We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting, for example, from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglement-based criteria for universality obtained in M. Van den Nest et al. [New J. Phys. 9, 204 (2007)] for the exact, deterministic case can be lifted to the much more general approximate, stochastic case. This allows us to move from the idealized situation (exact, deterministic universality) considered in previous works to the practically relevant context of nonperfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We prove that approximate, stochastic universality is in general a weaker requirement than deterministic, exact universality and provide resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurement-based quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglement-based criteria and recent results regarding the uselessness of states with a high degree of geometric entanglement as universal resources [D. Gross et al., Phys. Rev. Lett. 102, 190501 (2009); M. J. Bremner et al., Phys. Rev. Lett 102, 190502 (2009)].

We study the generation of singlets in quantum networks with nodes initially sharing a finite number of partially entangled bipartite mixed states. We prove that singlets between arbitrary nodes in such networks can be created if and only if the initial states connecting the nodes have a particular form. We then generalize the method of entanglement percolation, previously developed for pure states, to mixed states of this form. As part of this, we find and compare different distillation protocols necessary to convert groups of mixed states shared between neighboring nodes of the network into singlets. In addition, we discuss protocols that only rely on local rules for the efficient connection of two remote nodes in the network via entanglement swapping. Further improvements of the success probability of singlet generation are developed by using particular forms of “quantum preprocessing” on the network. This includes generalized forms of entanglement swapping and we show how such strategies can be embedded in regular and hierarchical quantum networks.

Ising interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e.g., for quantum computation or quantum cryptography). The presence of parasite magnetic fields destroys or alters the expected behavior for which it was intended. In addition, these pairs are generated with some dispersion in their original configuration, so their discrimination is necessary for applications. Nevertheless, discrimination should be made after Ising distortion. Quantum control helps in both problems; making some projective measurements upon the pair to decide the original state to replace it, or just trying to reconstruct it using some procedures which do not alter their quantum nature. Results about the performance of these procedures are reported. First, we will work with pure systems studying restrictions and advantages. Then, we will extend these operations for mixed states generated with uncertainty in the time of distortion, correcting them by assuming the control prescriptions for the most probable one.

We consider a one-dimensional structure where noninteracting spin-$s$ scattering centers, such as quantum impurities or multilevel atoms, are embedded at given positions. We show that the injection into the structure of unpolarized flying qubits, such as electrons or photons, along with path detection suffice to accomplish spin-state teleportation between two centers via a third ancillary one. No action over the internal quantum state of both the spin-$s$ particles and the flying qubits is required. The protocol enables the transfer of quantum information between well-separated static entities in nanostructures by exploiting a very low control mechanism, namely scattering.

We present a procedure for the construction of accurate Kohn-Sham potentials of quasispherical molecules starting from the first-principles valence densities. The method is demonstrated for the case of icosahedral ${\mathrm{C}}_{20}{}^{2+}$ and ${\mathrm{C}}_{60}$ molecules. Provided the density is $N$ representable the Hohenberg-Kohn theorem guarantees the uniqueness of the obtained potentials. The potential is iteratively built following the suggestion of R. van Leeuwen and E. J. Baerends [Phys. Rev. A 49, 2421 (1994)]. The high symmetry of the molecules allows a parametrization of the angular dependence of the densities and the potentials using a small number of symmetry-adapted spherical harmonics. The radial behavior of these quantities is represented on a grid and the density is reconstructed from the approximate potential by numerically solving the coupled-channel Kohn-Sham equations. Subsequently, the potential is updated and the procedure is continued until convergence is achieved.

We have studied the effect of atomic electrons on the nuclear transition from the isomeric ${}^{229m}\mathrm{Th}$ state to the ground ${}^{229g}\mathrm{Th}$ state in ${}^{229}\mathrm{Th}$${}^{+}$ due to the electronic bridge process. The exact value of the nuclear transition frequency is unknown so far; therefore, we have developed a formalism that can be used for any nuclear transition frequency. We have calculated positions of several high-lying even-parity states which are not presented in experimental atomic spectra databases. We have found their energy levels and $g$ factors.

