We determine all $2\times 2$ quantum states that can serve as useful catalysts for a given probabilistic entanglement transformation, in the sense that they can increase the maximal transformation probability. When higher-dimensional catalysts are considered, a sufficient and necessary condition is derived under which a certain probabilistic transformation has useful catalysts.

Graph states are multiparticle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of distributed quantum systems that play a significant role in quantum error correction, multiparty quantum communication, and quantum computation within the framework of the one-way quantum computer. We characterize and quantify the genuine multiparticle entanglement of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimensions, graphs that occur in quantum error correction, such as the concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier transform in the one-way computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphisms.

The energy loss of helium ions in zinc has been measured in the energy range from 37.5 to $1750\mathrm{keV}∕\mathrm{amu}$ using the transmission technique and the Rutherford backscattering method. In addition, calculations using the extended Friedel sum rule, the unitary convolution approximation, and the local plasma approximation have been performed. The contributions of the inner-shell and valence electrons to the total energy loss are separately evaluated. The measurements and calculations are in good agreement over an extended range of energies, and both of them yield stopping values higher than those provided by SRIM 2003.

We study the effects of the relativistic electronic dressing in laser-assisted electron-hydrogen atom elastic collisions. We begin by considering the case when no radiation is present. This is necessary in order to check the consistency of our calculations and we then carry out the calculations using the relativistic Dirac-Volkov states. It turns out that a simple formal analogy links the analytical expressions of the unpolarized differential cross section without laser and the unpolarized differential cross section in the presence of a laser field.

We have realized a two-species mirror-magneto-optical trap containing a mixture of ${}^{87}\mathrm{Rb}\left({}^{85}\mathrm{Rb}\right)$ and ${}^{133}\mathrm{Cs}$ atoms. Using this trap, we have measured the heteronuclear collisional loss rate ${\beta }_{\mathrm{Rb-Cs}}^{\prime }$ due to intraspecies cold collisions. We find a distinct difference in the magnitude and intensity dependence of ${\beta }_{\text{Rb-Cs}}^{\prime }$ for the two isotopes ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ which we attribute to the different ground-state hyperfine splitting energies of the two isotopes.

In this paper we obtain the rate equations for Zeeman coherences in the broad-line approximation and steady-state balance equations directly from optical Bloch equations without the use of the perturbation theory. The broad-line approximation allows us to use the adiabatic elimination procedure in order to eliminate the optical coherences from the optical Bloch equations, but the steady-state condition allows us to derive the balance equations in a straightforward way. We compare our approach with the perturbation-theory approach as given previously and show that our approach is more flexible for analyzing various experiments. Meanwhile we also show the validity and limitations of the application of the rate equations in experiments with coherent atomic excitation when either the broad-line approximation or steady-state conditions hold. Thus we have shown the basis for modeling the coherent atomic excitation experiments by using the relatively simple rate equations, provided that certain experimental conditions hold.

The quantum correlations between the beams generated by polariton pair scattering in a semiconductor microcavity above the parametric oscillation threshold are computed analytically. The influence of various parameters, including the cavity-exciton detuning, the intensity mismatch between the signal and idler beams, and the amount of spurious noise, is analyzed. We show that very strong quantum correlations between the signal and idler polaritons can be achieved. However, the quantum effects in the outgoing light fields are strongly reduced due to the large mismatch in the coupling of the signal and idler polaritons to the external photons.

We study the quantum dynamics of a neutral particle that posseses a permanent magnetic and electric dipole moments in the presence of an electromagnetic field. The analysis of this dynamics demonstrates the appearance of a quantum phase that combines the Aharonov-Casher effect and the He-Mckellar-Wilkens effect. We demonstrate that this phase is a special case of the geometric quantum phase. A series of field configurations where this phase would be found is presented. A generalized Casella-type effect is found in one of these configurations. A physical scenario for the quantum phase in an interferometric experiment is proposed.

Accurate QED calculations of the interelectron interaction corrections for the $\left(1s2p\right)2^1{P}_1$ and $\left(1s2p\right)2^3{P}_1$ two-electron configurations for ions with nuclear charge numbers $10⩽Z⩽92$ are performed within the line profile approach. Total energies of these configurations are evaluated. Employing the fully relativistic treatment based on the $j-j$ coupling scheme these energy levels become quasidegenerate in the region $Z⩽40$. To treat such states within the framework of QED we utilize the line profile approach. The calculations are performed within the Coulomb gauge.

We study a two-dimensional atomic mixture of bosons and fermions cooled into their quantum degenerate states and subject to an optical lattice. The optical lattice provides van Hove singularities in the fermionic density of states. We find that these van Hove singularities produce new and interesting features for the transition towards phase separation: an arbitrary weak interaction between the bosons and the fermions is sufficient to drive the phase separation at low temperatures. The phase-separated state turns stable for attractive and repulsive interactions between the bosons and fermions and can be cast into the standard form of a “liquid–gas” transition.

We experimentally studied the spin-dependent collision dynamics of ${}^{87}\mathrm{Rb}$ spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\mid F=2,m_F=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to $3.0\mathrm{G}$. The atom loss rate due to inelastic two-body collisions was found to be $1.4\left(2\right)\times {10}^{-13}{\text{cm}}^3{\mathrm{s}}^{-1}$. Spin mixing in the $F=2$ manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each $m_F$ component.

