In this paper, we construct families of nonbinary quantum codes from classical negacyclic codes. The BCH bound for negacyclic codes is applied to determine the dimension and distance of these quantum codes. The parameters of these quantum codes are good compared with the ones available in the literature. We also construct a family of quantum maximum-distance-separable codes with parameters ${\left[[q+1,q-2d+3,d]\right]}_q$, where $q\equiv 1\mathrm{mod}4$ and $2\le d\le (q+3)/2$.

The iterative approach to the line-shape calculations from the transport-relaxation equation was modified to allow its application for low pressures down to the Doppler limit. In our approach functions and operators are decomposed in the Burnett basis. This technique was applied to experimental data presenting the consistency between the line-shape model and measured spectrum corresponding to a signal-to-noise ratio higher than $9\times {10}^4$. Implications for precise molecular spectroscopy as well as for Doppler-width thermometry and spectroscopic Boltzmann constant determination are discussed.

We perform precision measurements on the $5D_{5/2}$ manifold hyperfine intervals of a single trapped ion, ${}^{137}$Ba${}^{+}$. rf spectroscopy is used to measure the hyperfine intervals to an accuracy of a few Hz. Our results provide a three orders of magnitude improvement in accuracy over previous work and also provide a 10-fold improvement in the value of $g_J$ for this level. These results complement our previous work on the 5$D_{3/2}$ manifold of ${}^{137}$Ba${}^{+}$, providing an independent measurement of the nuclear octupole, and a consistency check on atomic structure calculations.

We apply an independent electron model to study $q$-fold target-charge-state production in 25–600 keV/nucleon B${}^{2+}$-Ne collisions for which experimental and theoretical results were published recently [W. Wolff et al., Phys. Rev. A 84, 042704 (2011)]. The model treats projectile and target electrons using a common potential and makes use of a single-determinant wave function for the combined system. The calculated total cross sections for positive recoil ion production as well as for Ne${}^{q+}$ production ($q=1,...,4$) determined in coincidence with an unchanged projectile charge state agree well with experiment where available, i.e., in the 30–400 keV/nucleon energy range. At energies below 200 keV/nucleon the projectile electrons are shown to play a crucial role in reproducing the experimental data for $q=1,...,4$. For the $q\ge 2$ channels the inclusion of projectile electron contributions is needed even at energies above 200 keV/nucleon in order to reproduce the experimental data. As expected, the predictions for the $q=5$ recoil charge state overestimate the experimental data due to a failure of the independent electron model for this extreme channel.

We report ion momentum imaging measurements of dissociative electron attachment to N${}_2$O near the well-known 2.3-eV shape resonance. We have made a comparison to previous results and have used the formalism of O'Malley and Taylor [Phys. Rev. 176, 207 (1968)] to calculate angular O${}^{-}$ anion fragment distributions. Using these angular distributions along with the axial recoil approximation, we show a predominant $\Pi$ contribution to the observed angular O${}^{-}$ distribution with no significant indication of a $\Sigma$ contribution, as previously reported. We conclude that the dissociation takes place in a near-linear geometry and proceeds across a Renner-Teller barrier.

Anticipating the experimental realization of attosecond pulses with photon energies of a few hundred eV to 1 keV, we have developed a formalism that connects the evolution of a UV-pumped nonstationary electronic state to an x-ray probe signal, using the one-electron reduced density operator. The electronic states we wish to follow evolve on time scales of a few femtoseconds, and the valence occupancy structure of these states can be probed, resolved in both space and time, by taking advantage of the inherent locality of core-valence transitions and the comparatively short time scale on which they can be produced. The time-dependent reduced density operator is an intuitively simple quantity, representing the dynamic occupancy structure of the valence levels, but it is well defined for an arbitrary many-body state. This article outlines the connection between the complexities of many-body theory and an intuitive picture of dynamic local orbital occupancy.

