We investigate the thermal entanglement in the two-qubit Heisenberg XY model with a nonuniform magnetic field. Concurrence, the measurement of entanglement, is calculated. The behavior of concurrence is present at three different cases. Contrary to the uniform magnetic field case, we find that the entanglement and the critical temperature $T_C$ may be enhanced under a nonuniform magnetic field.

We present results on the self-energy correction to the energy levels of hydrogen and hydrogenlike ions. The self-energy represents the largest QED correction to the relativistic (Dirac-Coulomb) energy of a bound electron. We focus on the perturbation expansion of the self-energy of non-S states, and provide estimates of the so-called $A_{60}$ perturbation coefficient, which can be viewed as a relativistic Bethe logarithm. Precise values of $A_{60}$ are given for many P, D, F, and G states, while estimates are given for other states. These results can be used in high-precision spectroscopy experiments in hydrogen and hydrogenlike ions. They yield the best available estimate of the self-energy correction of many atomic states.

The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical Slepian-Wolf theorem. The optimal compression rate is found to be reduced from the Shannon entropy of the source by the Holevo information between the source and side information.

We demonstrate the cooling of a two species ion crystal consisting of one ${}^9{\mathrm{Be}}^{+}$ and one ${}^{24}{\mathrm{Mg}}^{+}$ ion. Since the respective cooling transitions of these two species are separated by more than 30 nm, laser manipulation of one ion has negligible effect on the other even when the ions are not individually addressed. As such this is a useful system for reinitializing the motional state in an ion trap quantum computer without affecting the qubit information. Additionally, we have found that the mass difference between ions enables a method for detecting and subsequently eliminating the effects of radio frequency micromotion.

Absolute total-, single-, and multiple-electron-loss cross sections are measured for $({\mathrm{Ar}}^{+}-,$ ${\mathrm{Ar}}^{2+}-,$ ${\mathrm{Xe}}^{3+})-(\mathrm{Ne},$ ${\mathrm{N}}_2,$ Ar) collisions at 0.74 and 1.4 MeV/u. In addition, a many-body classical trajectory Monte Carlo model was used to calculate total- and multiple-electron-loss cross sections for ${\mathrm{Ar}}^{+}$ impact. For ${\mathrm{N}}_2$ and Ar targets, excellent agreement between the measured and calculated cross sections is found; for the Ne target the experimental data are approximately 40% smaller than the theoretical predictions. The experimental data are also used to examine cross-section scaling characteristics for electron loss from fast, low-charge-state, heavy ions. It is shown that multiple electron loss increased the mean charge states of the outgoing argon and xenon ions by 2 and 3 respectively. The cross sections decreased with increasing number of electrons lost and scaled roughly as the inverse of the sum of the ionization potentials required to sequentially remove the most weakly bound, next most weakly bound, etc., electrons. This scaling was found to be independent of projectile, incoming charge state, and target. In addition, the experimental total loss cross sections are found to be nearly constant as a function of initial projectile charge state. As a function of impact energy, the theoretical predictions yield an $E^{-1/3}$ behavior between 0.5 and 30 MeV/u for the total loss cross sections. Within error bars, the data are consistent with this energy dependence but are also consistent with an $E^{-1/2}$ energy dependence.

The effect of autoionizing Rydberg states on photoelectron spectra in intense laser fields were studied. On the basis of the multichannel quantum defect theory combined with the artificial channel method, the spectral structures caused by the s-Rydberg series converging on ${\mathrm{CO}}^{+}{(X}^2{\Sigma }^{+},v=1)$ were calculated. It is found that the shape of spectra remarkably changes depending on the laser intensity. The spectra for higher Rydberg states undergo the change by a weaker laser field, reflecting sensitivity of a weakly bound Rydberg electron. A kind of n-scaling law for this sensitivity is discussed.

