By relevant modifications, the known global-fidelity limits of state-dependent cloning are extended to mixed quantum states. We assume that the ancilla contains some a priori information about the input state. As it is shown, the obtained results contribute to the stronger no-cloning theorem. An attainability of presented limits is discussed.

Physical implementation of quantum-information processing by liquid-state nuclear magnetic resonance, using weakly coupled spin-$\frac{1}{2}$ nuclei of a molecule, is well established. Nuclei with $\mathrm{spin}>1/2\mathrm{}$ oriented in liquid-crystalline matrices is another possibility. Such systems have multiple qubits per nuclei and large quadrupolar couplings resulting in well separated lines in the spectrum. So far, creation of pseudopure states and logic gates has been demonstrated in such systems using transition selective radio-frequency pulses. In this paper we report two developments. First, we implement a quantum algorithm that needs coherent superposition of states. Second, we use evolution under quadrupolar coupling to implement multiqubit gates. We implement the Deutsch-Jozsa algorithm on a spin-$\frac{3}{2}$ (2 qubit) system. The controlled-NOT operation needed to implement this algorithm has been implemented here by evolution under the quadrupolar Hamiltonian. To the best of our knowledge, this method has been implemented for the first time in quadrupolar systems. Since the quadrupolar coupling is several orders of magnitude greater than the coupling in weakly coupled spin-$\frac{1}{2}$ nuclei, the gate time decreases, increasing the clock speed of the quantum computer.

We have measured the hyperfine splitting and level isotope shifts (LIS) of the ${(6s6p}^2)$ ${}^4{P}_{1/2}$ level of ${}^{205}\mathrm{Tl}$ and ${}^{203}\mathrm{Tl}$ using laser absorption spectroscopy in a thallium oven near 1373 K. We determine that the hyperfine splitting between the $F=1\mathrm{}$ and 0 levels of the ${}^4{P}_{1/2}$ state in ${}^{205}\mathrm{Tl}$ is $75.179\pm 0.087\mathrm{GHz}.$ The $F=0\mathrm{}$ LIS is $-7.333\pm 0.025\mathrm{GHz}$ and the $F=1\mathrm{}$ LIS is $-6.500\pm 0.030\mathrm{GHz},$ with the ${}^{205}\mathrm{Tl}$ level below the ${}^{203}\mathrm{Tl}$ level in both cases. We use our results together with other data to analyze the configuration mixing of the ${}^4{P}_{1/2}$ state with the nearby ${(6s}^{2}10s)$ ${}^2{S}_{1/2}$ state. The mixing inferred from the hyperfine results is consistent with that inferred from the isotope shift results.

The intensity of the W $M\alpha$ line emitted by tungsten present in W/C multilayer interferential mirrors (MIM) under electron excitation is studied as a function of the detection angle of the photons. The measurements are performed for various incident-electron energies and several numbers of bilayers constituting the MIM. A spatial modulation of the x-ray intensity is observed in a domain of detection angle around the Bragg angle of the W/C multilayer for the W $M\alpha$ emission. The experimental results are compared to a model based on the reciprocity theorem using nonuniform ionization distributions. We suggest that the intensity modulation is due to the interferences between the forward and backward traveling waves inside the MIM.

Measurements of $L\beta$ spectra of gold using a high-resolution single-crystal x-ray spectrometer are presented. Energy values and intensities of the $L{\beta }_2$ satellite lines are confirmed by fitting Voigt functions to the observed spectra. Relative intensity ratios of $L{\beta }_2,$ $L{\beta }_3,$ $L{\beta }_{15},$ and $L{\beta }_2$ satellite lines are investigated at various excitation energies. The origin of the $L{\beta }_2$ satellite lines, $L{\beta }_2^{\prime }$ and $L{\beta }_2^{″},$ are confirmed to be mainly due to the $L-\mathrm{LM}$ Coster-Kronig transition, with intensities closely related to the photoionization cross section of the subshell $L_1.$

The high resolution Br $4s{\sigma }^{-1}$ photoelectron spectrum of HBr is presented together with the resonant Auger spectra resulting from excitations from the $3d$ core levels to the low-$n$ Rydberg orbitals $5s\sigma ,$ $5p\sigma ,$ and $5p\pi .$ The very complex spectra can be broadly assigned using two observations. First, the energy splittings of the $4p{\pi }^{-2}5s$ and $4p{\pi }^{-2}5p$ states are very similar to the splittings of the $4p{\pi }^{-2}{(}^1{\Sigma }^{+}{,}^1\Delta ,\mathrm{and}{}^3{\Sigma }^{-})$ final states seen previously in the normal Auger spectra. Second, the ${}^2{\Sigma }^{+}$ states, which are the dominant correlation satellites in the complex $4s{\sigma }^{-1}$ photoelectron spectrum, are often enhanced in the $5s\sigma$ resonance Auger spectra. Electron correlation and spin-orbit interaction in the final states are important to understand all of these spectra. Unlike the normal Auger spectra, vibrational excitations play only a minor role in these spectra, showing that the $5s$ and $5p$ Rydberg orbitals have some bonding character.

