorentz invariance.

Dipole polarizabilities at both correlated and uncorrelated levels are reported for ions of the [Ar]${\mathit{d}}^5$ ${}_{}{}^6{}_{}{}^{}$S configuration (${\mathrm{Cr}}^{+}$,${\mathrm{Mn}}^{2+}$,${\mathrm{Fe}}^{3+}$,${\mathrm{Co}}^{4+}$,${\mathrm{Ni}}^{5+}$,${\mathrm{Cu}}^{6+}$,${\mathrm{Zn}}^{7+}$). Values (in atomic units) range from 10.5 (${\mathrm{Cr}}^{+}$) to 0.38 (${\mathrm{Zn}}^{7+}$) with a smooth, monotonic dependence on nuclear charge. These systems are well described by a single-determinant wave function. Correlation contributions to polarizability range from 14% (${\mathrm{Cr}}^{+}$) to 0.1% (${\mathrm{Zn}}^{7+}$). Previously published approximate Hartree-Fock results are shown to be in error by 50% for ${\mathrm{Fe}}^{3+}$. It is shown that frozen-core and, by implication, pseudopotential methods are inadequate for the accurate calculation of electric properties of this series of ions.

Density-functional-theory calculations predict that (i) ${\mathrm{La}}^{\mathrm{-}}$ is a unique negative ion in that it has bound states of both even and odd parity in the configurations [Xe]5${\mathit{d}}^2$6${\mathit{s}}^2$ and [Xe]5${\mathit{d}}^1$6${\mathit{s}}^2$6${\mathit{p}}^1$, respectively, and (ii) the ground state of ${\mathrm{Ac}}^{\mathrm{-}}$ is of odd parity in the configuration [Rn]6${\mathit{d}}^1$7${\mathit{s}}^2$7${\mathit{p}}^1$ while the even-parity state [Rn]6${\mathit{d}}^2$7${\mathit{s}}^2$ is unlikely to be bound. The dominant relativistic effects have been included perturbatively and are essential for these predictions.

The effect of electron correlation is believed to be important at low energy for light elements and particularly for small scattering angles. With the availability of accurate theoretical values in recent years and of more accurate experimental results using synchrotron radiation, it might be possible to observe the effect of electron correlation experimentally. In one such experiment using synchrotron radiation, Ice, Chen, and Crasemann [Phys. Rev. A 17, 650 (1978)] demonstrated the effect of correlation for ${\mathrm{H}}_2$ and He for 5-, 6-, and 7-keV photons and 6- and 12-keV photons, respectively, at two scattering angles 60.9° and 135.6°. They compared their measured values with the values calculated using form factors for elastic scattering and incoherent scattering factors for inelastic scattering, with and without correlation. We show in this Brief Report that the use of accurate elastic scattering cross sections obtained from S-matrix formalism within the framework of the independent-particle approximation, even without electron correlation, improves the agreement of the measured values. Our results indicate the desirability of more accurate experimental measurements as well as the calculation of incoherent scattering cross sections at the S-matrix calculation level to observe the correlation effects from such experiments.

The correlation-energy density functional is studied here through an exact solution of a two-electron system bound by a harmonic-oscillator external potential. Since the correlation energy is a universal functional of density in density-functional theory, the same functional form is valid for two-electron atoms and ions as well. Using this fact we have proposed here density-functional schemes, within a local-density approximation as well as nonlocal considerations, for the study of correlation energies of two-electron atomic and ionic systems. The nonlocal scheme leads to significant improvement over the local ones, yielding results that show good agreement with the standard values.

We have carried out a relative measurement of the total photoionization cross section of the excited 7${\mathit{D}}_{5/2}$ state of cesium for photoelectron energies in the range 0.103–0.127 Ry above the ionization threshold. Separate measurements were made using two different combinations of laser sources to populate and photoionize the 7${\mathit{D}}_{5/2}$ state. The first measurement was made with a cw diode laser and two pulsed dye lasers, while the second was made with three pulsed dye lasers. The measured cross section was found to vary slowly within experimental uncertainty over this energy range but was otherwise featureless. This result disagrees with the cross section predicted by a Hartree-Slater calculation [J. Lahiri and S. T. Manson, Phys. Rev. A 33, 3151 (1986)], which displayed a deep minimum in this spectral region.

