Electron-energy-loss spectra of ${\mathrm{CO}}_2$ in the region of C $1s$ and O $1s$ excitations have been recorded over a wide range of momentum transfer (K), $(2\mathrm{}{\mathrm{a}.\mathrm{u}.\mathrm{}}^{\mathrm{-}2}<K^2<70\mathrm{}{\mathrm{a}.\mathrm{u}.\mathrm{}}^{\mathrm{-}2}).\mathrm{}$ The dipole-forbidden transition to the $(\mathrm{C}1s\hspace{0.5em}{\sigma }_g^{-1},{\sigma }_g^{*})$ ${}^1{\sum }_g^{+}$ state in ${\mathrm{CO}}_2$ is detected for the first time, to our knowledge. A detailed analysis, with careful consideration of minimization of systematic experimental errors, has been used to convert the measured relative cross sections to absolute, momentum-transfer-dependent, generalized oscillator strength (GOS) profiles for all resolved C $1s$ and O $1s$ transitions of ${\mathrm{CO}}_2.$ Theoretical results for the GOS, computed within the first Born approximation, were obtained with ab initio configuration interaction wave functions for the C $1s$ transitions and with ab initio generalized multistructural wave functions for the O $1s$ transitions. These wave functions include relaxation, correlation, and hole localization effects. Theory predicts large quadrupole contributions to the GOS for O $1s$ excitations. In addition the computed GOS for O $1\overrightarrow{s}\mathrm{ns}\sigma$ and $\mathrm{np}\sigma$ Rydberg states clearly show oscillations arising from interference between localized core excitations. Overall there is good agreement between the experimental and theoretical results, indicating that the first Born approximation holds to a surprisingly large momentum transfer for the core excitations studied.

A theoretical perspective of high-order harmonic generation is presented in which transitions between quantum Volkov states—stationary solutions to Schrödinger’s equation for an electron interacting with a quantized optical field—are the dominant mechanism for producing radiation. The picture proposed here is one in which the interaction of an intense optical field with an electron forms a photon-electron “quasiatom” and the stationary states of this complex can be viewed as the high optical field analog of bound states of an atom. Consequently, although momentum conservation for the overall harmonic generation process requires that an electron eventually return to the parent atom, the electron and fundamental optical field are treated as an isolated system with well-defined energy and momentum. To introduce a secondary photon (harmonic) field, the matrix element describing the electron-photon field interaction through quantum Volkov states is modified in a perturbative manner. The result is the production of harmonic photons by Volko$\overrightarrow{\mathrm{v}}$Volkov-state transitions, a process which has no classical counterpart. The generation of odd harmonics of the fundamental field and the requirement that the final state of the electron be the initial bound state of the atom follow directly from the theory. A clear connection between harmonic generation and above-threshold ionization (ATI) is drawn by maintaining the discrete, nonzero energies of photoelectrons injected into the driving optical field by ATI. For experiments in which the laser pulse width is ≳100–150 fs, only the lowest ATI photoelectron orders contribute significantly to harmonic generation, whereas higher-energy electrons escape from the parent atom during the pulse risetime. As the duration of the fundamental field is decreased, however, the rapid rise of the field intensity to its peak value effectively traps more energetic photoelectrons, thereby extending the harmonic response to shorter wavelengths. An analytic expression for the transition matrix for the harmonic generation process is derived and is compared with the predictions of semiclassical theory and published experimental results, including harmonic spectra and polarization data.

Relativistic configuration-interaction length and velocity lifetimes have been obtained for ${3s3p}^2$ $J=1/2,$ 5/2 levels in ${\mathrm{Au}}^{66+}$ and ${\mathrm{Br}}^{22+}.$ Results from the two gauges agree well, and we have moderately improved earlier multiconfigurational Dirac-Fock results, as compared to experiment. However, there remains a discrepancy for the ${\mathrm{Au}}^{66+}J=5/2\mathrm{}$ lifetime, which may be due to satellite spectra associated with $5g$ and other spectator electrons.

We show that the quantum phase of continua can be directly determined utilizing the phase of linearly/circularly polarized lasers. With this method the phase difference of continua with opposite as well as same parities can be obtained from the phase lag of the angle-resolved photoelectron signal with respect to the relative phase of lasers. For illustration, the proposed method is specifically applied to the Na atom.

