We propose an experiment to look for possible small violations of the symmetrization postulate of quantum mechanics, in systems composed of three identical particles. Such violations could be detected by investigating the population of particular rotovibrational states of symmetrical molecules containing three identical nuclei. We discuss the symmetry properties of such states, and the implications of the symmetrization postulate and the spin statistics connection. A high-sensitivity spectroscopic investigation of simple molecules such as ${\mathrm{SO}}_3,$ ${\mathrm{BH}}_3,$ and ${\mathrm{NH}}_3$ could lead, to our knowledge, to the first test of the symmetrization postulate for spin-0 and spin-1/2 nuclei.

We implemented the refined Deutsch-Jozsa algorithm on a three-bit nuclear magnetic resonance quantum computer. All of the balanced and constant functions were realized exactly. The results agree well with theoretical predictions and clearly distinguish the balanced functions from constant functions. Efficient refocusing schemes were proposed for the soft z pulse and J coupling, and it is shown that the thermal equilibrium state gives the same answer as the pure state for this algorithm.

In this paper we recall the description of molecular spectral staggering in terms of transition energies between neighboring rotational states and then describe the fitting procedure used to derive these energies from available experimental data, making use of theoretical models involving both Dunham-type expansions and q-deformed rotators. Using this procedure, we investigate $\Delta J=2\mathrm{}$ staggering in a few rotational bands of the homonuclear iodine molecule and analyze the quasiperiodic patterns that appear from the lowest to the highest values of angular momentum J. In addition to parity splitting, these patterns disclose a supershell structure involving magic numbers formally similar to those occurring in atom clusters. We propose to relate molecular staggering to tiny oscillations in the electron-level density induced by the rotating nuclear frame.

Antiproton $\left(\overline{p}\right)$ and negative muon $\left({\mu }^{-}\right)$ captures by helium and neon atoms are treated using the fermion- molecular-dynamics method, yielding capture cross sections, initial quantum numbers, and ejected-electron energies. The calculated angular-momentum distributions tend to pile up at $l=n-1$ and are not well fitted by the form ${\mathrm{}(2l+1)e}^{\alpha l},$ which is often assumed in experimental analyses. The residual electrons are generally left in a “shake-up” state. When capture is accompanied by multiple ionization, the second and later electrons escape with increasing kinetic energies, a process that is not well described as quasiadiabatic. In a 50:50 mixture of helium and neon, the calculated Ne:He capture ratios are 3.36 for $\overline{p}$ and 3.69 for ${\mu }^{-}.$ The ${\mu }^{-}$ per-atom capture probability is almost independent of the neon fraction and is in overall agreement with several ${\mu }^{-}$ and ${\pi }^{-}$ experiments; for $\overline{p}$ there is a rather strong dependence on neon fraction, but there are as yet no experiments. The possible experimental indication of a strong isotope effect on capture of ${\pi }^{-}$ in mixtures of ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ is not supported by the present calculation.

We study the analytic properties of the functions known as C3 and ${\Phi }_2,$ used in atomic collision theory for the description of the three-body continuum state. We analyze the bound states for both models obtained by analytic continuation in the case of ion-atom collision. The C3 wave function is an uncorrelated model represented by the product of two-body Coulomb functions and the bound states are found for negative relative energies of electron-target or electron-projectile pairs. On the other hand, the ${\Phi }_2$ model is based on a two-variable hypergeometric function that correlates the electron motion relative to both the target and projectile. We found that only decaying bound states are allowed and the atomic spectra becomes continuous. The bound states of the ${\Phi }_2$ model have a complex energy due to the action of the projectile. Expressions for the wave functions in the different thresholds are given and studied.

Using a crossed-beam method, we have measured electron energy-loss spectra for excitation of the Herzberg pseudocontinuum of molecular oxygen. The scattering angle and electron-impact energy ranges covered were from 12° to 156° and from 10 to 30 eV, respectively. We decomposed the spectra into contributions from three superposed Gaussian line shapes by means of computerized least-squares analysis. The three line shapes were identified as representing excitation of the $A{}^3{\Sigma }_u^{+},$ $A^{\prime }{}^3{\Delta }_u,$ and $c{}^1{\Sigma }_u^{-}$ states. Absolute differential and integrated cross sections for all three states’ excitations were obtained, along with linear electronic potential-energy curves for the Franck-Condon region.

