The cross-section ratio for double-to-single ionization has been investigated for collisions of 95-MeV/amu ${\mathrm{N}}^{7+}$ with He and Li target atoms. The measured values for Li and He are equal within the experimental uncertainties. First-order perturbation theory suggests that double ionization of Li is dominated by electron-nuclear interaction, whereas double ionization of He is dominated by electron-electron interactions such as shake-off and initial-state correlation. First-order perturbation theory can describe the ratio of double to single ionization of ${\mathrm{N}}^{7+}$+Li at 95 MeV/amu within the experimental uncertainties.

We have observed rectified dipole forces acting on three-level atoms in the cascade configuration. Laser cooled and trapped rubidium atoms are illuminated with an intense bichromatic standing wave (780 and 776 nm) tuned near resonance with the 5${\mathit{S}}_{1/2}$→5${\mathit{P}}_{3/2}$→5${\mathit{D}}_{5/2}$ transitions. The resulting rectified forces produce periodic potential wells (71-μm period), which localize the cold atoms. Experimental results are in reasonable agreement with theoretical predictions. These forces may be useful in atom optics and laser traps.

Collisional loss rates of ultracold atoms in a laser trap (formed by red-detuned laser beams) can be suppressed by using a sufficiently intense blue-detuned optical shielding laser to repel the atoms before they collide. We present calculations that reveal an additional mechanism for collisional loss in the presence of a blue-detuned laser that reduces optical shielding as the blue-detuned laser intensity increases, and even causes enhancement of collisional loss effects with increased blue-detuned intensity. This mechanism can strongly affect the saturation of the optical shielding.

Using a multichannel bound-state method we predict the highest bound states of the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ diatom system, which are closely related to the collisional behavior of ultracold atoms. The results agree well with a model where the hyperfine interaction is treated in first-order perturbation theory, except for the triplet level closest to the continuum, which we predict to be very weakly bound. This level is responsible for the large, positive scattering length of the ${\mathit{m}}_{\mathit{f}}$=±f states of the lower hyperfine manifold. Its experimental observation would confirm our prediction of a stable Bose condensate.

We report the observation of amplification of an xuv harmonic pulse in an xuv laser. The 21st harmonic of a frequency-doubled 1.3-psec neodymium chirped-pulse-amplification laser pulse was injected into the gain region of an 18-mm-long Ga XXII x-ray amplifier. A gain of approximately 3 was recorded for the 21st harmonic, relative to the unamplified 19th and 23rd harmonics when the harmonic wavelength was tuned to overlap the 25.11-nm J=2–1 laser transition.

We report a spatially resolved investigation of lasing on the 3p${\mathrm{}}^1$${\mathit{S}}_0$–3s${\mathrm{}}^1$${\mathit{P}}_1$ transition in neonlike ions ranging from titanium (Z=22) to germanium (Z=32). Slab targets were irradiated by the Asterix IV iodine laser at an intensity of about 2.0×${10}^{13}$ W/${\mathrm{cm}}^{\mathrm{-}2}$ with a prepulse 5.23 ns before the main pulse. The lasing position was measured as a function of the prepulse energy and the atomic number. It was found that with higher Z, the lasing occurs closer to the target surface and a larger prepulse brings the lasing farther away from the target. A 15% prepulse was found to be favorable for low-Z elements (such as titanium), while a 1.5% prepulse was found to be favorable for elements with Z higher than 26. A simple model taking into account the self-similar expansion of the plasma produced by the prepulse was found to agree qualitatively with the experimental results.

We study experimentally and numerically the influence of the fiber length on the stability of Brillouin lasers in both ring cavity and Fabry-Pérot configurations. For short enough fibers, experiments and numerical simulations show that the Brillouin emission is stable for any input pump power. This behavior, in contrast with that previously observed on long fibers, is interpreted within the framework of a modal analysis. Further experiments, involving a sweeping of pump frequency, emphasize the role of the frequency detunings, which was generally overlooked.

Second-harmonic generation from a subwavelength-thick Langmuir-Blodgett film of 2-docosylamine-5-nitropyridine is used to construct an effective dipole oscillator that radiates symmetrically in the forward and backward directions. We observe enhancement and suppression of the radiation at the second-harmonic frequency, which is achieved by using a reflecting boundary to modify the optical modes available to the dipole radiator.