We demonstrate an atomic-beam approach to obtaining isotope specific driven-atom spectra using samples of arbitrary isotopic composition. The method employs modulation of a target isotope ground-state population by an upstream preparation laser. Desired driven-atom signals generated downstream from the preparation laser are isolated using a lock-in amplifier referenced to the preparation laser modulation frequency. In our experiments, an intensity-modulated laser resonant with the barium ${(6s}^2{)}^1{S}_0{-\left(6s6p\right)\mathrm{}}^3{P}_1$ 791.1-nm intercombination transition selectively pumps ${}^{138}\mathrm{Ba}$ atoms via radiative decays to the ${\mathrm{}\left(6s5d\right)\mathrm{}}^3{D}_{1,2}$ metastable states. Dressed-atom gain studies using the ${(6s}^2{)}^1{S}_0{-\left(6s6p\right)\mathrm{}}^1{P}_1$ 553.5-nm transition demonstrate the efficacy of the method. This technique has general utility for selectively isolating specific isotopic signals in systems possessing optically controllable atomic-beam populations.

The notion of quantum-classical correspondence is carefully investigated in order to prepare firm grounds for studying the spatiotemporal evolution of quantum states in the same spirit as for corresponding classical cases. Three relevant problems, (1) the integrability of dynamical equations of quantum systems, (2) the initial minimum uncertainty states one-to-one correspondent to classical phase points, and (3) the effective Planck constants for systems having analogous dynamical properties but exhibiting different quantum effects, have been successfully resolved. Then the solution ${\rho }_{\gamma }\mathrm{}\left(t\right)\mathrm{}$ of the dynamical equation of a quantum integrable system is shown to be expressed as an analytical functional of the initial minimum uncertainty state ${\rho }_{\gamma }^0$ varying smoothly with $\gamma$ and t. Such a general character of the quantum regular motion serves as a reference for the study of quantum irregular motion under the action of perturbed Hamiltonian.

The hypervirial and Hellmann-Feynman theorems are used in the methods of $1/N$ expansion to construct Rayleigh-Schrödinger perturbation expansion for bound-state energy eigenvalues of spherical symmetric potentials. An iteration procedure of calculating correction terms of arbitrarily high orders is obtained for any kind of $1/N$ expansion. The recurrence formulas for three variants of the $1/N$ expansion are considered in this work, namely, the $1/n$ expansion and the shifted and unshifted $1/N$ expansions which are applied to the Gaussian and Patil potentials. As a result, their credibility could be reliably judged when account is taken of high-order terms of the eigenenergies. It is also found that there is a distinct advantage in using the shifted $1/N$ expansion over the two other versions. However, the shifted $1/N$ expansion diverges for s states and in certain cases is not applicable as far as complicated potentials are concerned. In an effort to solve these problems we have incorporated the principle of minimal sensitivity in the shifted $1/N$ expansion as a first step toward extending the scope of applicability of that technique, and then we have tested the obtained approach to some unfavorable cases of the Patil and Hellmann potentials. The agreement between our numerical calculations and reference data is quite satisfactory.

Analyses of the runs (i.e., uninterrupted sequences of identical outcomes) were made of the temporal succession of decays from three nuclear processes: (1) β decay of ${}^{137}\mathrm{Cs},$ (2) electron capture decay of ${}^{54}\mathrm{Mn},$ and (3) β decay of ${}^{214}\mathrm{Bi}$ followed by α decay of ${}^{214}\mathrm{Po}.$ Sample half lives vary widely from about 30 yr ${(}^{137}\mathrm{Cs})$ to 20 min ${(}^{214}\mathrm{Bi}).\mathrm{}$ For each process, the numbers of runs of length k $(1\mathrm{}<~k<~20)$ were determined from three distinct types of generating procedures: (a) runs with respect to a target value, (b) runs with respect to parity, and (c) runs with respect to sequential differences. Comparison of experimental results with those predicted by the theory of runs (on the assumption that every distinguishable arrangement of a temporal sequence of disintegrations is equally likely) provides comprehensive support of the hypothesis that the spontaneous decay of a nucleus is a random occurrence unaffected by past history.