Polarization degrees of lines emitted by ${\mathrm{Kr}}^{7+}$ excited ions produced by single-electron capture during ${\mathrm{Kr}}^{8+}+\mathrm{Li}\mathrm{}\left(2s\right)\mathrm{}$ collisions were experimentally measured for projectile energies between 0.1 and $2.5$ ${\mathrm{keV}\mathrm{}\mathrm{amu}}^{-1}.$ They were compared with theoretical polarization degrees obtained from $n\mathcal{l}{m}_{\mathcal{l}}$ distributions calculated by using the classical trajectory Monte Carlo (CTMC) method; radiative cascades have been included in the calculations. The fair agreement between experimental and calculated polarization degrees confirms the reliability of the CTMC method and allows one to analyze the $m_{\mathcal{l}}$ distributions in terms of dynamical couplings responsible for the state-selective electron capture process.

Close-coupling calculations are performed on the photodetachments of the metastable ${\mathrm{nsnp}}^2$ ${}^{4}P$ states of the negative beryllium $\mathrm{}(n=2\mathrm{}),$ magnesium $\mathrm{}(n=3\mathrm{}),$ and calcium $\mathrm{}(n=4\mathrm{})\mathrm{}$ ions by using the R-matrix method. The calculations are carried out with the consideration of excitations of one electron from core. The results show that this effect is much more important for ${\mathrm{Ca}}^{-}$ than for ${\mathrm{Be}}^{-}$ and ${\mathrm{Mg}}^{-}.$ For ${\mathrm{Be}}^{-},$ the total and partial cross sections are obtained from the threshold to a photon energy of 0.5 Ry. The calculated total cross section exhibits two ${}^4{P}^o$ Feshbach resonances and one ${}^4{D}^o$ shape resonance. Close agreement is found with the available theoretical calculations and the only experimental datum of Pegg and co-workers [Phys. Rev. A 50, 3861 (1994)]. For the ${\mathrm{Ca}}^{-}$ and ${\mathrm{Mg}}^{-}$ ions, the total and partial cross sections are calculated from the threshold to a photon energy of 0.25 Ry. For the ${\mathrm{Ca}}^{-}$ ion, the resonances are found for both ${}^4{P}^o$ and ${}^4{D}^o$ symmetries just below the ${}^{3}D$ threshold. For the ${\mathrm{Mg}}^{-}$ ion, only a ${}^4{P}^o$ resonance is predicted. No rapid increase associated with the opening of the $4s5s{\hspace{0.5em}}^{3}S$ channel is found in the total cross section of ${\mathrm{Ca}}^{-}.$ The rapid increase of the photodetachment cross section of ${\mathrm{Ca}}^{-}$ in the experiment by Hanstorp et al. [D. Hanstorp et al., Phys. Rev. Lett. 63, 368 (1989)] should not be attributed to the ${\mathrm{Ca}}^{-}{(4s4p}^2{}^{4}P)+h\overrightarrow{\nu }\mathrm{Ca}(4s5s{}^{3}S)+kp$ ionization process. This result is consistent with the conclusion of Petrunin and co-workers [Phys. Rev. Lett. 76, 744 (1996)] that there was no ${\mathrm{Ca}}^{-}$ ${(4s4p}^2{}^{4}P)$ ions observed by Hanstorp et al.

