We study entanglement distribution in quantum complex networks where nodes are connected by bipartite entangled states. These networks are characterized by a complex structure, which dramatically affects how information is transmitted through them. For pure quantum state links, quantum networks exhibit a remarkable feature absent in classical networks: it is possible to effectively rewire the network by performing local operations on the nodes. We propose a family of such quantum operations that decrease the entanglement percolation threshold of the network and increase the size of the giant connected component. We provide analytic results for complex networks with an arbitrary (uncorrelated) degree distribution. These results are in good agreement with numerical simulations, which also show enhancement in correlated and real-world networks. The proposed quantum preprocessing strategies are not robust in the presence of noise. However, even when the links consist of (noisy) mixed-state links, one can send quantum information through a connecting path with a fidelity that decreases with the path length. In this noisy scenario, complex networks offer a clear advantage over regular lattices, namely, the fact that two arbitrary nodes can be connected through a relatively small number of steps, known as the small-world effect. We calculate the probability that two arbitrary nodes in the network can successfully communicate with a fidelity above a given threshold. This amounts to working out the classical problem of percolation with a limited path length. We find that this probability can be significant even for paths limited to few connections and that the results for standard (unlimited) percolation are soon recovered if the path length exceeds by a finite amount the average path length, which in complex networks generally scales logarithmically with the size of the network.

Usually it is accepted that the probabilities of the electric-multipole electron transitions are rapidly decreasing functions of their multipolarity. Therefore while calculating the probabilities of electronic transitions between the configurations of certain chosen parities, it seems sufficient to take into account the first nonzero term, i.e., to consider the electron transitions of lowest multipolarity permitted by the exact selection rules. This paper aims at verifying this assumption on the example of electric-octupole transitions in ${\mathrm{W}}^{24+}$ ion. For this purpose the large-scale multiconfiguration Hartree-Fock and Dirac-Fock calculations have been performed for the configurations [Kr]$4d^{10}4f^4$ and [Kr]$4d^{10}4f^{3}5s$ energy levels of ${\mathrm{W}}^{24+}$ ion. The relativistic corrections were taken into account in the quasirelativistic Breit-Pauli and fully relativistic Breit (taking into account QED effects) approximations. The role of correlation, relativistic, and QED corrections is discussed. Line strengths, oscillator strengths, and transition probabilities in Coulomb and Babushkin gauges are presented for $E1$ and $E3$ transitions among these levels.

Multielectron coincidence spectroscopy has been used to study multiple ionization of atomic mercury. The binding energies of triply and quadruply ionized states of Hg have been determined from three- and fourfold electron coincidences. Relativistic ab initio theory has been used to calculate the state energies and predict the experimental findings.

When the continuum distorted wave with eikonal initial state (CDW-EIS) [D. S. Crothers and J. F. McCann, J. Phys B 16, 3229 (1983)] theory is applied to the evaluation of ionization cross sections, many additional approximations are assumed. However, usually, the influence of these approximations is not clear. Aiming to estimate them, we compare the differential and total cross sections obtained with diverse approximations for ionization of He atoms by proton impact. We analyze the post-prior discrepancy, which depends on the perturbative Hamiltonian applied in the scattering amplitude. We study the dependence of the cross sections on the description of the initial and final states. For this purpose, we use the 1Z and 5Z variational and numerical Optimized Potential Model (OPM) [J. D. Talman, Comput. Phys. Commun. 54, 85 (1989)] bound states for the initial target state, and for the final target state we set Coulomb waves with proper effective charges or the continuum state of an OPM potential model. The cross sections resulting from OPM post and prior versions are identical and show excellent agreement with experimental data in each case. Nevertheless, the cross section derived by the prior CDW-EIS, 5Z initial wave, and corresponding continuum state gives comparable results, requiring shorter computational work. Then we study the determination of the impact parameter ionization probability from the transition amplitudes, also including an axial symmetry for the ionization process. The hypothesis of this axial symmetry saves an angular integration in the evaluation of the probabilities. We analyze the variation of these probabilities within the post and prior formalisms and mention initial and final states, according to the supposed symmetry. We found that the probabilities derived with the axial symmetry concentrate at a lower impact parameter than the usual ones and are quite sensitive to the approximations used for the CDW-EIS evaluation. Furthermore, these probabilities underestimate distant collisions. In the last section we introduce the projectile-residual ion potential, and we discuss the effect of the diverse approximations on the dependence of the cross section as a function of the projectile scattering angle. We compare the projectile angular distribution resulting from a full Coulomb interaction between the ions with the one obtained by a screened potential, but in the latter case the theoretical distributions underestimate the experimental data. The OPM and 5Z functions give a good description of the experimental data.