We report on an efficient rf-induced forced evaporative cooling of an ensemble of ${}^{87}\mathrm{Rb}$ atoms in state $|F=2,m_F=2\rangle$ magnetically trapped in a quadrupole-Ioffe configuration trap. The cigar-shaped trap is oriented with its weak confining axis along the direction of gravity leading to, first, a significant separation of the trapping positions for low-field-seeking atoms with different $m_F$ value and, second, a reduced resonance volume for rf-induced evaporation confined to a small region around the lower tip of the cigar-shaped ensemble. This results in an enhancement of the evaporation efficiency $\alpha \equiv d\ln T/(d\ln N)$ due to either reduced or completely vanishing scattering events between cooled and evaporated atoms. We present data illustrating this effect.

A basic set of equations describing the interaction of a Bose-Einstein condensate (BEC) with a laser field is derived based on a semiclassical model and applied to the problem of mutual guiding of laser and BEC atomic beams. Within this framework we have studied stationary spatially localized solutions of the nonlinear system which describe possible laser and BEC atomic beam guiding and have shown their stability as well. It is also shown that a self-guiding effect can be realized through both single- and multiple-scaled structures of a BEC atomic and a laser beam.

The advent of increasingly precise gyroscopes has played a key role in the technological development of navigation systems. Ring-laser and fiber-optic gyroscopes, for example, are widely used in modern inertial guidance systems and rely on the interference of unentangled photons to measure mechanical rotation. The sensitivity of these devices scales with the number of particles used as $1/\sqrt{N}$. Here we demonstrate how, by using sources of entangled particles, it is possible to do better and even achieve the ultimate limit allowed by quantum mechanics where the precision scales as $1/N$. We propose a gyroscope scheme that uses ultracold atoms trapped in an optical ring potential.

We present a simple model to describe the transient response of two coupled resonators probed by a monochromatic wave whose frequency is rapidly swept across the resonances with respect to their characteristic photon lifetimes. The model is applied to analyze the dynamic behavior of the modal coupling between two degenerate resonances of the same cavity. In particular, this can be used to describe the coupling of counterpropagating whispering gallery modes (WGMs) by Rayleigh scattering. The theory is successfully compared to experiments carried out in silica microspheres. These results show that this ringdown technique can be extended to accurately measure linear properties and frequency splittings of high-quality factor WGM microresonators.

In this article we explore the quantum properties of a degenerate optical parametric oscillator when it is tuned to the first family of transverse modes at the down-converted frequency. Recently we found [C. Navarrete-Benlloch et al., Phys. Rev. Lett. 100, 203601 (2008)] that above threshold a TEM${}_{10}$ mode following a random rotation in the transverse plane emerges in this system (we denote it as the bright mode), breaking thus its rotational invariance. Then, owing to the mode orientation being undetermined, we showed that the phase quadrature of the transverse mode orthogonal to this one (denoted as the dark mode) is perfectly squeezed at any pump level and without an increase in the fluctuations on its amplitude quadrature (which seems to contradict the uncertainty principle). In this article we go further in the study of this system and analyze some important features not considered previously. First we show that the apparent violation of the uncertainty principle is just that—“apparent”—as the conjugate pair of the squeezed quadrature is not another quadrature but the orientation of the bright mode (which is completely undetermined in the long term). We also study a homodyne scheme in which the local oscillator is not perfectly matched to the dark mode, as this could be impossible in real experiments due to the random rotation of the mode, showing that even in this case large levels of noise reduction can be obtained (also including the experimentally unavoidable phase fluctuations). Finally, we show that neither the adiabatic elimination of the pump variables nor the linearization of the quantum equations are responsible for the remarkable properties of the dark mode (which we prove analytically and through numerical simulations, respectively), which were simplifying assumptions used in Navarrete-Benlloch et al. [Phys. Rev. Lett. 100, 203601 (2008)]. These studies show that the production of noncritically squeezed light through spontaneous rotational symmetry breaking is a robust phenomenon.

