We analyze the classical behavior and the quantum fluctuations for the system of degenerate four-wave mixing inside a doubly resonant optical cavity. Two frequency-degenerate but orthogonally polarized modes are coupled together in a ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ medium. We include all significant phase-matched interactions that occur in a third-order polarization (self-phase modulation, cross-phase modulation, and four-wave mixing). Two critical points are predicted to occur in the system. The first occurs for low pumping, associated with the excitation of the single mode. The second critical point occurs for higher pumping, associated with the onset of self-pulsing. Quantum fluctuations are analyzed for the various regions of pumping. At the first critical point, perfect squeezing is possible in both the pump and the signal modes when the damping of the signal mode is greater than the damping of the pump (${\gamma }_{\mathit{a}}$>${\gamma }_{\mathit{b}}$). In the case where the damping of the signal mode is much greater than that of the pump (${\gamma }_{\mathit{a}}$≫${\gamma }_{\mathit{b}}$), nearly perfectly squeezed states of the signal mode are possible in the entire region between the two critical points.

The multimode even and odd coherent states (multimode Schrödinger cat states) are constructed for polymode parametric oscillators of the electromagnetic field. The evolution of the photon distribution function is evaluated explicitly. The distribution function is expressed in terms of multivariable Hermite polynomials; the means and dispersions of the function are calculated. The conditions for the existence of squeezing are formulated. The correlations between the different modes of the Schrödinger cat states are studied. The transformation of the initial Schrödinger cat states under the action of a resonant external force is investigated.

We present here a systematic scheme for improving the variational wave functions and corresponding energy levels for quantum systems. By expanding the wave function around a variational parameter value, a family of independent functions can be systematically generated. The eigenstates are then obtained by diagonalizing the Hamiltonian matrix within the basis and optimized with respect to the variational parameter. As a test, the ground state of the quartic anharmonic oscillator has been investigated, and it is found that this scheme converges more rapidly than the conventional Lanczos method and yields better approximations of the energy levels than other variational methods. The effectiveness of this scheme for larger systems remains to be seen.

We introduce a quantitative measure of nonclassical behavior based on negative regions of quasiprobability distributions. Zeros of the antinormal ordered phase-space representation characterize a state to be maximally nonclassical with respect to this measure. All pure states of a particle or of a single field mode, except those with Gaussian quasiprobability distributions, have one or more zeros in this representation.

We give the explicit form of the common eigenstate ‖ξ〉 of the center-of-mass coordinate ${\mathrm{\mu }}_1$${\mathit{Q}}_1$+${\mathrm{\mu }}_2$${\mathit{Q}}_2$ and the mass-weighted relative momentum ${\mathrm{\mu }}_2$${\mathit{P}}_1$-${\mathrm{\mu }}_1$${\mathit{P}}_2$ of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators ${\mathit{Q}}_2$-${\mathit{Q}}_1$ and ${\mathit{P}}_1$+${\mathit{P}}_2$. The orthonormal and completeness relation of ‖ξ〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for ${\mathrm{\mu }}_1$${\mathit{Q}}_1$+${\mathrm{\mu }}_2$${\mathit{Q}}_2$ and ${\mathrm{\mu }}_2$${\mathit{P}}_1$-${\mathrm{\mu }}_1$${\mathit{P}}_2$ is also derived by using the ‖ξ〉 representation.

We present a simple example that shows nonlocality in quantum mechanics. The basic elements are two microwave cavities equipped with correlated quantized fields that interact with two atoms. We perform state-selective measurements on these atoms that subsequently reveal a type of nonlocality recently described by Hardy [Phys. Rev. Lett. 71, 1665 (1993)].

By using laser reduced fluorescence techniques, molecular absorption from the first relaxed excited excimer states of krypton is obtained in the 960–990-nm wavelength range. Five bands are observed and analyzed by comparison with an ab initio calculated spectrum. The fine structure is thus evidenced.