We show that Bell’s-inequality experiments can be carried out using four harmonic oscillators, pairs of which interact with each other at suitable instants of time to allow for the exchange of energy. Between interactions, the oscillators are shifted in phase relative to each other in a controllable manner. Energy becomes distributed among the four harmonic oscillators in a manner that is incompatible with a local realism picture in which information is exchanged only when the oscillators interact with each other. Entanglement is dynamically generated from an initial product state.

We invert the well-developed strategy of studying dynamics in terms of probability densities and investigate the problem of the most likely microscopic propagation scenario, which is consistent with the given priori (possibly phenomenological) input-output statistics data for the process taking place in a finite-time interval. A solution of this so-called Schrödinger problem is known to provide an adequate probabilistic framework for the measure preserving dynamics which is Markovian. We pay particular attention to the subclass of nonstationary solutions, determined by unitary-wave-packet evolution (Schrödinger wave mechanics). The existence of the pertinent Markovian diffusion is known on general grounds, but no explicit demonstration (through detailed computational arguments) until now was available even in the simplest cases. We give a definitive probabilistic description of the free quantum dynamics as a stochastic process solving Schrödinger’s interpolation problem. The Markov diffusion arised as a particular case singled out by a suitable Feynman-Kac semigroup.

Many-body perturbation theory in the screened Coulomb interaction was used to calculate energy levels, E1 trransition amplitudes, and the parity-nonconserving (PNC) E1 amplitude of the 7s-8s transition in francium. The method takes into account the core-polarization effect, the second-order correlations, and the three dominating sequences of higher-order correlation diagrams: screening of the electron-electron interaction, particle-hole interaction, and the iterations of the self-energy operator. The result for the PNC amplitude for ${}_{}{}^{223}{}_{}{}^{}\mathrm{Fr}$ is E1(7s-8s)=(1.59±∼1%)×${10}^{\mathrm{-}10}$${\mathit{iea}}_{\mathit{B}}$(-${\mathit{Q}}_{\mathit{W}}$/N), where ${\mathit{Q}}_{\mathit{W}}$ is the weak charge of the nucleus, N=136 is the number of neutrons, e=‖e‖ is the elementary charge, and ${\mathit{a}}_{\mathit{B}}$ is the Bohr radius. Our prediction for the position of the 8s energy level of Fr, which has not been measured yet, is 13 110 ${\mathrm{cm}}^{\mathrm{-}1}$ below the limit of the continuous spectrum. The accuracy of the calculations was controlled by comparison with available experimental data and analogous calculations for cesium. It is estimated to be ∼0.1% for the energy levels and ∼1% for the transition amplitudes.

Gutzwiller’s trace formula yields the exact quantum-mechanical single-particle level density in two- and more-dimensional harmonic-oscillator potentials with irrational frequency ratios, where only isolated stable periodic orbits exist. By analytical continuation, the results are shown to hold also for oscillators with commensurable frequencies and with continuous symmetries, where most classical orbits are degenerate; the divergences of the trace formula occurring in these cases are shown to cancel exactly. In the two-dimensional case, we give a closed formula for the Maslov index that does not repeat itself in succesive periods.

We study the Wigner-Araki-Yanase theorem by utilizing a slightly modified version of a formulation recently proposed by Ozawa [Phys. Rev. Lett. 67, 1950 (1991)]. After characterizing the quantities that are conserved in the evolution of the total system (object plus apparatus), we suitably decompose the Hamiltonian and show that the Wigner-Araki-Yanase theorem can be formulated in terms of the conserved quantities of the object system and of some observables of the apparatus. A few examples clarify our general arguments.

An approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=${\mathit{Ax}}^6$+${\mathit{Bx}}^2$ is introduced, starting from particular analytic solutions which are valid when certain relations between the parameters A and B are held.

Classical and quantum (semiclassical) theory of the radiation reaction interaction is applied to the harmonic oscillator. Spontaneous emission is analyzed and it is shown that both approaches give the same result. The energy shift of bound states is described.