The classical trajectory Monte Carlo method was applied to the description of the fragmentation of the positronium (Ps) in collision with He atoms. The collision system was simplified to a three-body system consisting of the electron and the positron of the Ps, as well as the He atom that was considered as a structureless particle. The interaction of the $e^{-}$ and $e^{+}$ with the He was approximated by a static, fully screened Coulomb potential. The calculations were carried out for collision energies 13, 18, 25, and 33 eV. The obtained total break-up cross sections and the longitudinal energy distributions of the emitted positrons were compared with the recent experimental results of Armitage et al. [Phys. Rev. Lett. $89,$ 173402 (2002)]. The present theory overestimates the measured cross sections by a factor of 1.6–2.5, but it correctly reproduces the peak found by Armitage et al. in the positron spectra at about half of the residual Ps energy.

A gauge-invariant formalism is developed to describe the effect of parity-violating weak-nuclear interactions on nuclear magnetic chemical shift in molecules. Such effect is computed for two molecules with ab initio techniques and it is found to be orders of magnitude smaller than experimental resolution for the molecules considered.

We investigate the properties of hard-core bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body density matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the “natural” single-particle orbitals and their occupation, including the condensate fraction. At low boson density, ${\mathrm{na}}^3<{10}^{-5},$ where $n=N/V$ and a is the hard-core diameter, the condensate is localized at the center of the trap. As ${\mathrm{na}}^3$ increases, the condensate moves to the edges of the trap. At high density, it is localized at the edges of the trap. At ${\mathrm{na}}^3<~{10}^{-4},$ the Gross-Pitaevskii theory of the condensate describes the whole system within $1\%.$ At ${\mathrm{na}}^3\approx {10}^{-3},$ corrections are $3\%$ to the Grass-Pitaevskii energy but $30\%$ to the Bogoliubov prediction of the condensate depletion. At ${\mathrm{na}}^3\gtrsim {10}^{-2},$ mean-field theory fails. At ${\mathrm{na}}^3\gtrsim 0.1,$ the bosons behave more like a liquid ${}^4\mathrm{He}$ droplet than a trapped boson gas.

We have studied effects of magnetic sublevel degeneracy on the polarization of superfluorescent pulses generated on the Ca $4s4p{}^1{P}_1–3d4s{}^1{D}_2$ transition at $5.5\mu \mathrm{m}.$ These pulses were generated from a cell of length 50 cm by optically pumping calcium vapor on the ${4s}^2{}^1{S}_0–4s4p{}^1{P}_1$ transition in the presence of Ar gas. The axis of ellipticity of superfluorescence (SF) polarization is oriented parallel to the axis of the pump-laser polarization at large detunings, and undergoes an abrupt rotation through $90°$ for detunings close to resonance. The distribution of populations in the magnetic sublevels of the ${}^1{P}_1$ state can be estimated using a simple model based on previously calculated cross sections for collisionally aided absorption in the presence of an intense (pump) field. For large detunings, these estimates are consistent with the polarized SF intensity measured in the experiment. A direct measurement of the populations of the ${}^1{P}_1$ magnetic sublevels also supports the collisional redistribution predicted by the calculated cross sections. We therefore suggest that SF polarization can be a useful signature of collisional redistribution. However, the change in ellipticity is unexpected, and probable causes for this effect are discussed.

Josephson junctions have been shown to be a promising solid-state system for implementation of quantum computation. The two-qubit gates are generally realized by the capacitive coupling between the nearest-neighbor qubits. We propose an effective Hamiltonian to describe charge qubits coupled through the microwave cavity. We find that nontrivial two-qubit gates may be achieved by this coupling. The ability to interconvert localized charge qubits and flying qubits in the proposed scheme implies that quantum network can be constructed using this large scalable solid-state system.

In a scheme of nonadiabatic purely geometric quantum gates in nuclear-magnetic-resonance systems we propose proper magnitudes of magnetic fields that are suitable for an experiment. We impose a natural condition and reduce the degree of freedom of the magnetic fields to the extent. By varying the magnetic fields with essentially a one-dimensional degree of freedom, any spin state can acquire an arbitrary purely geometric phase ${\phi }_g=-2\pi \left(1\mathrm{}-\cos \theta \right),$ $0<~\cos \theta <~1.$ This is an essential ingredient for constructing universal geometric quantum gates.