We report measurements of a significant increase in the two-body loss rate in an ${}^{85}\mathrm{Rb}$ magneto-optic trap (MOT) caused by the addition of light resonant with the $5P_{3/2}$-to-$5D_{5/2}$ transition (776 nm) in Rb. Exposure to the additional light resulted in up to a factor of 5 decrease in the steady-state number of atoms in the MOT. This loss is attributed to more than an order of magnitude increase in the light-assisted collision rate brought about by the 776-nm light. By measuring the intensity dependence of the loss rate, the loss channel was identified to be the relatively long-lived $5S_{1/2}$-$5D_{5/2}$ molecular potential.

The atom-by-atom characterization of quantum gases requires the development of novel measurement techniques. One particularly promising new technique demonstrated in recent experiments uses strong fluorescent laser scattering from neutral atoms confined in a short-period optical lattice to measure the positions of individual atoms in the sample. A crucial condition for the measurements is that atomic hopping between lattice sites must be strongly suppressed despite substantial photon recoil heating. This paper models three-dimensional polarization gradient cooling of atoms trapped within a far-detuned optical lattice. The atomic dynamics are simulated using a hybrid Monte Carlo and master-equation analysis in order to predict the frequency of processes which give rise to degradation or loss of the fluorescent signal during measurements. It is shown, consistently with the experimental results, that there exists a wide parameter range in which the lifetime of strongly fluorescing isolated lattice-trapped atoms is limited by background gas collisions rather than radiative processes. In these cases the total number of scattered photons can be as large as ${10}^8$ per atom. The performance of the technique is related to relevant experimental parameters.

We show that the interplay between spin-changing collisions and quadratic Zeeman coupling provides a mechanism for the formation of repulsively bound composites in high-spin fermions, which we illustrate by considering spin flips in an initially polarized hard-core one-dimensional Mott insulator of spin-$3/2$ fermions. We show that after the flips the dynamics is characterized by the creation of two types of exciton-biexciton composites. We analyze the conditions for the existence of these bound states and discuss their intriguing properties. In particular we show that the effective mass and stability of the composites depends nontrivially on spin-changing collisions, on the quadratic Zeeman effect, and on the initial exciton localization. Finally, we show that the composites may remain stable against inelastic collisions, opening the possibility of interesting quantum composite phases.

Analytical solutions for (1+1)-dimensional surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using these analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, along with solutions for surface dipole and tripole solitons, are also given.

We study the steady optical response of a five-level atomic system in the parametric region where resonant two-photon transitions are much stronger than far-detuned single-photon transitions. We find that the concurrent absorption of two weak probe fields can be well suppressed in a narrow spectral region to attain electromagnetically induced transparency (EIT) via quantum destructive interference between different two-photon transition pathways. To gain a deeper insight into relevant physics, we adiabatically reduce this five-level system with trivial single-photon transitions into a three-level system with vanishing single-photon transitions by deriving an effective Hamiltonian. The two systems have almost the same two-photon absorption spectra exhibiting typical EIT features but are a little different in fine details. This means that most characteristics of two-photon quantum destructive interference are reserved after the adiabatic elimination approximation. In addition, we verify by numerical calculations that the two-photon EIT spectra are insensitive to the dipole-dipole interaction of cold Rydberg atoms when the uppermost level has a high principle quantum number.

An optical realization of the phenomenon of many-body coherent destruction of tunneling, recently predicted for interacting many-boson systems by Gong, Molina, and Hänggi [Phys. Rev. Lett. 103, 133002 (2009)], is proposed for light transport in engineered waveguide arrays. The optical system enables a direct visualization in Fock space of the many-body tunneling control process.

We study the concurrence of arbitrary dimensional bipartite quantum systems. An explicit analytical lower bound of concurrence is obtained which detects entanglement for some quantum states better than some well-known separability criteria and improves the lower bounds, such as from the positive partial transposition, realignment criteria, and Breuer’s entanglement witness.

