We investigate the separability properties of quantum two-party Gaussian states in the framework of the operator formalism for the density operator. Such states arise as natural generalizations of the entangled state originally introduced by Einstein, Podolsky, and Rosen. We present explicit forms of separable and nonseparable Gaussian states.

We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev-like decomposition of the wave function. We derive for a fixed hyper-radius an integro-differential equation for the angular eigenvalue and wave function. We discuss properties of the solutions and illustrate with numerical results. The correlations lower the interaction energy for $N=20\mathrm{}$ by about a factor of 5.

In light of new data on neutron distributions from experiments with antiprotonic atoms [Trzcinska et al., Phys. Rev. Lett. 87, 082501 (2001)], we reexamine the role of nuclear-structure uncertainties in the interpretation of measurements of parity violation in atoms using chains of isotopes of the same element. With these new nuclear data, we find an improvement in the sensitivity of isotopic chain measurements to “new physics” beyond the standard model. We compare possible constraints on “new physics” with the most accurate to date single-isotope probe of parity violation in the Cs atom. We conclude that presently isotopic chain experiments employing atoms with nuclear charges $Z\lesssim 50$ may result in more accurate tests of the weak interaction.

Recent work has raised the possibility that quantum-information-theory techniques can be used to synchronize atomic clocks nonlocally. One of the proposed algorithms for quantum clock synchronization (QCS) requires distribution of entangled pure singlets to the synchronizing parties [R. Jozsa et al., Phys. Rev. Lett. $85$ 2010 (2000)]. Such remote entanglement distribution normally creates a relative phase error in the distributed singlet state, which then needs to be purified asynchronously. We present a relativistic analysis of the QCS protocol that shows that asynchronous entanglement purification is not possible, and, therefore, the proposed QCS scheme remains incomplete. We discuss possible directions of research in quantum-information theory, which may lead to a complete, working QCS protocol.

The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation that can realize such a transformation. The result obtained is universal for arbitrary entangled two-qubit states and it discloses that the corresponding local filter is not unique for density matrices with rank $n=2\mathrm{}$ and can be exclusively determined for that with $n=3\mathrm{}$ and 4. As illustrations, a four-parameter family of mixed states are explored, the local filter as well as the transformation probability are given explicitly, which verify the validity of the general result.

The interaction of a Rydberg electron with a ground-state atom is modeled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for ${}^1{\Sigma }^{+}$ and ${}^3{\Sigma }^{+}$ states of LiH and ${\mathrm{H}}_2,$ also ${}^2{\Sigma }^{+}$ states of LiHe, for up to the ninth state of a specified symmetry. Results for LiNe are also discussed. Overall, good qualitative and in some cases quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single nonzero potential emerges from the remaining flat manifold. Such behavior explains, for example, the presence of high barriers at large distances seen in ab initio calculations for the ${}^{1,3}{\Sigma }_{g,u}^{+}$ $n=3\mathrm{}$ states of molecular hydrogen. For the systems involving H the Fermi results are generally better for the weaker, triplet, interactions than the singlets. In the case of near-degenerate levels the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. In LiHe, where the interactions are weaker, generally for separations larger than about ${10a}_0$ the Fermi model obtains barrier positions within ${1a}_0$ and maxima within 10 ${\mathrm{cm}}^{\mathrm{-}1}$. For LiNe, because of the very small scattering length for electrons in neon, largely qualitative results are obtained. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.

Some properties of Grassmann products of one-electron operators and of cumulants and related quantities for two-electron reduced density matrices (2-RDMs) are reported. The results suggest that any physical significance of the Grassmann product plus cumulant decomposition must be based on the physics of the system described, not just on the mathematical structure. The Grassmann product plus cumulant decomposition of the 2-RDM is resolved into components based on unitary invariants. Simple examples using mathematically acceptable but physically unlikely wave functions show that a Grassmann product differing from the usual one may better approximate the 2-RDM, and that the usual Grassmann product, cumulant, and 2-RDM can be mutually proportional.

Helium double photoionization $(\gamma ,2e)$ triple differential cross sections (TDCSs) were measured at an excess energy of 60 eV using a dual toroidal spectrometer and synchrotron radiation from a helical undulator (BL-28A, Photon Factory, Japan). Energy-sharing ratios ${(R=E}_2{/E}_1)$ for the two ejected electrons of 5 and 11 are studied with both right- and left-handed elliptically polarized light. The TDCSs are found to be in good agreement with those obtained using the hyperspherical R matrix with semiclassical outgoing waves theory. The circular dichroism for a limited mutual angular range $({\phi }_{12}\approx 110°–200°)$ is determined from the experimental data for both $R=5\mathrm{}$ and 11, and compared to theoretical calculations performed over the complete range of mutual angles. No dynamic nodes are found in either the experimental (within the explored ${\phi }_{12}$ range) or theoretical circular dichroism for these R values at this excess energy.

Hard x-ray emission in the energy range of 30–300 keV from copper plasmas produced by 100-fs, 806-nm laser pulses at intensities in the range of ${10}^{15}-{10}^{16}\hspace{0.5em}{\mathrm{W}\mathrm{}\mathrm{cm}}^{-2}$ is investigated. We demonstrate that surface roughness of the targets overrides the role of polarization state in the coupling of light to the plasma. We further show that surface roughness has a significant role in enhancing the x-ray emission in the above mentioned energy range.