We have measured the single $K-K$ electron-transfer cross sections along with the single K-shell ionization cross sections of Ar induced by H-like and bare C,O, and F projectiles, and of Kr by F, S, and Cl ions in the energy range 1.5–6 ${\mathrm{MeV}\mathrm{}\mathrm{u}}^{-1}.$ The target x-ray yields as a function of the number of K shell vacancies in the incident beam were used to derive the K ionization cross sections of the targets and the $K-K$ (i.e., target K shell to projectile K shell) electron-transfer cross sections. The enhancement in the fluorescence yield due to multiple vacancies in the target atom was deduced from the energy shifts and intensity ratios of the characteristic x-ray lines to derive vacancy production cross sections from the measured x-ray production cross sections. The energy shifts of K x-ray lines were found to be dependent on the incident charge states of the projectiles. Continuum-distorted-wave eikonal-initial-state calculations are found to underestimate the ionization cross-section data in general, and the deviations are most pronounced for Kr. Perturbed stationary-state calculations, including corrective terms due to energy loss, Coulomb deflection, and relativistic wave function, agree with the data only for asymmetric collisions ${(Z}_1{/Z}_2<~0.4),$ and largely overestimate for relatively symmetric systems. The $K-K$ electron-transfer cross sections are well reproduced by the two-center close-coupling calculations for both targets except, for the asymmetric collisions. The perturbed stationary state (PSS) calculations of Lapicki and McDaniel are also used to explain the $K-K$ electron-transfer data for the asymmetric systems. In addition, the $K-L$ electron-transfer cross sections are also measured for S and Cl ions on Kr, and compared with the PSS calculations.

A recent experiment [Deng et al., Nature (London) 398, 218 (1999)] demonstrated four-wave mixing of matter wave packets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wave packets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low-momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum- mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this formulation to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum, and energy conservation (i.e., phase matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.

A Langevin equation for the complex amplitude of a single-mode Bose-Einstein condensate is derived. The equation is first formulated phenomenologically, defining three transport parameters. It is then also derived microscopically. Expressions for the transport parameters in the form of Green-Kubo formulas are thereby derived and evaluated for simple trap geometries, a cubic box with cyclic boundary conditions, and an isotropic parabolic trap. The number fluctuations in the condensate, their correlation time ${\tau }_c,$ and the temperature-dependent collapse time of the order parameter as well as its phase-diffusion coefficient are calculated.

The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is switched on. It is followed by an asymptotic, monochromatic wave which at long times reveals the oscillation frequency of the source. For a source with a sharp onset the forerunner is exponentially larger than the monochromatic solution and a transition from the transient regime to the asymptotic regime occurs only at asymptotically large times. In this case, the traversal time for tunneling already plays a role only in the transient regime. To enhance the monochromatic solution compared to the forerunner we investigate (a) frequency-band-limited sources and (b) the short-time Fourier analysis (the spectrogram) corresponding to a detector which is frequency band limited. Neither of these two methods leads to a precise determination of the traversal time. However, if they are limited to determine the traversal time only with a precision of the traversal time itself both methods are successful: In this case the transient behavior of the evanescent waves is at a time of the order of the traversal time followed by a monochromatic wave which reveals the frequency of the source.

The work of Meyer, Scully, and Walther [Phys. Rev. A 56, 4142 (1997)] is generalized to study the operation of a two-mode mazer with particular reference to the question of mode-mode correlations. The explicit expression for the detailed balance steady-state photon distribution has been derived. It is shown that the two-mode mazer exhibits much stronger sub-Poissonian statistics for each mode. The photon-number distributions are found to be quite sensitive to the presence of blackbody photons in the cavity. The interferences among contributions from different dressed states enable one to obtain the phase of the transmission amplitude of finding the atom in the initial excited state by considering a set of two measurements involving two different initial states of the atom-field system.

We utilize the generation of large atomic coherence in optically dense media to enhance the resonant nonlinear magneto-optic effect by several orders of magnitude, thereby eliminating power broadening and improving the fundamental signal-to-noise ratio. A proof-of-principle experiment is carried out in a dense vapor of Rb atoms. Applications such as optical magnetometry, the search for violations of parity and time-reversal symmetry, and nonlinear optics at low light levels are feasible.