We present improved calculations of variational energy eigenvalues for the $1s^{2}2s\hspace{0.5em}{}^{2}S$, $1s^{2}3s\hspace{0.5em}{}^{2}S$, and $1s^{2}2p\hspace{0.5em}{}^{2}P$ states of lithium using basis sets with up to 30 224 terms in Hylleraas coordinates. The nonrelativistic energies for infinite nuclear mass are $-7.478\hspace{0.5em}060\hspace{0.5em}323\hspace{0.5em}910\hspace{0.5em}143\hspace{0.5em}7(45)$ a.u. for $1s^{2}2s\hspace{0.5em}{}^{2}S$, $-7.354\hspace{0.5em}098\hspace{0.5em}421\hspace{0.5em}444\hspace{0.5em}316\hspace{0.5em}4(32)$ a.u. for $1s^{2}3s\hspace{0.5em}{}^{2}S$, and $-7.410\hspace{0.5em}156\hspace{0.5em}532\hspace{0.5em}651\hspace{0.5em}6(5)$ a.u. for $1s^{2}2p\hspace{0.5em}{}^{2}P$, which represent the most accurate variational upper bounds to date. An important advantage of the basis sets with multiple distance scales is their exceptional numerical stability.

We introduce a squeezed state source for microwave radiation with tunable parameters in circuit quantum electrodynamics. We show that when a superconducting artificial multilevel atom interacting with a transmission line resonator is suitably driven by external classical fields, two-mode squeezed states of the cavity modes can be engineered in a controllable fashion from the vacuum state via adiabatic following of the ground state of the system. This scheme appears to be robust against decoherence and is realizable with present techniques in circuit quantum electrodynamics.

We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudospin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center-of-mass motion, the atomic collective spin, and the cavity field leads to a strong nonlinearity, resulting in multistable behavior in both matter wave and light wave at the few-photon level.

By using the dynamics described with the quantum Langevin equation and the inseparability criterion for continuous-variable systems [L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).], we discuss a method to judge whether entanglement exists in the evolutions of bipartite systems with continuous variables in their baths. By using this method we investigate a nontrivial example, namely, we judge when the entanglement exists in the evolution of the two coupled anharmonic oscillators in their environments.

We study the Casimir interaction between a dielectric nanosphere and a metallic plane, using the multiple scattering theory. Exact results are obtained with the dielectric described by a Sellmeier model and the metal by a Drude model. Asymptotic forms are discussed for small spheres and large or small distances. The well-known Casimir-Polder formula is recovered at the limit of vanishingly small spheres, while an expression that behaves better at small distances is found for any finite value of the radius. The exact results are of particular interest for the study of quantum states of nanospheres in the vicinity of surfaces.

Understanding the effect of strong laser pulses on the evolution of an atomic or molecular wave function is important in the context of coherent control in the strong-field regime, when power broadening and dynamic Stark shifts become comparable with or bigger than the bandwidth of the control field. We experimentally demonstrate the method of complete characterization of a complex-valued amplitude of a quantum state driven by a strong two-photon field. The method is based on coherent scattering of a weak probe pulse from the strong-field-induced atomic coherence, followed by the detection of the time- and frequency-resolved parametric four-wave-mixing signal. We show that the proposed technique corresponds to a cross-correlation frequency-resolved optical gating (XFROG) of the highly perturbed evolution of an atomic quantum state. Utilizing the XFROG retrieval algorithm, we determine both the amplitude and phase of an atomic wave function at any time moment throughout the interaction with the driving field. The direct retrieval of the time-dependent phase of the wave function, rather than the population dynamics only, enables us to observe the strong-field effects with arbitrary time and frequency resolution.

In an optical superlattice of triple wells containing two mutually interacting atom species in adjacent wells, we show that one species can be transported through the positions of the other species while avoiding significant overlap and direct interaction. The transfer protocol is optimized to be robust against missing atoms of either species in any lattice site, as well as against lattice fluctuations. The degree and the duration of the interspecies overlap during passage can be tuned, making possible a controlled large-scale interaction-induced change of internal states.

We investigate the quantum properties of solitons with nonlocal self-interaction. We find significant changes when compared to the local interaction. Quantum phase diffusion of nonlocal solitons is always reduced with respect to the local interaction and vanishes in the strongly nonlocal limit. Thus, coherence is increased in the nonlocal case. Furthermore, we compare the intrinsic quantum wave packet spreading to the recently discussed classical Gordon-Haus effect for nonlocal solitons [V. Folli and C. Conti, Phys. Rev. Lett. 104, 193901 (2010)].

We show that the entanglement of an initially frequency-entangled photon pair propagating through a disordered scattering medium can be read off in transmission from the coincidence counting rate. The very same quantity also encodes the Thouless time, which is the typical time it takes for a photon to traverse the disordered medium by diffusion.