We study the properties of coreless vortices (skyrmions) in spinor Bose-Einstein condensates. We find that this excitation is always energetically unstable, it always decays to an uniform spin texture. We obtain the skyrmion energy as a function of its size and position, a key quantity in understanding the decay process. We also point out that the decay rate of a skyrmion with high winding number will be slower. The interaction between skyrmions and other excitation modes are also discussed.

The effect of photon beam splitting in a time-varying medium is described by classical and quantum theoretical models. It generalizes the concept of time refraction, introduced recently by the authors as a natural extrapolation of the usual concepts of refraction and reflection into the time domain. Total time reflection is shown to exist. A sequence of time refraction processes is shown to lead to temporal interference effects. The concept of temporal beam splitter is introduced. Bogoliubov transformations for the temporal beam splitter are derived. Resonant amplification of light by change in time in the optical medium is shown to exist.

The imploding dynamics of ${}^{85}\mathrm{Rb}$ condensates is obtained in terms of the nonadiabatic dynamical characteristics of the homoclinic bifurcation giving rise to the collapse of the cloud. The agreement with the recent experimental observation of the imploding dynamics is excellent.

We propose a technique for coherent population inversion of a two-state system, which uses an amplitude-modulated pulse. In the modulation-free adiabatic basis, the modulation introduces oscillating interaction between the adiabatic states. In a second rotating-wave approximation picture, this oscillating interaction induces a pair of level crossings between the energies of the adiabatic states if the modulation frequency is chosen appropriately. By suitably offsetting the modulation with respect to the center of the pulse, one can make the modulation act only in the vicinity of one of these crossings. In a higher-order adiabatic basis, this crossing shows up as an avoided crossing between the energies of the higher-order adiabatic states. As a result robust and efficient population transfer can be achieved between the adiabatic states, and hence, between the original bare states. We derive analytically the conditions on the interaction parameters for this technique and verify them with numerical simulations. Possible experimental implementations are discussed.

The expansion of a one-dimensional Bose gas after releasing its initial harmonic confinement is investigated employing the Lieb-Liniger equation of state within the local-density approximation. We show that during the expansion the density profile of the gas does not follow a self-similar solution, as one would expect from a simple scaling ansatz. We carry out a variational calculation, which recovers the numerical results for the expansion, the equilibrium properties of the density profile, and the frequency of the lowest compressional mode. The variational approach allows for the analysis of the expansion in all interaction regimes between the mean-field and the Tonks-Girardeau limits, and in particular shows the range of parameters for which the expansion violates self-similarity.

Analytical expressions for the entanglement measures concurrence, i-concurrence, and 3-tangle in terms of spin correlation functions are derived using general symmetries of the quantum spin system. These relations are exploited for the one-dimensional XXZ model, in particular the concurrence and the critical temperature for disentanglement are calculated for finite systems with up to six qubits. A recent NMR quantum error correction experiment is analyzed within the framework of the proposed theoretical approach.

The jump phenomenon between two S-matrix poles induced by a small potential strength variation is studied in the framework of the nonrelativistic scattering by a central potential $\mathrm{gV}\left(r\right),$ $g\in \mathrm{C}.$ Let $R_g^{\mathrm{}\left(l\right)\mathrm{}}$ denote the Riemann surface over the complex g plane, on which the pole function ${k=k}^{\mathrm{}\left(l\right)\mathrm{}}\mathrm{}\left(g\right)\mathrm{}$ is single valued and analytic. By associating a sheet ${\Sigma }_n^{\mathrm{}\left(l\right)\mathrm{}}$ of $R_g^{\mathrm{}\left(l\right)\mathrm{}}$ and its k-plane image ${\Sigma }_n^{\prime \mathrm{}\left(l\right)\mathrm{}}$ to a state with the quantum numbers $\mathrm{}(l,n),$ the jump between the states $\mathrm{}(l,n)\mathrm{}$ and $\mathrm{}(l,m),$ induced by the potential strength variation, is understood as the jump between the sheet images ${\Sigma }_n^{\prime \mathrm{}\left(l\right)\mathrm{}}$ and ${\Sigma }_m^{\prime \mathrm{}\left(l\right)\mathrm{}}.$ The rules for the jumps $\mathrm{}(l,n)\mathrm{}\mathrm{}(l,m)\mathrm{}$ as a consequence of a small potential strength variation are deduced. The influence of the exotic resonant states on the selection rules for the jumps is discussed. The occurrence of the local degeneracy with respect to l of the resonant levels $(l-1,n),$ $\mathrm{}(l,m),$ and $\mathrm{}(l+1,p)\mathrm{}$ for the rectangular central potential and the level stability with respect to the potential strength variation are also discussed.