Most of the theoretical work about channeling of fast particles in crystal structures takes as a starting point a particle already in the target’s bulk. In this paper, we address theoretically the channeling process itself, i.e., the injection of a relativistic electron from vacuum into the crystalline target. We show that, contrary to that general assumption, the target surface induces longitudinal as well as transversal dynamics into the channeled electron wave function. We present an efficient method for computing the eigenstates of the general relativistic electron-target scattering problem, and use it to the case of planar $\mathrm{}\left(110\right)\mathrm{}$ channeling in silicon. The angular distribution of the transmitted electron is analyzed, and shown to depend strongly on the target thickness. In addition, we derive analytical closed formulas for the probability of the incident electron to be channeled in the different crystal states, and check their validity by comparison with the results of the exact numerical solutions. Finally, we identify the electron initial conditions that create a population inversion in the channeled states.

We present a scheme for a reconstruction of states of quantum systems from incomplete tomographiclike data. The proposed scheme is based on the Jaynes principle of maximum entropy. We apply our algorithm for a reconstruction of motional quantum states of neutral atoms. As an example we analyze the experimental data obtained by Salomon and co-workers and we reconstruct Wigner functions of motional quantum states of Cs atoms trapped in an optical lattice.

We generalize the basic concepts of the positive-P and Wigner representations to unstable quantum-optical systems that are based on nonorthogonal quasimodes. This lays the foundation for a quantum description of such systems, such as, for example an unstable cavity laser. We compare both representations by calculating the tunneling times for an unstable resonator optical parametric oscillator.

We find that the anomalous behavior of optical spatial screening solitons observed in the high-symmetry paraelectric phase is a consequence of nonlinear dielectric effects. These, coupled to space charge in saturated conditions, change the effective optical nonlinearity even far from the phase-transition regime.

Absolute differential and total cross sections for single electron loss of ${\mathrm{He}}^{+}$ ions impinging on Ne were measured in the energy range from 2.0 to 5.0 keV. The absolute differential cross sections display a decreasing behavior with increasing angle. The measured electron-loss cross sections show a monotonically increasing behavior as a function of the incident energy and are found to be of the order of magnitude between ${10}^{-5}$ and ${10}^{-4}{\AA }^2.$ The total cross section is compared with other available measurements and theoretical models at high energy. An extrapolation of the high-energy data to low energies shows good agreement with the present data.

We report the experimental estimation of arbitrary qubit states using a succession of N measurements on individual qubits, where the measurement basis is changed during the estimation procedure conditioned on the outcome of previous measurements (self-learning estimation). Two hyperfine states of a single trapped ${}^{171}{\mathrm{Yb}}^{+}$ ion serve as a qubit. It is demonstrated that the difference in fidelity between this adaptive strategy and passive strategies increases in the presence of decoherence.

In quantum operations, probabilities characterize both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of $\mathrm{pure}\to \mathrm{pure}$ state transformations, covering both probabilistic and deterministic cases. We then discuss the role of majorization in describing the dynamics of mixing in quantum operations. The conditions for mixing enhancement for all initial states are derived. We show that mixing is monotonically decreasing for deterministic $\mathrm{pure}\to \mathrm{pure}$ transformations, and discuss the relationship between these transformations and deterministic local operations with classical communication entanglement transformations.

We show that deterministic and conclusive transformation properties of bipartite entanglement in the nonasymptotic scenario (when many but a finite number of copies of a source state are collectively manipulated) are fundamentally different from those in both the single-copy and asymptotic limits. For instance, by generalizing the notion of local comparability of entanglement in the single-copy case, we provide a complete classification of bipartite entanglement transformations in the nonasymptotic scenario. We also show that, unlike the asymptotic case, collective operations need not always be advantageous for the many-copy case. In particular, we show that (1) there exists a class of states for which the optimal conclusive transformation probability decreases exponentially with increasing number of copies, even if the source state has more entropy of entanglement, and (2) optimal conclusive transformation probability need not be a monotonic function of the number of copies.

We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.

Cross sections for capture of negative muons $\left({\mu }^{-}\right)$ and antiprotons $\left(\overline{p}\right)$ by helium, neon, argon, krypton, and xenon atoms are calculated using the fermion molecular dynamics method. These cross sections are used to estimate the capture ratios in mixtures.

Momentum distributions of the recoil target ion and the ejected electron have been calculated for 75-keV ${\mathrm{H}}_2^{+}+\mathrm{He}$ collisions by applying the classical trajectory Monte Carlo (CTMC) and the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) theory. A qualitative agreement was found between the calculated centroid values of the momentum distributions and the corresponding experimental data published recently by An et al. [Phys. Rev. A 63, 030703 (2001)]. The presence of postcollision interaction effects in the momentum distributions was analyzed repeating the CTMC calculations with a short-range model potential between the electron and the projectile ion as a function of the interaction length. The role of two-center effects was investigated by comparing the CDW-EIS results with those obtained in the first-Born approximation.