We describe a blue-detuned optical lattice for atom trapping which is intrinsically two-dimensional, while providing three-dimensional atom localization. The lattice is insensitive to optical phase fluctuations since it does not depend on field interference between distinct optical beams. The array is created using an arrangement of weakly overlapping Gaussian beams that creates a two-dimensional array of dark traps which are suitable for magic trapping of ground and Rydberg states. We analyze the spatial localization that can be achieved and demonstrate trapping and detection of single Cs atoms in 6- and 49-site two-dimensional arrays.

Magnetic domain patterns in a ferromagnetic Bose-Einstein condensate (BEC) show different properties depending on the quadratic Zeeman effect and dissipation. Another important factor that affects domain patterns and domain growth is superfluid flow of atoms. Domain growth in a ferromagnetic BEC with negative quadratic Zeeman energy is characterized by the same growth law as a (classical) binary fluid in the inertial hydrodynamic regime. In the absence of the superfluid flow, the domain growth law for negative quadratic Zeeman energy is the same as that of scalar conserved fields, such as binary alloys.

We characterized the spectro-polarimetric emission properties of random lasers in the regime of strong scattering. The study involved the preparation of microstructured samples, which were shown to support very stable random laser modes in spectral location and intensity. We show that random lasing modes from such samples are highly polarized in statically random, but well-defined states that can be used as a unique sample identifier. Our findings reveal a strong dependency of the emission spectrum on the pump polarization and demonstrate how the spectro-polarimetric emission can be efficiently manipulated.

Violation of the Bell inequality (or Bell-type inequalities) by nonlocal correlations is justified by relaxation of at least one of the plausible physical constraints used to model such inequality. Based on this fact, in this Brief Report we present a procedure to simulate three-qubit Greenberger-Horne-Zeilinger correlation relaxing two constraints—determinism and no signaling—simultaneously. We have also derived the minimum amount of indeterminism and signaling to be introduced in a system. The corresponding number of signaling and local bits of mutual information needed to communicate are also provided, and thus we are able to focus on the utility of relaxation of these two constraints as useful resources.

The well-known Simpson's paradox, or Yule-Simpson (YS) effect, is often encountered in social-science and medical-science statistics. It occurs when the correlations present in different groups are reversed if the groups are combined. Simpson's paradox also exists in quantum measurements. In this Brief Report, we experimentally realized two analogous effects: the quantum-classical YS effect and the quantum-quantum YS effect in the quantum-dot system. We also compared the probability of obtaining those two effects under identical quantum measurements and found that the quantum-quantum YS effect is more likely to occur than the quantum-classical YS effect.

Chen et al. [Phys. Rev. A 81, 033422 (2010)] claim that adding ${}^4\mathrm{He}$ to spin-exchange optical pumping (SEOP) cells confines ${}^3\mathrm{He}$ atoms to a diffusion-limited region, which effectively reduces the wall relaxation factor $X$. Here $X$ is a phenomenological parameter used to characterize typical SEOP cells; it quantifies the observation that the measured linear slope of the relaxation rate with alkali-metal-atom density exceeds the spin-exchange rate. In addition they claim to demonstrate that magnetic-field gradients cause a diffusive motion of ${}^3\mathrm{He}$. We argue that these claims and other central conclusions drawn by Chen et al. [Phys. Rev. A 81, 033422 (2010)] are inconsistent with the physics of diffusion or should not be made from the data as presented. We also draw attention to several additional issues associated with the results, analysis, and presentation of data in Chen et al. [Phys. Rev. A 81, 033422 (2010)] that confound clear interpretation.

We present a scheme for generating a synthetic magnetic field and spin-orbit coupling via Raman coupling in highly magnetic lanthanide atoms such as dysprosium. Employing these atoms offers several advantages for realizing strongly correlated states and exotic spinor phases. The large spin and narrow optical transitions of these atoms allow the generation of synthetic magnetic fields that are an order of magnitude larger than those in the alkali metals, but with considerable reduction of the heating rate for equal Raman coupling. The effective Hamiltonian of these systems differs from that of the alkali metals' by an additional nematic coupling term, which leads to a phase transition in the dressed states as detuning varies. For high-spin condensates, spin-orbit coupling leads to a spatially periodic structure, which is described in a Majorana representation by a set of points moving periodically on a unit sphere. We name this a “Majorana spinor helix,” in analogy to the persistent spin-$\frac{1}{2}$ helix observed in electronic systems.

