We examine a gedanken experiment described by Hardy, which purports to prove that the ‘‘elements of reality’’ corresponding to Lorentz-invariant observables cannot themselves be Lorentz invariant without violating quantum mechanics. We consider a number of criticisms of this proof and show that these criticisms are not convincing. We demonstrate that the contradiction, which arises in the gedanken experiment and forms the basis of Hardy’s proof, has nothing to do with realism, but is a consequence of the well-known noncovariance of the reduction postulate. A reexamination of the gedanken experiment, using a more appropriate formalism, helps to clarify its implications. We conclude with a brief appraisal of realist interpretations of quantum mechanics in the relativistic domain.

The nonlinear theory of stimulated Raman scattering of high-energy long laser pulses in two-level media is constructed and provides a unified global interpretation of the experiments of Drühl, Wenzel, and Carlsten [Phys. Rev. Lett. 51, 1171 (1983)]. It is proved that the model, resulting from the slowly varying envelope approximation and including phase mismatch and detuning from Raman resonance, is integrable by the spectral transform method for arbitrary boundary values. The essential variable in the theory is the phase of the Stokes pulse relative to the pump. For long duration input pump pulses and when pump and Stokes pulses experience a rapid π phase shift, an anomalous spike of pump radiation is created in the pump depletion zone. It is shown in particular that the decay of Raman spikes is related to the velocity of this π phase shift. For fast flips, the possibility of observing spike overflow is established and, with multiple phase flips, a multiple-spike phenomenon is produced, suggesting new experiments. Lastly, the number of optical phonons participating to the interaction is explicitly calculated.

We calculate the scale of the critical fluctuations in the quantum parametric oscillator at threshold. This allows us to calculate asymptotically the size of both the depletion of the pump mode and the amount of squeezing produced in the signal mode for large system size. In this driven, open quantum system, there is no known solution to the equilibrium density matrix. For this reason these results cannot be obtained using standard canonical ensemble methods. The calculations are compared to time dependent quantum stochastic simulations of the fully nonlinear coupled mode equations. We find that the critical squeezing variance in the output spectrum will scale as ${\mathit{N}}^{\mathrm{-}1/2}$, giving the feature that these fluctuations are reduced rather than enhanced near the critical point.

The use of liquid-crystal light valves (LCLV’s) as nonlinear elements in diffractive optical systems with feedback leads to the formation of a variety of optical patterns. The spectrum of possible spatial instabilities is shown to be even richer when the LCLV’s capability for polarization modulation is utilized and internal threshold and saturation effects are considered. We derive a model for the feedback system based on a realistic description of the LCLV’s internal function and coupling to a polarizer. Thresholds of pattern formation are compared to the common Kerr-type approximation and show transitions involving rolls, squares, hexagons, and tiled patterns. Numerical and experimental results confirm our theoretical predictions and unveil how patterns and their typical length scales can be easily controlled by changes of the parameters.

Raman interaction between two internal levels and its sideband cooling of a trapped ion or atom are investigated in copropagating traveling-wave light fields for localization beyond the Lamb-Dicke limit. Under certain conditions, only the first-order sideband excitations (‖n〉→‖n±1〉 with ‖n〉 being a Fock state) may play a significant role. This provides an experimental realization of the Jaynes-Cummings model with quantized center-of-mass motion beyond the Lamb-Dicke regime, which can be used to measure the statistics of the quantized motion, and thus to detect nonclassical states of motion. Moreover, the multichromatic two-photon Raman excitations of the trapped particle can be used for the preparation of coherent squeezed states of motion.

We study the effects of squeezed pump fluctuations in the degenerate parametric amplifier on signal squeezing. We find, both through semiclassical calculations and through several detailed analytic methods, that pump squeezing is responsible for two competing processes: Reduced pump phase fluctuations improve limitations to squeezing; at the same time, increased pump intensity fluctuations can lead to a ‘‘spillover’’ of pump fluctuations onto negative pump phases and a consequent reduction in signal squeezing.

The position-dependent mass Green’s function is connected to the constant-mass Green’s function by means of a time and space rescaling. Application is made for step and rectangular-barrier potentials and masses. Reflection and transmission coefficients are deduced from the continuity conditions.

A synchronously pumped passive ring resonator, containing an optical fiber as a nonlinear element, is studied experimentally and numerically. Period doubling cascades up to period 32 and chaos are observed in the sequence of pulse energies emerging from the resonator. We provide evidence that beyond this instability, individual pulses encounter an instability of their temporal profile. Pulse shapes develop a substructure that may be stationary, periodic, or chaotic. The full problem thus actually involves formation of a spatiotemporal structure. In contrast to many other spatiotemporal instabilities studied in optics, we deal here with strictly one-dimensional, longitudinal spatial structure.

The Coulomb explosion imaging method is used for the measurement of the vibrational state distribution of ${\mathrm{He}}_2^{+}$, under various conditions of excitation. Application of this method to the measurement of vibrational excitation of molecular ions stored in heavy-ion storage rings is discussed, especially in view of the recent results obtained for the dissociative recombination of molecular ions with electrons using a merged-beam technique in a storage ring.