We consider the problem of estimating the state of a large but finite number N of identical quantum systems. As N becomes large the problem simplifies dramatically. The only relevant measure of the quality of estimation becomes the mean quadratic error matrix. Here we present a bound on this quantity: a quantum Cramér-Rao inequality. This bound succinctly expresses how in the quantum case one can trade information about one parameter for information about another. The bound holds for arbitrary measurements on pure states, but only for separable measurements on mixed states—a striking example of nonlocality without entanglement for mixed but not for pure states. Cramér-Rao bounds are generally only derived for unbiased estimators. Here we give a version of our bound for biased estimators, and a simple asymptotic version for large N. Finally we prove that when the unknown state belongs to a two-dimensional Hilbert space our quantum Cramér-Rao bound can always be attained, and we provide an explicit measurement strategy that attains it. Thus we have a complete solution to the problem of estimating as efficiently as possible the unknown state of a large ensemble of qubits in the same pure state. The same is true for qubits in the same mixed state if one restricts oneself to separable measurements, but nonseparable measurements allow dramatic increase of efficiency. Exactly how much increase is possible is a major open problem.

A method is proposed to prepare an effective pure state corresponding to the pure state $|0〉|0〉\cdot \cdot \cdot |0〉$ for any number of spins on a nuclear magnetic resonance quantum computer, where $|0〉$ stands for the spin-up state of a nuclear spin. The method is based on the spatial labeling proposed by Cory et al. [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)].

We give a complete, hierarchic classification for arbitrary multiqubit mixed states based on the separability properties of certain partitions. We introduce a family of N-qubit states to which any arbitrary state can be depolarized. This family can be viewed as the generalization of Werner states to multiqubit systems. We fully classify those states with respect to their separability and distillability properties. This provides sufficient conditions for nonseparability and distillability for arbitrary states.

A general formalism for constructing configuration localized states for one-dimensional potentials is presented. It allows the evaluation of accurate approximations to the vibrational matrix elements of the momentum operator and of arbitrary functions of the coordinate. The formalism is applied to three potentials of interest in molecular physics: the harmonic oscillator, Morse, and Pöschl-Teller potentials. Quadratures specifically designed for each potential are used. The infrared vibrational spectrum of ${}^{12}{\mathrm{C}}^{16}\mathrm{O}$ is studied as a way to test the results obtained for different potentials in connection with their ability to model the anharmonicity.

A method was developed for the accurate measurement of cross sections. This method involves the measurement of a differential incoherent cross section in terms of the K-shell cross section in the target, such that source strength, source-target, and target-detector solid angle terms cancel out in the final expression used to evaluate the differential incoherent scattering cross section. Differential cross sections for incoherent scattering of 59.54-keV γ rays by Zr, Nb, and Mo have been measured for angles ranging from 40° to 135° using a high-resolution Si(Li) detector. The experimental values have been compared with those estimated on the basis of the nonrelativistic Hartree-Fock wave functions.

We compute nonrelativistic ab initio electronic potential surfaces for two metastable ${2p}^{5}3s$ neon atoms using a multiconfiguration all-electron valence-bond method. Spectroscopic constants and long-range $C_6$ dispersion coefficients are presented for ${}^{3,5}{\Sigma }_{g/u},$ ${}^{3,5}{\Pi }_{g/u},$ and ${}^{1,3,5}{\Delta }_{g/u}$ symmetries. In addition, we analyze the role of various atomic configurations in the formation of the neon dimer. Our results can be used to model the suppression of collision-induced ionization of metastable neon, which is believed to be a good candidate for Bose-Einstein condensation.

We demonstrate numerically the conditions where a wave packet adiabatic passage method yields optimal results for selective excitation of a vibrational level on excited electronic states in molecules. In a recent contribution Garraway and Suominen [Phys. Rev. Lett. 80, 932 (1998)] introduced the method of adiabatic passage by light-induced potentials (APLIP). Here we test and analyze the robustness of the APLIP process under realistic conditions for exciting the ground vibrational state of the ${\mathrm{Na}}_2$ molecule to the ground vibrational level of the excited ${}^1{\Sigma }_g\mathrm{}\left(4s\right)\mathrm{}$ state. The spatial and temporal adiabaticity of the process assures the conservation of the vibrational quantum number during the passage and leads to the remarkable robustness of the method, which at some extent prevents the usual rotating-wave approximation to be employed.