Coincidence detections are measured between the output ports of a beam splitter whose input is an orthogonally polarized two-photon state produced in type-II spontaneous parametric down-conversion. When the delays between the two optical paths leading to each detector are varied by two spatially separated Pockel cells, a two-photon interference effect is seen that highlights a simultaneous entanglement in both spin and space-time variables. In contrast to all previous experimental tests of Bell’s in- equalities, which have utilized states entangled with respect to only one type of observable, the double entanglement realized here allows the demonstration of two different types of Bell inequality violations in one experimental setup.

Exact N-body solutions for the harmonic oscillator and lower bounds provided by the equivalent two-body method are used as basis results for an application of spectral geometry. It is proved that the relative energy scrE of a system of N identical particles interacting by the attractive pair potential ${\mathit{V}}_0$f(r/a) and obeying nonrelativistic quantum mechanics is given approximately by the expression E≊${\min }_{\mathit{r}>0\mathrm{}}${K(N)/${\mathit{r}}^2$+vf(r)}, where E=(${\mathit{mscrEa}}^2$)/(N-1)${\mathrm{ħ}}^2$ and v=${\mathit{NmV}}_0$${\mathit{a}}^2$/2${\mathrm{ħ}}^2$. A table of K numbers is provided for bosons and fermions (with arbitrary spin) in one and three dimensions. If the potential shape f(r) is a convex function of -1/r and a concave function of ${\mathit{r}}^2$, then the approximations yield both upper and lower energy bounds. Detailed results are given for the case of gravitating fermion systems.

A one-dimensional massless scalar field coupled to a dispersive mirror models a jellium sheet coupled to electromagnetic waves propagating along the normal. The quantum radiation emitted when the mirror moves [with velocity β(t)] exerts a reactioin force F. For β≪c, perturbation theory yields, without appeal to cutoffs or to regularization, the delayed response function ${\mathit{G}}_{\mathit{q}}$ of the mean-field momentum 〈q〉 to β and thence 〈F〉=-d〈q〉/dt. A finite inertial-mass shift is absorbed by renormalization. Alternatively, the Fourier transform of ${\mathit{G}}_{\mathit{q}}$ can be determined, up to renormalization, through its dispersion representation; the requisite input is its imaginary part, supplied via the fluctuation-dissipation theorem by the fluctuations of the force on a stationary mirror. Unfortunately, without stepping outside a strictly local theory, one cannot define a useful response function linking 〈F〉 directly to β.

A goal of quantum-mechanical models of the computation process is the description of operators that model changes in the information-bearing degrees of freedom. Iteration of the operators should correspond to steps in the computation, and the final state of halting computations should be stable under iteration. The problem is that operators constructed directly from the process description do not have these properties. In general these operators annihilate the halted state. If information-erasing steps are present, there are additional problems. These problems are illustrated in this paper by consideration of operators for two simple one-step processes and two simple Turing machines. In general the operators are not unitary and, if erasing steps are present, they are not even contraction operators. Various methods of extension or dilation to unitary operators are discussed. Here unitary power dilations are considered as a solution to these problems. It is seen that these dilations automatically provide a good solution to the initial- and final-state problems. For processes with erasing steps, recording steps must be included prior to the dilation, but only for the steps that erase information. Hamiltonians for these processes are also discussed. It is noted that H, described by exp(-iHΔ)=${\mathit{U}}^{\mathit{T}}$, where ${\mathit{U}}^{\mathit{T}}$ is a unitary step operator for the process and Δ a time interval, has complexity problems. These problems and those noted above are avoided here by the use of the Feynman approach to constructing Hamiltonians directly from the unitary power dilations of the model operators. It is seen that the Hamiltonians so constructed have some interesting properties.

Using a two-photon interference technique, we measure the delay for single-photon wave packets to be transmitted through a multilayer dielectric mirror, which functions as a ‘‘photonic band-gap’’ medium. By varying the angle of incidence, we are able to confirm the behavior predicted by the group delay (stationary-phase approximation), including a variation of the delay time from superluminal to subluminal as the band edge is tuned toward the wavelength of our photons. The agreement with theory is better than 0.5 fs (less than one-quarter of an optical period) except at large angles of incidence. The source of the remaining discrepancy is not yet fully understood.