We report here on a type of dichroism, which is zero order in the electric-field strength, in contrast to the well-known Pockels effect, which is first order, and the Kerr effect, which is second order. This dichroism appears in the energy gap between the classical ionization thresholds with and without field and is off resonant. A numerical calculation using the hydrogenic approximation shows that it should be possible to observe the effect experimentally.

A systematic study of semiclassical and quantum cross sections of l-resolved intercombination transitions in Rydberg atoms due to collisions with fast electrons is performed in the Ochkur approximation for principal quantum numbers n≤15 and all possible orbital numbers l and changes Δl. The semiclassical approach provides reasonable estimates for cross sections over the angular-momentum range up to l∼n/2. Intercombination transitions are shown to obey the ‘‘Bethe rule’’: at large l the transitions with n and l changing in the same direction dominate transitions with changes in opposite directions. It is also demonstrated that the more deeply inelastic the collision is, the higher the multipoles Δl that prevail in the total cross section. The semiclassical approach makes it possible to derive simple analytic formulas for cross sections with an explicit dependence on principal and orbital quantum numbers.

We show that the selective-state electron-capture cross sections to the level n=4 by multicharged ions colliding with H and He targets satisfy scaling rules derived from the eikonal impulse approximation. Partial capture cross sections for different bare projectiles are plotted together, and they compare quite well with recent selective experiments.

The collision velocity dependence of total (elastic plus radiative quenching) cross sections for metastable 2s state H atoms with Ar, Xe, and ${\mathrm{CCl}}_4$ has been measured in a crossed-beam experiment, in the velocity range between 4 and 40 km ${\mathrm{s}}^{\mathrm{-}1}$. Cross sections are obtained in well-controlled velocity and angular resolution conditions, allowing a meaningful comparison with theoretical calculations. The calculated cross sections, based on estimated potentials, are in good agreement with the experimental results and indicate that collisions in the present velocity range essentially probe the long-range van der Waals portion of both the ${\mathrm{H}}^{\mathrm{*}}$(2s) and ${\mathrm{H}}^{\mathrm{*}}$(2p) potentials with the target. Simple considerations indicate that previous low-resolution experiments underestimated the elastic component.

The electron-impact excitation cross section for the 1${\mathit{s}}^2$ 2s${(}^2$S)→1s2s2p${(}^4$P) transition in ${\mathrm{O}}^5$ has been calculated using the R-matrix method. Resonance contributions are found to increase the background cross section by factors of 2–5 in the 550–700-eV energy region when convoluted with a 1-eV full-width-at-half-maximum Gaussian profile. When convoluted with the Compton profile for ${\mathrm{H}}_2$, however, the difference between the background and resonance enhanced cross sections is less than 5% near the peak. Thus, experiments involving collisions of ${\mathrm{O}}^{5+}$ ions with ${\mathrm{H}}_2$ targets shed little light on the resonance scattering dynamics found in the near-threshold energy region.

We have measured the longitudinal nuclear relaxation rate ${\mathit{T}}_1^{\mathrm{-}1}$ for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the presence of molecular oxygen in the temperature range T≊200–400 K. At room temperature, ${\mathit{T}}_1^{\mathrm{-}1}$=0.448±0.010 ${\mathrm{s}}^{\mathrm{-}1}$ per amagat ${\mathrm{O}}_2$, in approximate agreement with theoretical models for intermolecular dipolar relaxation. Furthermore, in this temperature range, ${\mathit{T}}_1^{\mathrm{-}1}$∝${\mathit{T}}^{\mathrm{-}0.42\pm 0.04}$. Our results are of practical importance for the growing number of applications involving hyperpolarized noble gases.

This paper shows that a classical electron may get trapped within the field of two atomic nuclei even though it is free, i.e., the total energy of the electron is greater than that at large distances from the attractive centers. The consequences of this phenomenon for the emission of high-energy electrons during slow-atom bombardment of solids are discussed.

In order to investigate a discrepancy between existing literature values for the normalization constant in the asymptotic form of three-body wave functions for (dtμ${)}^{+}$, we report the results of a calculation of the normalization constants for this system as well as the related system (ddμ${)}^{+}$. These were obtained by fitting to accurate variational wave functions with special care being taken to describe the long-range (tμ)+d or (dμ)+d behavior. The implications of this reevaluation of the normalization constants are discussed in relation to the theoretical formation rates of molecules such as (dtμ)dee and (ddμ)dee, which are key intermediates in the muon-catalyzed fusion cycle.

An explicit and reasonable definition of the quantum soliton states in optical fibers is given. Based on this definition we construct the quantum soliton states from the exact solution of the quantum nonlinear Schrödinger equation. The dispersion effect of the quantum soliton is also exactly analyzed.

We investigate asymmetric stimulated photorefractive scattering (fanning) in the framework of a two-dimensional model, based on the solution of nonlinear material equations and parabolic equations for electromagnetic radiation. We focus on the spatial distribution of electromagnetic fields and the nonlinear refractive index generated by fanning. In the region of developed fanning the structure of the refractive index corresponds to regions of relatively smooth index with abrupt transitions between them. These transitions trace lines of zero field.

A generalization of the transition radiation rate given by Glauber and Lewenstein, taking into account interference effects, is presented.