Mesoscopic phenomena—including population oscillations and persistent currents driven by quantal phases—are explored theoretically in the context of multiply connected Bose-Einstein systems composed of trapped alkali-metal gas atoms. These atomic phenomena are bosonic analogs of electronic persistent currents in normal metals and Little-Parks oscillations in superconductors. Differences between oscillatory phenomena due to quantal phases in Bose-Einstein systems and in conventional superconductors are discussed, particularly with regard to their potential for discriminating between the standard BCS scenario and the Bose-Einstein condensation of preformed pairs scenario for the superconducting transition in high-temperature superconductors.

We report the characterization of a saturated collisional Ni-like Ag soft-x-ray laser at 13.9 nm. A main pumping pulse of 140 J in 100 ps $(I\approx 8\times {10}^{13}\hspace{0.5em}\mathrm{W}{\mathrm{cm}}^{-2}),$ the preceded 3 ns before by a prepulse of variable intensity was used to create the amplifying medium. The target length was varied up to 2 cm for the single target and 4 cm for the double target. For the double target the quasi-traveling-wave excitation (QTWE) technique has been used. Time-integrated as well as time-resolved measurement of the $4d-4p$ $J=0\mathrm{}-1$ line have been performed for different pumping configurations and target geometry. Due to the very high pumping intensity and the resulting plasma overheating, an exceptionally high-gain coefficient of $19\hspace{0.5em}{\mathrm{cm}}^{-1}$ has been measured leading to the saturation regime for plasma length longer than 8 mm. Time-resolved and time-integrated $3d-4f$ spectra of the plasma are also displayed and ionization balance is discussed. Using double-target geometry a narrow divergence is observed due to efficient coupling factor as well as a temporal increase of the x-ray laser pulse duration in the direction of QTWE. The far-field pattern of the x-ray laser beam has been characterized. Two vertically separated bright spots were observed for the double target, while a single spot was observed for the single target. The energy of the double-target x-ray laser beam has been measured to be $\sim 300\hspace{0.5em}\mu \mathrm{J}$ which closely corresponds to an output power of 5 MW.

A model of a four-wave mixer operated in a nonlinear regime, studied by Yurke and Stoler [Phys. Rev. A 35, 4846 (1987)], is reexamined. Yurke and Stoler have shown that this device, under a certain condition, acts as an even-odd filter, switching even-photon-number states from the pump mode to the signal mode. An initial coherent state in the pump is converted into an entanglement of even and odd coherent states with vacuum states in the output signal and pump modes. We point out that under a different condition and with an even-photon-number state initially in the pump and a vacuum in the signal, the device creates a maximally entangled state between the number state and the vacuum. Using the device to replace the first beamsplitter of a Mach-Zehnder interferometer, phase uncertainties at the Heisenberg limit $(\Delta \phi =1/n)$ can be obtained. Since number states are difficult to generate, we point out that an even coherent state obtained from the output of one device can be used as input to a second to achieve the phase uncertainties $\Delta \phi {=1/n}_e,$ where $n_e$ is the average photon number of the even coherent state.

We report the observation of unexpected line strengths in the resonant multiphoton laser excitation of high-angular-momentum ${7d}_{5/2}{n}^{\prime }{l}^{\prime }$ and ${8p}_{3/2}{n}^{″}{l}^{″}{(n}^{″}\ne 16)$ states in Sr. The results differ from expected isolated-core excitation features usually explained on the basis of the multichannel-quantum-defect theory. In the present case, the observed line strengths and, in particular, the disappearance of single resonances can be explained by a configuration-interaction calculation, giving explicitly the multipole character of the correlation between the electrons. The spectra offer a sensitive way to test calculations involving electronic correlation.

The quantum harmonic-parabola system, whose potential energy is the negative harmonic potential, is analyzed and applied to the cases of a quantum well, barrier, and periodic lattices. The eigenstate of the quantum Hamiltonian of the harmonic-parabola system is obtained. It is shown that any function may be expanded in terms of the eigenfunctions of the system in a finite interval, and the propagator of the system can be obtained from the eigenfunctions. The energy eigenvalues, uncertainty, and probability density for the first few states are treated for the infinite harmonic-parabola well. The energy eigenvalues and their enumeration, the energy band, and the probability density for the first few states are obtained for a well composed of the parabola and constant potentials. The transmission coefficients and each potential interval dependence are determined for this well and the barrier of the parabola-constant potential structure. Periodic lattices composed of the parabola potential and parabola-constant potentials are constructed, and their dispersion relations, energy states, and bands are obtained.