With use of the coordinate representation of the one-mode squeeze operator, the coordinate representation wave function of the one-mode squeezed state is simply rederived. A parallel treatment for the two-mode squeeze operator yields the two-mode squeezed state wave function.

It was recently shown that large amounts of squeezing can be obtained in the Jaynes-Cummings model by choosing the initial photon number to be large enough. A general property of squeezed states can be used to derive the complementary result that for small initial photon numbers the squeezing that is produced will be relatively weak for all times. It also illustrates the fact that for some quantum effects to be substantial, large photon numbers are required.

It is shown that a mapping between the matrix elements of moments of the phase-related cos and sin operators C and S of the simple harmonic oscillator and the probabilities arising from random walks with absorbing boundaries may be established. Such a mapping may be used to calculate the expectation values of positive integer powers of the operators C and S. Using the power-series expansions for ${\sin }^{\mathrm{-}1}$ and (${\sin }^{\mathrm{-}1}$${)}^2$ the variance of the operator (${\sin }^{\mathrm{-}1}$S), when the oscillator is in a number state, is calculated.

A method is presented that yields exact closed-form solutions in curvilinear coordinates for the partial differential equations determining the electric field in a stationary flow of unipolar ions with constant mobility. The method is applied to the parabolic cylindrical, elliptic cylindrical, bipolar, parabolic, and spheroidal coordinates. The new solutions approach infinity roughly in the manner of the classical parallel-plate solution. They are expected to apply to analyses of non-self-sustained ion flows.

Recently, anisotropic anomalies in the damping and velocity of ultrasound near the smectic-A–hexatic-B liquid-crystal phase transition have been observed. By using generalized hydrodynamics we explain this anisotropy by an anisotropic, reversible dynamical coupling between the bond-orientational order parameter and elongational flow. It turns out that only in-plane elongational flow induces (critically) bond-orientational order at the phase transition, whereas flow perpendicular to the layers is inefficient.

The crossover modified-hypernetted-chain equation, extended to take into account three-body forces, is tested against recent simulation results for realistic models of krypton and xenon which include also the three-body Axilrod-Teller interaction $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$. The effect of $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ on g(r) is reproduced so well that this equation can also be used in the framework of inversion of structural data to separate the true two-body contribution out of the extracted effective potential. We also study the way $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ influences the critical point of the liquid-vapor phase transition for Ar, Kr, and Xe. We find that both ${\rho }_c$ and $T_c$ are lowered by $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ and that the small deviations from the law of corresponding states are as much due to $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ as to the different shape of the pair interaction.

Two-electron capture involving simultaneous transfer of an electron to the continuum (or to a Rydberg state) and a bound state has been investigated for collisions of 3.5 MeV/u ${\mathrm{Ne}}^{10+}$ with He, Ne, and Ar targets. The extent of this double capture to nonequivalent electron configurations is found to exceed expectations of the independent-particle model suggesting that electron correlation may contribute significantly to two-electron capture even in fast ($v\sim 10$ a.u.) collisions.

With the application of high-resolution laser spectroscopy to a molecular beam of CaF the Stark effect of individual rotational lines of the $A{}_{}{}^2{}_{}{}^{}\Pi -X{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ (603.7 nm) and $C{}_{}{}^2{}_{}{}^{}\Pi -X{}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ (330.8 nm) systems was measured. The electric dipole moments of the $A{}_{}{}^2{}_{}{}^{}\Pi$ and $C{}_{}{}^2{}_{}{}^{}\Pi$ states were determined as $\mu \left(A{}_{}{}^2{}_{}{}^{}\Pi \right)=2.45\mathrm{}\left(6\right)\mathrm{}$ D and $\mu \left(C{}_{}{}^2{}_{}{}^{}\Pi \right)=9.24\mathrm{}\left(17\right)\mathrm{}$ D. These extremely different values can be explained by the different polarization of the unpaired, ${\mathrm{Ca}}^{+}$-centered electron in the two electronically excited states. The main contributions to the two corresponding orbitals derive from the same ${\mathrm{Ca}}^{+}$ wave functions.

It has long been known that gain exists at the odd harmonics of a free-electron laser. Using a dispersive intracavity element to alter the cavity lengths for the fundamental and harmonic lasing, we have demonstrated harmonic lasing between 1.4 and 1.8 μm using the Stanford Mark III infrared free-electron laser. Gain at the third harmonic was seen to agree with theory to within experimental limits. The wavelength of the third harmonic was not quite equal to one third of the fundamental due to saturation and bandwidth effects. Power output was somewhat smaller than expected. This may have been due to losses in the optical transport system.