Oscillations in the mean-charge state of swift ions as a function of the atomic number ${\mathit{Z}}_1$ are reported for a wide range of ions of identical velocity (isotachic ions). A previously suggested mechanism for the enhancement of the mean charge for certain ion-charge combinations that involves closed shells is shown to be an inadequate explanation. Post-foil-Auger processes, however, are demonstrated to be a more plausible explanation for the observed behavior of the mean charge of the ions.

The retarded dipole-dipole dispersion interaction potential in helium is evaluated from a set of very accurate effective dipole transition frequencies and oscillator strengths already obtained from a variational calculation. The asymptotic form changes from the inverse sixth to the inverse seventh power of the nuclear separation as the atoms move apart. Simple representations of the potential are given for use in scattering and structure calculations.

A multiple-crossing Landau-Zener model is applied to calculate mutual neutralization cross sections for the reactions ${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{H}}_2^{+}$+${\mathrm{H}}^{\mathrm{-}}$ as a function of the principal quantum number n of the resulting H atom. For low-energy collisions (E≤10 eV), the total cross section for ${\mathrm{H}}_2^{+}$+${\mathrm{H}}^{\mathrm{-}}$ is a factor of 8 larger than the one for ${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{-}}$. The cross section for the process including ${\mathrm{H}}_2^{+}$, in which the H atom is excited to the quantum state n (2≤n≤8), has a nonmonotonic behavior as a function of the atomic quantum state. Comparison of the calculated results with newly received experimental data is made.

We show numerically that the complex hyperbolic secant pulse provides robust selective inversion of vibrational overtones. A density-matrix analysis is performed for a ten-level Morse-oscillator approximation of a diatomic molecule. We also show that in the limit of adiabatic excitation the complex-hyperbolic-secant pulse yields an inversion spectrum that is narrower than its spectral bandwidth.

Rydberg atoms are ionized by nearly unipolar, subpicosecond electromagnetic pulses. Deviations from a perfectly unidirectional pulse are found to alter substantially the ionization probability as a function of peak field. Quantitative agreement between classical theory and experiment is achieved if the pulse imperfections are significantly attenuated.

An observation of light-induced drift (LID) of atoms with an intermediate metastable level between the ground and excited resonance levels is reported. The drift of atoms of barium was investigated. Molecular nitrogen was used as a buffer gas. The 5d ${}_{}{}^1{}_{}{}^{}$D metastable state of Ba atoms was quenched in collisions with ${\mathrm{N}}_2$ molecules. It has been deduced from the experimental results that the collision cross section of Ba atoms with ${\mathrm{N}}_2$ molecules is larger for Ba atoms in the ground state than in the 6p ${}_{}{}^1{}_{}{}^{}$P excited state. The maximal LID velocity was about 250 cm/s.

Two sets of coherent states of a two-level atom are constructed by the displacement-operator technique from the choices of the ground and excited states as the extremal state. Particular forms of both of these sets of coherent states are minimum-uncertainty states. Radiation-induced forces are determined for a two-level atom prepared in such coherent states. In geneal, these forces are affected by the presence of a second atom. For a minimum-uncertainty state, the force on a two-level atom is inedpendent of the state of the field. The significance of the calculations is discussed in relation to the pure atomic state occurring in the midst of the ‘‘collapse region’’ of the atomic inversion in the Jaynes-Cummings model. The existence of such a pure state may provide a possible means of experimentally generating two-level atomic minimum-uncertainty states.

The steady-state gain for a simple three-level atomic system has been analyzed. It is shown that lasing without population inversion between the lower excited state and the ground state can be established over a wide frequency range for probe field and driving field. With the same atomic system, a large refractive index with zero absorption can also be generated.

The nonclassical effects of radiation are defined to be when its P function [R. J. Glauber, Phys. Rev. Lett. 10, 84 (1963)] is not positive definite, and antibunching is defined to be when the conditional waiting time in the photodetection is longer than the unconditional one. Based on these two definitions, it is proven rigorously that antibunching implies nonclassical effects of cavity radiation detected externally by an imperfect detector.