We present an experimental study of the internal mechanical vibration modes of a mirror. We determine the frequency repartition of acoustic resonances via a spectral analysis of the Brownian motion of the mirror, and the spatial profile of the acoustic modes by monitoring their mechanical response to a resonant radiation pressure force swept across the mirror surface. We have applied this technique to mirrors with cylindrical and plano-convex geometries, and compared the experimental results to theoretical predictions. We have in particular observed the Gaussian modes predicted for plano-convex mirrors.

Using the coarse-grain averaged hydrodynamic approach, we calculate the excitation spectrum of vortex lattices sustained in rotating Bose-Einstein condensates. The spectrum gives the frequencies of the common-mode longitudinal waves in the hydrodynamic regime, including those of the higher-order compressional modes. Reasonable agreement with the measurements taken in a recent experiment is found, suggesting that one of the longitudinal modes reported in the experiment is likely to be the $n=2,m=0\mathrm{}$ mode.

The additivity of both the entanglement of formation and the classical channel capacity is known to be a consequence of the strong superadditivity conjecture. We show that, conversely, the strong superadditivity conjecture follows from the additivity of the entanglement of formation; this means that the two conjectures are equivalent and that the additivity of the classical channel capacity is a consequence of them.

Muonic three-body bound states are investigated within a hyperspherical adiabatic expansion representation. We have used a method for determining the basis functions of the expansion, which consists of decomposing these functions into Faddeev-type components and an equivalent treatment of all two-body contributions. Through this approach, and using partial waves for components, the binding energy of the ground state and the lowest eigenpotentials for the muonic molecules $(pd\mu ,pt\mu ,dt\mu )$ are calculated in extreme and uncoupled adiabatic approximation. The obtained results are very close to variational calculations.

Order-${\alpha }^2$ corrections to the decay rate of parapositronium are calculated. A QED scattering calculation of the amplitude for electron-positron annihilation into two photons at threshold is combined with the technique of effective field theory to determine a nonrelativistic QED Hamiltonian, which is then used in a bound-state calculation to determine the decay rate. Our result for the two-loop correction is $5.1243\left(33\right)\mathrm{}$ in units of $(\alpha /\pi {)}^2$ times the lowest-order rate. This is consistent with but more precise than the result $5.1\left(3\right)\mathrm{}$ of a previous calculation.

The hyperspherical hidden-crossing method (HHCM) has been applied to s-, p-, and d-wave positronium formation in positron-lithium collisions in the energy range 0–1.8 eV, using a model potential to describe the atomic core. The calculations have provided a test of the HHCM. The s-, p-, and d-wave positronium formation cross sections are reported and compared with variational and close-coupling calculations. A minimum is obtained in the s-wave positronium formation cross section which is due to the Stuckelberg phase having a value of $\pi .$ The cross sections have also been computed including the correction term which emerges from the one-Sturmian theory.

Using a merged-beam technique, the absolute, total electron-capture cross section has been measured for collisions of ${\mathrm{Ne}}^{2+}$ ions with hydrogen (deuterium) atoms at collision energies between 139 and 1490 eV/u. These data are compared to three other published measurements, two of which differ from one another by a factor greater than two. Early quantal rate coefficient calculations for ${\mathrm{Ne}}^{2+}$ ions with hydrogen at eV/u energies predict a cross section many orders of magnitude below the previously measured cross section at 40 eV/u. A possible explanation is given for the discrepancy between theory and experiment.