We investigate the mode structure of a random laser consisting of a porous semiconductor matrix infiltrated with and surrounded by laser dye. The experimental parameters that influence the types of lasing that are observed are identified. The spatial structure of random laser modes is accessed experimentally by a spatially and spectrally selective detection scheme. We show that random laser modes are distinct from laser speckle.

We study pure phase damping of two qubits due to fluctuating fields. As frequently employed, decoherence is thus described in terms of random unitary (RU) dynamics, that is, a convex mixture of unitary transformations. Based on a separation of the dynamics into an average Hamiltonian and a noise channel, we are able to analytically determine the evolution of both entanglement and purity. This enables us to characterize the dynamics in a concurrence-purity (CP) diagram: We find that RU phase-damping dynamics sets constraints on accessible regions in the CP plane. We show that initial state and dynamics contribute to final entanglement independently.

We present a detailed experimental and theoretical study of edge enhancement in optically pumped Rb vapor in coated cylindrical pyrex glass cells. The Zeeman polarization of Rb atoms is produced and probed in the vicinity ($~$${10}^{-4}$ cm) of the cell surface by evanescent pump and probe beams. Spin-polarized Rb atoms diffuse throughout the cell in the presence of magnetic field gradients. In the present experiment the edge enhanced signal from the back surface of the cell is suppressed compared to that from the front surface, due to the fact that polarization is probed by the evanescent wave at the front surface only. The observed magnetic resonance line shape is reproduced quantitatively by a theoretical model and yields information about the dwell time and relaxation probability of Rb atoms on Pyrex glass surfaces coated with antirelaxation coatings.

Coherence properties of the down-converted beams generated in spontaneous parametric down-conversion are investigated in detail using an iCCD camera. Experimental results are compared with those from a theoretical model developed for pulsed pumping with a Gaussian transverse profile. The results allow us to tailor the shape of correlation area of the signal and idler photons using pump-field and crystal parameters. As an example, splitting of a correlation area caused by a two-peak pump-field spectrum is experimentally studied.

The relativistic nuclear recoil, higher-order interelectronic-interaction, and screened QED corrections to the transition energies in Li-like ions are evaluated. The calculation of the relativistic recoil effect is performed to all orders in $1/Z$. The interelectronic-interaction correction to the transition energies beyond the two-photon-exchange level is evaluated to all orders in $1/Z$ within the Breit approximation. The evaluation is carried out employing the large-scale configuration-interaction Dirac-Fock-Sturm method. The rigorous calculation of the complete gauge invariant sets of the screened self-energy and vacuum-polarization diagrams is performed utilizing a local screening potential as the zeroth-order approximation. The theoretical predictions for the $2p_j$-$2s$ transition energies are compiled and compared with available experimental data in the range of the nuclear charge number $Z=10$–60.

We demonstrate an iterative scheme for coupled-cluster property calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline-earth-metal ions are calculated using relativistic coupled-cluster theory and the role of electron correlation is examined. Then a detailed analysis of the higher-order terms is carried out. Based on the results, we arrive at an optimal form of the dressed operator, which we recommend for properties calculations with relativistic coupled-cluster theory.

We present a generic approach for treating the effect of nuclear motion in high-order harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters as a nuclear correlation function. We express the nuclear correlation function in terms of Franck-Condon factors, which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the high-order harmonic generation process. We show results for the isotopes CH${}_4$ and CD${}_4$ and thereby provide direct theoretical support for a recent experiment [S. Baker et al., Science 312, 424 (2006)] that uses high-order harmonic generation to probe the ultrafast structural nuclear rearrangement of ionized methane.

We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.