Using group-theoretical methods and numerical simulations, we show how to act on the topological charge of individual vortices in Bose-Einstein condensates by using control potentials with appropriate discrete symmetries. As examples of our methodology we study charge inversion and vortex erasing by acting on a set of control-laser Gaussian beams generating optical dipole traps.

A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schrödinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models.

We propose the use of a structured planar mirror as the way to obtain the physical conditions for which the combination of an evanescent field and a surface plasmon potential would result in an atom-trap well located at $\sim 0.6\mu \mathrm{m}$ above the mirror’s surface. We present calculations from which we obtain a well depth slightly bigger than $7\mu \mathrm{K}$. The configuration and calculations we present are for a single trap, however, there would appear to be no restrictions to extend this idea to a two-dimensional matrixlike array of traps, hinting on the possibility for tailored design of latticelike trap structures.

In this Rapid Communication a generalization of the BEC-BCS crossover theory to a multicomponent superfluid is presented by studying a three-species mixture of Fermi gas across two Feshbach resonances. At the BEC side of resonances, two kinds of molecules are stable which gives rise to a two-component Bose condensate. This two-component superfluid state can be experimentally identified from the radio-frequency spectroscopy, density profile, and short noise measurements. As approaching the BCS side of resonances, the superfluidity will break down at some point and yield a first-order quantum phase transition to normal state, due to the mismatch of three Fermi surfaces. Phase separation instability will occur around the critical regime.

We derive a Bell inequality for testing violation of local realism. Quantum nonlocality of several four-qubit states is investigated. These include the Greenberger-Zeilinger-Horne (GHZ) state, $W$ state, linear cluster state, and the state $\mid \chi ⟩$ that has recently been proposed in [Phys. Rev. Lett. 96, 060502 (2006)]. The Bell inequality is optimally violated by $\mid \chi ⟩$ but not violated by the GHZ state. The linear cluster state also violates the Bell inequality though not optimally. The state $\mid \chi ⟩$ can thus be discriminated from the linear cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by considering the usefulness of a family of four-qubit mixed states as resources for two-qubit teleportation. Our results generalize those in [Phys. Rev. Lett. 72, 797 (1994)].

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, $XY$, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the $XY$ models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.

Random-bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require “strong” RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random-bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the “min-entropy” of the system, and we employ this value to distill a truly random-bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.

One of the most basic computational problems is the task of finding a desired item in an ordered list of $N$ items. While the best classical algorithm for this problem uses ${\log }_{2}N$ queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using $4{\log }_{605}N\approx 0.433{\log }_{2}N$ queries, which improves upon the previously best known exact algorithm.

We investigate the entanglement transfer from a bipartite continuous-variable (CV) system to a pair of localized qubits assuming that each CV mode couples to one qubit via the off-resonance Jaynes-Cummings interaction with different interaction times for the two subsystems. First, we consider the case of the CV system prepared in a Bell-like superposition and investigate the conditions for maximum entanglement transfer. Then we analyze the general case of two-mode CV states that can be represented by a Schmidt decomposition in the Fock number basis. This class includes both Gaussian and non-Gaussian CV states, as, for example, twin-beam (TWB) and pair-coherent (TMC, also known as two-mode-coherent) states, respectively. Under resonance conditions, equal interaction times for both qubits and different initial preparations, we find that the entanglement transfer is more efficient for TMC than for TWB states. In the perspective of applications such as in cavity QED or with superconducting qubits, we analyze in detail the effects of off-resonance interactions (detuning) and different interaction times for the two qubits, and discuss conditions to preserve the entanglement transfer.

In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential $v_{ee}\left(\mathbf{r}\right)$. In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is $v_{ee}\left(r\right)=v_{ee}\left(0\right)+\beta r+O\left(r^2\right)$, with $v_{ee}\left(0\right)$ being finite. By assuming that the Schrödinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange $v_x\left(\mathbf{r}\right)$ and correlation $v_c\left(\mathbf{r}\right)$ potentials. These functions also approach the nucleus linearly with the linear term of $v_x\left(\mathbf{r}\right)$ being solely due to the lowest-order correlation kinetic effects, and the linear term of $v_c\left(\mathbf{r}\right)$ being due solely to the higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.