A formal method is presented to evaluate the second-order Born approximation of the laser-assisted potential scattering. It is an implicit closure technique that includes intermediate virtual-state transitions and enables one to find the exact explicit expression of the transition amplitude. This is of interest from two standpoints: first, one can deal with ranges of parameters in which the first-order Born approximation is a poor one; second, one can set limits of on-shell approximations that are also widely used to analyze recent laser-assisted experiments. The off-shell character yields new terms in the exact amplitude, and in particular, it is shown to play a crucial role in forward scattering from a long-range potential.

Electron-positron propagators are discussed in the context of the many-body theory of composite electronic-positronic systems. They are shown to be useful for obtaining positron affinities of open-shell systems with one unpaired electron. The approximation schemes obtained are simpler than those in the analogous two-electron case.

Under favorable circumstances, a pulse-amplified cw dye laser can be used to excite three-photon resonant, four-photon transitions without significant power broadening. We have used this technique to make precise vacuum ultraviolet measurements, and to observe the cancellation of three-photon resonances due to third-harmonic generation at much lower number densities than has previously been possible. Three transitions to the B and C states of molecular hydrogen near 100 000 ${\mathrm{cm}}^{\mathrm{-}1}$ have been measured with an accuracy up to 0.04 ${\mathrm{cm}}^{\mathrm{-}1}$, twice that of previous measurements.

We show that some lasers and nonlinear optical devices with dissipation have in common certain characteristics that lead to a kind of phase anholonomy when such dissipative systems undergo a periodic motion with some frequency, say Ω. The amount of the phase anholonomy accumulated in a period of 2π/Ω is defined generally for such systems and further calculated for a subclass of such systems near the Hopf-bifurcation point. It turns out that the phase accumulation is generally determined by the size of the periodic orbit. By constructing a simple Hamiltonian, we show precisely that the phase anholonomy in these dissipative sytems can indeed be interpreted as Berry’s phase.

Previous work [B. Yurke, J. Opt. Soc. Am. B 4, 1557 (1987)] published on quantizing Josephson parametric amplifiers has involved a constrained Lagrangian. This paper proposes a simpler, consistent Hamiltonian approach to quantizing a Josephson parametric amplifier, without constriants.

We rederive the normal-ordering theorem of Blow et al. [Phys. Rev. A 42, 4102 (1990)] by the use of functional derivatives. This method does not require the introduction of a set of noncontinuous operators as an intermediate step.

Wave equations describing optical phase conjugation in photorefractive crystals are solved using a technique that transforms a boundary-value problem into an initial-value problem. Boundary conditions are satisfied using an iterative map constructed in the parameter space. Within the iterative procedure unstable situations arise, leading to a chaotic response of the crystal. A strange attractor is discovered in the reflectivity of the crystal, existing in the multiparameter space of the single-interaction-region four-wave-mixing process.

We consider the finite-temperature cavity electrodynamics with a single Morse oscillator and its spectral aspects. It has been shown that the single-peak structure of the emission spectrum in the presence of weak coupling splits up into a doublet in the limit of strong coupling. In the finite-temperature case, for small average number of photons n¯ in the cavity, the line shape first shows doublet structure as the coupling increases. However, these merge to a single peak structure with increasing n¯ at values as small as 3 to 4 photons.

The quantum nature of sidebands in resonance fluorescence from one as well as two coherently driven two-level atoms in a squeezed bath is studied by deriving expressions for intensity-intensity correlation functions and photon statistics that are phase sensitive. The nonexponential decay of the population inversion for the two-atom case is explicitly shown under certain conditions of parameters.