We report direct excitation of the strongly forbidden ${5s}^2{}^1{S}_0-5s5p{}^3{P}_0$ transition in ${}^{87}\mathrm{Sr}.$ Its frequency is 429 228 004 235(20) kHz. A resonant laser creates a small leak in a magneto-optical trap (MOT): atoms build up to the metastable ${}^3{P}_0$ state and escape the trapping process, leading to a detectable decrease in the MOT fluorescence. This line has a natural width of ${10}^{-3}\mathrm{Hz}$ and can be used for a new generation of optical frequency standards using atoms trapped in a light-shift-free dipole trap.

We present calculations of cross sections and rate coefficients for the dissociative recombination of ${\mathrm{H}}_2^{+}$ ions initially in $v=0\mathrm{}–6$ vibrational levels, together with rate coefficients for the competing electron-induced vibrational deexcitation. We used the multichannel quantum defect theory with a second-order treatment of the K matrix, and show that electronic interactions dominate not only the dissociative recombination but also the vibrational relaxation induced by slow electrons. Most of our rate coefficients for dissociative recombination are in good agreement with the measurements at the TSR storage ring [S. Krohn et al., Phys. Rev. A 62, 032713 (2000)]. On the contrary, our rates for vibrational deexcitation, close to former results obtained by R-matrix calculations [B. K. Sarpal and J. Tennyson, Mon. Not. R. Astron. Soc. 263, 909 (1993)], are smaller by up to one order of magnitude than the experimental values which are deduced from the time evolution of the vibrational populations, measured by the Coulomb explosion imaging method.

We compute numerically the quantum action for the inverse square potential and compare the global fit method with a new method, the flow equation. We investigate the error of fitting quantum-mechanical transition amplitudes by the quantum action. The flow equation works well in the regime of large T giving results consistent with the global fit method.

We study generalized measurements [positive-operator-valued measure (POVM measurements)] on a single d-level quantum system which is in a completely unknown pure state, and derive the best estimate of the postmeasurement state. The mean postmeasurement estimation fidelity of a generalized measurement is obtained and related to the operation fidelity of the device. This illustrates how the information gain about the postmeasurement state and the corresponding state disturbance are mutually dependent. The connection between the best estimates of the premeasurement and postmeasurement state is established and interpreted. For pure generalized measurements the two states coincide.

We show that for any lowest-Landau-level state of a trapped, rotating, interacting Bose gas, the particle distribution in coordinate space in a free expansion (time of flight) experiment is related to that in the trap at the time it is turned off by a simple rescaling and rotation. When the lowest-Landau-level approximation is valid, interactions can be neglected during the expansion, even when they play an essential role in the ground state when the trap is present. The correlations in the density in a single snapshot can be used to obtain information about the fluid, such as whether a transition to a quantum Hall state has occurred.

Muonic molecular ions in excited states have been predicted to form in collisions between excited muonic atoms and hydrogen molecules. We have calculated radiative and Coulombic decay rates for $\mathrm{pp}{\mu }^{*}$ and $\mathrm{dd}{\mu }^{*}$ molecular states located below the $2s$ threshold, using the complex rotation method. The x-ray spectrum from the radiative decay is shown to exhibit several maxima, corresponding to the vibrational motion of the decaying molecule. The branching ratio of the radiative decay mode was calculated to be less than 15% for $\mathrm{pp}{\mu }^{*},$ while a radiative yield of more than 80% is predicted for the decay of $\mathrm{dd}{\mu }^{*}.$ Our results have a significant impact on the analysis of the muon catalyzed fusion cycle as well as on the interpretation of exotic hydrogen spectroscopy.

To address the shortage of experimental data for electron spectra of triply ionized rare-earth elements we have calculated energy levels and lifetimes of ${4f}^{n+1\mathrm{}}$ and ${4f}^{n}5d$ configurations of Nd IV $\mathrm{}(n=2\mathrm{}),$ Pm IV $\mathrm{}(n=3\mathrm{}),$ Sm IV $\mathrm{}(n=4\mathrm{}),$ and Eu IV $\mathrm{}(n=5\mathrm{})\mathrm{}$ using Hartree-Fock and configuration-interaction methods. To control the accuracy of our calculations we also performed similar calculations for Pr III, Nd III, and Sm III, for which experimental data are available. The results are important, in particular, for physics of magnetic garnets.