We have theoretically demonstrated that circularly polarized laser pulses induce electric currents and magnetic moments in ring-shaped molecules ${\mathrm{Na}}_{10}$ and benzene. The time-dependent adiabatic local density approximation is employed for this purpose, solving the time-dependent Kohn-Sham equation in real space and real time. It has been found that the electric currents are induced efficiently and persist continuously even after the laser pulses were switched off provided the frequency of the applied laser pulse is in tune with the excitation energy of the electronic excited state with the dipole strength for each molecular system. The electric currents are definitely revealed to be a second-order nonlinear optical response to the magnitude of the electric field. The magnetic dipole moments inevitably accompany the ring currents, so that the molecules are magnetized. The production of the electric currents and the magnetic moments in the present procedure is found to be much more efficient than that utilizing static magnetic fields.

Only part of the correlation energy can be obtained from the wave function when expanded as a finite and linear combination of Slater determinants. For the remaining part, it was proposed by several authors to use density-functional theory. Thus, various methods coupling wave functions with density functionals were investigated in the past. In the present a class of such methods was developed, relying on a partition of the orbital space. Notably, for this coupled method special efforts were made to avoid double countings between the contributions of the wave function and the density functional. Moreover, the coupling was defined in order to allow a systematic improvement of the results. As a second step, the method was put to the test for spherically symmetric systems, especially in the case of near degeneracy. The numerical results obtained were discussed in order to improve the model. Finally, the wave function contribution that was retained relied on a coupled-cluster formalism restricted to a small orbital space, whereas the density functional was chosen as a semilocal expression based on the physical picture of one-particle ionization potentials.

We calculate the electron energy spectrum of ionization by a high-energy photon, accompanied by creation of an $e^{-}{e}^{+}$ pair. The total cross section of the process is also obtained. The asymptotics of the cross section does not depend on the photon energy. At the photon energies exceeding a certain value ${\omega }_0$ this appears to be the dominant mechanism of formation of the ions. The dependence of ${\omega }_0$ on the value of nuclear charge is obtained. Our results are consistent with experimental data.

Three-dimensional fully differential cross sections for heavy-particle-impact ionization of helium are examined. Previously, the three-body distorted-wave (3DW) model has achieved good agreement with experiment in the scattering plane for small momentum transfers, but poor agreement for large momentum transfers. Poor agreement was also observed outside the scattering plane for all momentum transfers. In particular, the 3DW calculations predicted cross sections that were too small both perpendicular to the scattering plane and for large momentum transfers. The important unanswered question concerns the physical effects that cause the significant disagreement between experiment and theory. In previous works, the role of the projectile-ion interaction has been examined. Although the importance of exchange between the ejected electron and the residual bound electrons has been well established, and frequently studied, for electron-impact ionization, the importance of this effect has not been examined for heavy-particle scattering. In this paper we examine the role of this effect for heavy-particle scattering.