We experimentally investigate the evolution of the transverse spatial coherence of light as it traverses a random, multiple-scattering medium. For near-forward scattering, it has been proposed that the wave-transport process can be well described by a transport equation for the spatial-angular Wigner function of the light, or equivalently for the two-point spatial coherence function (mutual intensity). We find good agreement between the wave-transport theory and our experimental results for media of different thickness. In a dense medium (for example, optical distance, or density, greater than 5), the nature of the scattered light field can be qualitatively described by a complex Gaussian-Schell model, which raises an interesting interpretation about the process of long-path optical transport.

For mixed states of a pair of spin-1/2 particles, the positivity of the sum of the conditional linear entropies is a sufficient condition for the nonviolation of the Bell-CHSH (Clauser-Horne-Shimony-Holt) inequalities.

We show that atoms from a wide velocity interval can be concurrently involved in Doppler-free two-photon resonant four-wave mixing that is far from being frequency dependent, with the aid of an auxiliary electromagnetic field. This gives rise to substantial enhancement of the output radiation generated in an optically thick medium. Numerical illustrations of typical experimental conditions are given.

We suggest a method to test the premise of “macroscopic local realism” that is sufficient to derive Bell inequalities when measurements of photon numbers are only accurate to an uncertainty of order n photons, where n is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy “elements of reality” that have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of macroscopic local realism. Quantum states violating this macroscopic local realism are presented.

Starting from the postulate that the electromagnetic field appearing in the transverse set of microscopic Maxwell-Lorentz equations governing field-matter interactions, properly normalized, can be looked upon as describing one-photon-emission and -absorption processes in space and time, a first-quantized initiation of photon emission by a single atom is presented. The wave function for the emerging photon is introduced as a six-vector object constructed from the complex analytical signals of the Riemann-Silberstein vectors belonging to opposite photon helicities. When the atom is no longer electrodynamically active, the emitted photon is described in first quantization by the so-called energy wave function well known for photons in free space. From the momentum representation of the emerging photon wave function a condition on the analytical part of the transverse atomic current density is established which ensures that precisely one photon is emitted. A propagator description of the emerged photon dynamics in the coordinate representation is established. The photon propagator is introduced as a two-component spinor, where upper and lower tensor components are constructed, respectively, from positive and negative helicity combinations of the propagators describing the time-space evolution of the transverse electric and magnetic fields. It is shown that the emission region for the photon coincides with the region in space where the transverse atomic current density is nonvanishing. For a photon emitted in an electric dipole transition the emission region essentially is the near-field zone of the atom, and this zone therefore determines the initial (and best) spatial confinement of the photon. The photon emerging from an atom active for a finite time necessarily is of the polychromatic sort and the associated wave packet essentially is confined between spherical shells moving outwards with the vacuum speed of light. To illustrate the main principles of the fundamental theory in a heuristic fashion we apply it to a study of the emission of a one-photon sinusoidal wavetrain from a pointlike atom. It is found that the atomic current density needed to create just one photon is independent of the oscillation period in the train and thus depends only on the number of periods in the wave train. An explicit expression for the one-photon energy is derived, and it is shown that only for extremely short pulse trains pronounced deviations from the textbook result, $E=ħ{\omega }_0,$ occur. The radial energy flow in the coupled atom-photon system in the near-field zone of the atom is investigated, and the cycle-averaged outwards energy transport carried by the emerging photon in a given distance from the atom is determined.

A high-precision calculation of the $7s-8s$ parity-nonconserving (PNC) transition amplitude in francium, based on a relativistic all-order method, is presented. Our values for the PNC amplitudes in ${}^{223}\mathrm{Fr}$ and ${}^{210}\mathrm{Fr}$ are $E_{\mathrm{PNC}}=15.41\mathrm{}\left(17\right)\mathrm{}$ and $14.02\left(15\right),$ respectively, in units ${10}^{-11}i|e|a_0(-Q_W/N),$ where $Q_W$ is the weak charge and N is the neutron number. Spin-dependent contributions to the PNC amplitude are calculated for Fr isotopes with nucleon numbers $A=207,$ 209, 211, and 213. To assess the accuracy of our calculations, we apply the present all-order method to the $6s-7s$ PNC amplitude in cesium and obtain a result in close agreement with previous high-precision calculations.