It is theoretically shown how a two-photon laserlike oscillator with strongly squeezed output can be constructed. The physical mechanism leading to squeezed laserlike oscillator is the strong competition among the nonlinear gain due to resonant four-wave mixing process, nonlinear losses due to the absorption of generated photons, and linear losses from the cavity. In the balanced case, the photon correlations result in a linewidth that is narrower than the Schawlow-Townes limit.

We report direct high-resolution observation of nonlinear steepened plasma waves excited in the wake of an intense, self-pinched electron beam. Oscillations in both accelerating and deflecting fields are measured, and analyzed in the context of linear and nonlinear plasma-wave theory. The degree of nonlinearity in the wake fields is shown to be consistent with analytical predictions of the beam self-pinching. The impact of these results on plasma acceleration and focusing schemes is discussed.

An incoherent multiple scattering model for Bragg scattering in the cholesteric blue phases is considered. it is shown that this mechanism can explain recent experimental results which appear otherwise to contradict the generalized selection rules applicable to Bragg reflections at optical wavelengths.

Crossed magnetic and electric fields were applied to the chiral liquid crystal p-decyloxybenzylidene-p’-amino-2-methyl- butylcinnamate (DOBAMBC) in the smectic-A phase in such a way as to maintain the director orientation normal to the smectic layers. Near the smectic-$C^{\mathrm{*}}$ transition it was found that E∝$H^2$ and that dE/${\mathrm{dH}}^2$ versus temperature exhibits behavior consistent with a temperature-dependent polarization-tilt coupling coefficient. This result offers an explanation for the anomalous electroclinic susceptibility exponent γ=1.11 observed by Garoff and Meyer [Phys. Rev. Lett. 38, 848 (1977)].

Measurements of the magnetic-field-induced birefringence are reported for the micellar system potassium laurate-1-decanol-${\mathrm{D}}_2$O in the vicinity of a Landau point on a nematic-isotropic transition line. The cubic coefficient of the Landau expansion for the isotropic phase changes sign with composition. In presence of the field the nematic-isotropic transition smooths out on one side of the Landau point, while on the other side a sharp transition from a uniaxial to a biaxial state persists.

A method is presented for the calculation of tight upper and lower bounds for the energy eigenvalues of the Schrödinger equation. The method is based on a rational functional approximation for the series expansion of the solution of the Riccati equation for the logarithmic derivative of the wave function. Specific applications for one-dimensional anharmonic oscillators and for the Yukawa potential are given, and the present results are compared with those obtainable by other procedures.

The M1 transition (γM1:2s-1s) may serve as a probe to observe parity-nonconserving effects in muonic atoms with an atomic number Z≤14. These atoms can be useful probes, if they are ionized of all but the two K-shell electrons and electron refilling does not occur. Our experiment shows that muonic neon, argon, and krypton atoms are highly ionized by the time the muon reaches the circular (n=5) state at pressures less than 1000 h Pa. The mean K-shell occupation numbers $N_K$¯ amount to 0.07≤$N_K$¯≤0.68, 0.04≤$N_K$¯≤0.38, and 0.76≤$N_K$¯≤0.84, respectively. For muonic neon at a pressure below 500 h Pa, electron refilling does not take place during the radiative lifetime of the 2s state (200 ps).

We address the problem of choosing an initial state and final measurement that enable maximal retrodiction of the result of an unknown intermediate spin measurement of a spin-(1/2 particle, along any one of a given set of directions. Details are given of the derivation of the most general possible solution of the problem, which we reported recently. The maximal retrodiction is shown to be the determination of the result of the intermediate spin measurement, along any of four different directions that span three-dimensional space and satisfy a specific linear relation.

The relation ξ=(1/2D${ħ}^{\mathrm{-}2}$ between the localization length ξ and the diffusion coefficient D of the kicked rotor is derived in the framework of the scaling theory for localization. It is argued that this relation, first found by Shepelyansky [Phys. Rev. Lett. 56, 677 (1986); Physica 28D, 103 (1987)], reveals the special importance of the Lloyd model for the understanding of the quantal behavior of the kicked rotor and other dynamical systems. The finite-size-scaling form of the localization length and the conductance of the Lloyd model are derived.