We report the first measurement of the spin-exchange rate coefficient for binary collisions between Cs and ${}^{129}\mathrm{Xe}$ atoms in the temperature range $110<T<150°\mathrm{C}$ at a $9.4\text{−}\mathrm{T}$ magnetic field. Under these conditions, binary spin-exchange collisions dominate the longitudinal nuclear spin-relaxation rate $1∕T_1$ of ${}^{129}\mathrm{Xe}$ gas. We measured $1∕T_1$ of a thermally polarized Xe gas using the saturation-recovery of conventional nuclear magnetic resonance. We also directly measured the Cs atomic number density [Cs] by using Faraday rotation of the linear polarization of a probing laser beam passing through the sample. The measured rate coefficient is $\kappa \left(9.4\mathrm{T}\right)=d(1∕T_1)∕d\left[\mathrm{Cs}\right]=(2.81\pm 0.2)\times {10}^{-16}{\mathrm{cm}}^3∕\mathrm{s}$, which is about a factor of 1.6 higher than the previously measured spin-exchange rate coefficient of ${}^{129}\mathrm{Xe}\text{−}\mathrm{Rb}$ binary collisions. Using a calculated magnetic decoupling factor, we extrapolate our result to zero magnetic field: $\kappa \left(0\mathrm{T}\right)=(4.1\pm 0.3)\times {10}^{-16}{\mathrm{cm}}^3∕\mathrm{s}$.

We consider a detection of pair of recoiling reaction fragments, each by its own interferometer, to demonstrate Hardy’s contradiction between quantum mechanics and local hidden variables. Our interferometry is based on momentum entanglement and is independent of the identity and internal state of the fragments.

The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Rényi entropies at the output of a channel. The conjecture is proven true for all Rényi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment.

We study the temporal evolution of entanglement pertaining to two qubits interacting with a thermal bath. In particular we consider the simplest nontrivial spin bath models where symmetry breaking occurs and treat them by mean field approximation. We analytically find decoherence free entangled states as well as entangled states with an exponential decay of the quantum correlation at finite temperature.

A short-time approximation is developed for system-environmental bath mode interactions involving a general non-Hermitian system operator $\Lambda$ and its conjugate ${\Lambda }^{†}$ in order to evaluate the onset of decoherence at low temperatures in quantum systems interacting with the environment. The developed approach is complementary to Markovian approximations and appropriate for the evaluation of quantum computing schemes. An example of a spin system coupled to a bosonic heat bath via $\Lambda \propto {\sigma }_{-}$ is worked out in detail.

The lowest adiabatic potential expressed in hyperspherical coordinates is estimated for two boson systems in an external harmonic trap. Corresponding conditions for stability are investigated and the related structures are extracted for zero-range interactions. Strong repulsion between non-identical particles leads to two features, respectively, when identical particles attract or repel each other. For repulsion stable structures arise with displaced center of masses. For attraction the mean-field stability region is restricted due to motion of the center of masses.

The anisotropic and isotropic binary collision-induced spectra scattered by gaseous methane have been measured in absolute units up to $900{\text{cm}}^{-1}$ from the Rayleigh line. Corresponding theoretical intensities taking into account multipolar polarizabilities have been calculated using a semiclassical procedure. From the analysis of, mainly, our isotropic scattering data, values of the dipole-quadrupole and dipole-octopole polarizabilities are deduced. They are found to be in good agreement with recent ab initio calculations.

The $K\alpha$ and $K\beta$ satellite and hypersatellite x-ray lines emitted by highly ionized sulfur projectiles passing with energies from $65\text{MeV}$ up to $122\text{MeV}$ through carbon foils of thickness of $15\text{−}210\mu {\mathrm{g}\text{cm}}^{-2}$ have been recorded using a Si(Li) detector. The additional hypersatellite $K{y}^h$ peak proves that for such high energies of the sulfur ions very high subshells ($4p$ and $5p$) could be occupied. In order to study the dynamics of formation of $K$-shell vacancy fractions of sulfur projectiles passing through a carbon foil the dependence of sulfur $K$ x-ray production cross sections on foil thickness has been examined separately for each recorded line using the three component model. For each projectile energy the values of $K$-shell hole production cross sections and $K$-shell electron capture cross sections (both common for all recorded x-ray lines in the case of each projectile energy) have been fitted, as well as the specific values (for each recorded x-ray line) of $K$-shell hole filling cross sections, which are directly connected with average lifetimes of appropriate states of sulfur ions. The obtained “experimental” values of $K$-shell vacancy production cross sections are much higher than the theoretical predictions. This suggests that apart from the ionization process the excitation from $K$ shell into higher shells is responsible for a production of $K$-shell vacancies, which has been confirmed by recent classical trajectory Monte Carlo calculations.

We report on a series of calculations for electron-impact excitation of the $\left(5p^{5}6p\right)$ states in xenon from the ground state $\left(5p^6\right){}^{1}S_0$. As in previous calculations for other noble-gas targets, we find strong evidence of channel coupling for all incident energies considered (between threshold and $200\text{eV}$). Although qualitative agreement with the experimental results of Fons and Lin [Phys. Rev. A 58, 4603 (1998)] is achieved, severe quantitative discrepancies of sometimes more than a factor of 2 remain.