There has been a surprising degree of uncertainty about how, or even whether, the standard semiclassical theory of Van Vleck and Gutzwiller (VVG) can be used to treat the time-dependent dynamics of tunneling through barriers. At issue is how semiclassical theory describes the time evolution of tunneling. This uncertainty has hindered development of practical techniques for semiclassical calculations of multidimensional systems. It is shown here that the VVG theory can indeed be applied to barrier tunneling, but generally requires consideration of classical trajectories with both complex initial conditions and complex time paths, even for systems with one degree of freedom. The present approach is verified by applying it to the classically forbidden propagation of a wave packet through a one-dimensional barrier—a very basic problem that cannot be treated by the VVG theory without the modifications described here.

We prove that the closest Gaussian state to an arbitrary $N$-mode field state through the relative entropy is built with the covariance matrix and the average displacement of the given state. Consequently, the relative entropy of an $N$-mode state to its associate Gaussian one is an exact distance-type measure of non-Gaussianity. In order to illustrate this finding, we discuss the general properties of the $N$-mode Fock-diagonal states and evaluate their exact entropic amount of non-Gaussianity.

Braiding of Majorana fermions gives accurate topological quantum operations that are intrinsically robust to noise and imperfection, providing a natural method to realize fault-tolerant quantum information processing. Unfortunately, it is known that braiding of Majorana fermions is not sufficient for the implementation of universal quantum computation. Here we show that topological manipulation of Majorana fermions provides the full set of operations required to generate random numbers by way of quantum mechanics and to certify its genuine randomness through violation of a multipartite Bell inequality. The result opens a perspective to apply Majorana fermions for the robust generation of certified random numbers, which has important applications in cryptography and other related areas.

We report on the experimental generation of an entangled state with a spectrally pure heralded single-photon state and a weak coherent state. Our source, which was as efficient as that reported in our previous report [Phys. Rev. A 83, 031805 (2011)], was much brighter than those reported in earlier experiments using similar configurations. This entanglement system is useful for quantum information protocols that require indistinguishable photons from independent sources.

Correcting errors is a vital but expensive component of fault-tolerant quantum computation. Standard fault-tolerant protocol assumes the implementation of error correction, via syndrome measurements and possible recovery operations, after every quantum gate. In fact, this is not necessary. Here we demonstrate that error correction should be applied more sparingly. We simulate encoded single-qubit rotations within the [7,1,3] code and show via fidelity measures that applying error correction after every gate is not desirable.

The K and Cs atom pair and its $X{}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ electronic molecular states are studied by Fourier-transform spectroscopy with special emphasis on bound states close to the ground state asymptote $\left(4s\right)\text{K}+\left(6s\right)\text{Cs}$. Significant vibrational mixing due to hyperfine coupling was observed leading to improved potential energy curves for both states. The observed intensity pattern of the hyperfine structure for the last vibrational levels of $X{}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ reveals deep insight into the multicomponent wave function of such levels with its influence for modeling the asymptotic behavior of the excited electronic states involved in the reported observations. Examples of derived properties of cold collisions are given and the importance of the present results for efficient production schemes for ultracold KCs is discussed.

Intense attosecond-magnetic-field pulses are predicted to be produced by intense few-cycle attosecond circularly polarized UV pulses. Numerical solutions of the time-dependent Schrödinger equation for H${}_2$${}^{+}$ are used to study the electronic dynamical process. Spinning attosecond circular electron wave packets are created on subnanometer molecular dimensions, thus generating attosecond magnetic fields of several tens of Teslas (${10}^5$ G). Simulations show that the induced magnetic field is critically dependent on the pulse wavelength $\lambda$ and pulse duration $n\tau$ ($n$ is number of cycles) as predicted by a classical model. For ultrashort few-cycle circularly polarized attosecond pulses, molecular orientation influences the generation of the induced magnetic fields as a result of preferential ionization perpendicular to the molecular axis. The nonspherical asymmetry of molecules allows for efficient attosecond-magnetic-field-pulse generation.