Cross sections for elastic and inelastic electron collisions with $\mathrm{C}{\mathrm{H}}_{3}X$ $(X=\mathrm{Cl},\mathrm{Br},\mathrm{I})$ molecules are calculated. For the lowest partial wave, the resonance $R$-matrix theory, and for the higher partial waves, the theory of scattering by dipolar plus polarization potential, are used. It is shown that the rotationally elastic scattering amplitude for a polar molecule in the fixed-nuclei approximation is logarithmically divergent for the forward direction, and a closure formula is derived to speed up the convergence at small angles. In treating the nuclear motion, only $\mathrm{C}\text{−}X$ stretch vibrations are taken into account. The dipole moment as a function of the $\mathrm{C}\text{−}X$ distance is modeled by a function incorporating the experimental value of the molecular dipole moments at the equilibrium distance and the derivatives of the dipole moments extracted from the experimental data on infrared intensities. This is supplemented by ab initio calculations of the dipole moment function for $\mathrm{C}{\mathrm{H}}_3\mathrm{Br}$ using the multiconfigurational valence bond method. The results for scattering cross sections show pronounced features caused by vibrational Feshbach resonances and threshold cusps. The features are most noticeable at the $v=6$, 7, and 8 thresholds in $\mathrm{C}{\mathrm{H}}_3\mathrm{Cl}$, at the $v=3$ and 4 thresholds in $\mathrm{C}{\mathrm{H}}_3\mathrm{Br}$, and at the $v=1$ threshold in $\mathrm{C}{\mathrm{H}}_3\mathrm{I}$.

We report measurements of total, positronium (Ps) formation, and excitation cross sections for 0.1–60-eV positrons $\left(e^{+}\text{’s}\right)$ and total and excitation cross sections for 6–200-eV electrons ($e^{-}$’s) scattered by Cs atoms. Ps formation cross sections are measured by both detecting $\gamma$ ray coincidences and a beam transmission technique while all other cross sections are measured using beam transmission techniques. We discuss our findings and compare them with other experimental results and theoretical calculations.

We propose an alternative scenario for the generation of entanglement between rotational quantum states of two polar molecules. This entanglement arises from dipole-dipole interaction, and is controlled by a sequence of laser pulses simultaneously exciting both molecules. We study the efficiency of the process, and discuss possible experimental implementations with cold molecules trapped in optical lattices or in solid matrices. Finally, various entanglement detection procedures are presented, and their suitability for these two physical situations is analyzed.

We describe two-photon photoassociation (PA) experiments operated in an ultracold gas of metastable ${}^4\mathrm{He}^{*}$ atoms in the $2{}^{3}S_1$ state. Atom-molecule dark resonances as well as Raman signals provide information on the exotic molecule in the least bound vibrational $J=2$, $v=14$ state of the ${}^5\Sigma _g^{+}$ interaction potential of two spin-polarized metastable atoms. The physical origin of the various two-photon PA signals is first discussed. Their linewidths are interpreted in terms of processes limiting the lifetime $\tau$ of the exotic molecule. A value of $\tau =1.4\pm 0.3\mathrm{\mu }\mathrm{s}$ is found, which significantly differs from two recent calculations of the Penning ionization rate induced by spin-dipole coupling [T. J. Beams et al., Phys. Rev. A 74, 014702 (2006); M. Portier and G. V. Shlyapnikov (unpublished)]. The limitation of $\tau$ by atom-molecule inelastic collisions is investigated and ruled out.

We present a rigorous study of cold and ultracold collisions of $\mathrm{Yb}\mathrm{F}\left({}^2\Sigma \right)$ molecules with He atoms in external electric and magnetic fields based on an accurate calculation of the interaction potential surface and quantum theory of atom-molecule scattering. We analyze the mechanisms of collisional depolarization of the electron and nuclear spins of YbF and demonstrate that the rate constants for elastic and inelastic collisions of YbF with He are sensitive to the magnitudes of the applied fields. Collisions of heavy polar molecules like YbF may thus be easily manipulated with external electromagnetic fields. We show that collisional spin relaxation of YbF molecules in rotationally excited states is suppressed by electric fields much more significantly than the spin relaxation in the ground rotational state. We explain this by the influence of electric-field-induced Feshbach resonances, which occur at much lower collision energies when the molecule is rotationally excited. Our results suggest that heavy polar molecules may be amenable to magnetic trapping in a buffer gas of He, which could greatly enhance the sensitivity of spectroscopic experiments to measure the electric dipole moment of the electron.

We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard-wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well-isolated Rabi resonances, where the detuning-adapted Rabi frequency coincides with the transition frequency between vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined.