We propose an implementation of the Grover’s search algorithm in a nonclassical database using a linear chain of trapped ions. The database comprises all collective states with two ionic excitations; hence the number of database entries scales quadratically with the number of ions $N$. The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with $N$ ions sharing two excitations. The reflection-about-the-mean operator is produced merely by global addressing of the ion string by an off-resonant pulse with a suitable area, whereas the oracle operator is a control-phase gate. This simplification should allow a demonstration of quantum search in a database of hundreds of elements without needing to synthesize multiqubit quantum gates. The technique does not rely on coherent addition or subtraction of phonons, and hence the ion chain can be sympathetically cooled throughout the process.

We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of the vertices have the same scattering properties except for a subset of special vertices. The object of the search is to find a special vertex. A quantum circuit implementation of these walks is presented in which the set of special vertices is specified by a quantum oracle. We consider the complete graph, a complete bipartite graph, and an $M$-partite graph. In all cases, the dimension of the Hilbert space in which the time evolution of the walk takes place is small (between three and six), so the walks can be completely analyzed analytically. Such dimensional reduction is due to the fact that these graphs have large automorphism groups. We find the usual quadratic quantum speedups in all cases considered.

We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol in the light of quantum algorithmic information. While Shannon’s information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The program length necessary to describe an object, Kolmogorov complexity, plays the most fundamental role in the theory. In the context of algorithmic information theory, we formulate a security criterion for the quantum key distribution by using the quantum Kolmogorov complexity that was recently defined by Vitányi. We show that a simple BB84 protocol indeed distributes a binary sequence between Alice and Bob that looks almost random for Eve with a probability exponentially close to 1.

Differential, direct, state-to-state, and summed charge-transfer cross sections in collisions of protons with argon atoms have been studied at collision energies ranging from $10\mathrm{eV}\text{to}100\mathrm{keV}$ by means of two different methods: a semiclassical coupled-channel and a nonadiabatic electron-nuclear dynamics approach. Our results for the direct differential cross section show excellent agreement between theory and the available experimental data. We discuss the effect of the interference in the differential cross sections caused by different projectile trajectories that have the same scattering angle. A comparison of the methods shows that the repulsive and attractive parts of the interaction potential are required in the trajectory dynamics for the correct description of the deflection of the projectile and the electron capture probability at the low-intermediate energies and intermediate to low impact parameter region. For energies greater than $\sim 4\mathrm{keV}$, the theoretical methods follow the trend of the experimental data. We find that the $2s$, $2p$, and total cross sections change about three orders of magnitude for energies below $1\mathrm{keV}$ down to $0.01\mathrm{keV}$. We also find that the electron capture probability into the $1s$ orbital as a function of the projectile energy and impact parameter forms a ridge that extends toward the high impact parameter region and low projectile energies.

The mutual neutralization of ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{-}$ at low collision energies is studied by means of a molecular close-coupling approach. All degrees of freedom are treated at the full quantum level also taking into account the identity of the nuclei. The relevant ${}^1\Sigma _g^{+}$ and ${}^1\Sigma _u^{+}$ electronic states as well as the associated nonadiabatic radial couplings are calculated for internuclear distances between 0.5 and $50a_0$. Following a transformation into a strictly diabatic basis, these quantities enter into a set of coupled equations for the motion of the nuclei. Numerical solution of these equations allows the cross sections for neutralization into the $\mathrm{H}\left(1\right)+\mathrm{H}\left(n\right)$, $n=1,2,3$ final states to be calculated. In the present paper, results are reported for the collision energy region $0.001–100\mathrm{eV}$, with special emphasis on the important energy region below $10\mathrm{eV}$. The low temperature rate coefficient is obtained from a parametrization of the calculated cross section and is estimated to be valid over the range $10–10000\mathrm{K}$.

The radiation emitted by $180-\mathrm{GeV}∕c$ volume-reflected electrons and positrons impinging on a bent crystal has been measured by the H8RD22 Collaboration on the H8 beamline at the CERN SPS. A dedicated spectrometer has been developed to measure high-energy photon spectra (up to $\sim 100\mathrm{GeV}$) under volume reflection: photon and charged particle beams have been separated by a bending magnet and leptons were detected and tagged by microstrip silicon detectors and a Pb-scintillator sampling calorimeter. A comparison between the experimental and analytical data for the amorphous and volume-reflection cases is presented and the differences are discussed.

Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the partially compressible regions characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in appendixes, and whose validity is not limited to the system under concern.

We investigate an integrable Hamiltonian modeling a heterotriatomic molecular Bose-Einstein condensate. This model describes a mixture of two species of atoms in different proportions, which can combine to form a triatomic molecule. Beginning with a classical analysis, we determine the fixed points of the system. Bifurcations of these points separate the parameter space into different regions. Three distinct scenarios are found, varying with the atomic population imbalance. This result suggests the ground-state properties of the quantum model exhibit a sensitivity on the atomic population imbalance, which is confirmed by a quantum analysis using different approaches, such as the ground-state expectation values, the behavior of the quantum dynamics, the energy gap, and the ground-state fidelity.

An expression for the correlation energy density of the uniform electron gas is derived based on the adiabatic connection method. It covers with a single form the transition between high-density and low-density regions in the range $0.1⩽r_s⩽30$, parsing the entire spin-polarization range $0⩽\xi ⩽1$. The pair-correlation function used to generate the result has been used previously to describe mainly finite systems. We argue that the universality implied by the short-wavelength hypothesis goes both ways, and a model that works well for finite systems may be adapted to describe the uniform electron gas as well.

We consider a quantum harmonic oscillator linearly coupled to a bath of harmonic oscillators and evaluate the degree of entanglement between system and bath using the negativity as an exact entanglement measure. We establish the existence of a critical temperature above which the system-bath negativity vanishes. Our results imply that system-bath entanglement is not responsible for the violation of the Clausius inequality observed in the low-temperature–strong-coupling regime [Phys. Rev. Lett. 85, 1799 (2000)], as the latter still occurs well above the critical temperature.

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to multipartite $d$-dimensional systems. All the Bell inequalities based on this generalization take the same simple form as the CHSH inequality. For small systems, numerical results show that the new inequalities are tight and we believe this is also valid for higher-dimensional systems. Moreover, the new inequalities are relevant to the previous ones and, for bipartite systems, our inequality is equivalent to the Collins-Gisin-Linden-Masser-Popescu inequality.

We investigate the violation of local realism in Bell tests involving homodyne measurements performed on multimode continuous-variable states. By binning the measurement outcomes in an appropriate way, we prove that the Mermin-Klyshko inequality can be violated by an amount that grows exponentially with the number of modes. Furthermore, the maximum violation allowed by quantum mechanics can be attained for any number of modes, albeit requiring a quantum state whose generation is hardly practicable. Interestingly, this exponential increase of the violation holds true even for simpler states, such as multipartite GHZ states. The resulting benefit of using more modes is shown to be significant in practical multipartite Bell tests by analyzing the increase of the robustness to noise with the number of modes. In view of the high efficiency achievable with homodyne detection, our results thus open a possible way to feasible loophole-free Bell tests that are robust to experimental imperfections. We provide an explicit example of a three-mode state (a superposition of coherent states) which results in a significantly high violation of the Mermin-Klyshko inequality (around 10%) with homodyne measurements.

The cascade calculations presented have led to a more detailed understanding of the atomic cascade in $K^{-}x$ (where $x$ can be either $p$ or $d$) atoms. The density dependence of the $K$-series x-ray yields of kaonic hydrogen and deuterium atoms is investigated. It shows that two processes, nuclear absorption and Stark mixing, have an important role in atomic cascades at high-density targets. ${\Gamma }_{2p}=0.105\pm 0.002\mathrm{meV}$ is approximately suggested for the $2p$ strong interaction width of $K^{-}p$ atoms by fitting our results with existing experimental data. In order to obtain the optimum density for measurement of the $1s$ strong interaction shift and width, we have investigated the stopping power of kaons in the targets together with the x-ray yields of kaonic hydrogen and deuterium. We have predicted the optimum range of the target density $\varphi \simeq 0.03–0.06$ of liquid hydrogen density (LHD) for $K^{-}p$ atoms and $\varphi \simeq 0.06–0.2$ of LHD for $K^{-}d$ atoms in a forthcoming SIDDHARTA experiment.

Relativistic configuration-interaction calculations have been performed for anion states representing $6p$ attachments to $4f^{m}5d6s^2$ states in Gd and Tb as well as $6s$ attachments to $4f^{m}5d^{2}6s$ thresholds in Pr and Gd. The $4f$ subshell was treated as corelike with the same occupancy in all correlation configurations, and recently developed methods for reducing the complexity of the $4f^m$ subgroup were also employed. Results predict a single weakly bound $\left(24\mathrm{meV}\right)$ even state for ${\mathrm{Pr}}^{-}$, 12 even states and three odd states for ${\mathrm{Gd}}^{-}$ (the lowest level having an electron affinity of $234\mathrm{meV}$), and six odd states for ${\mathrm{Tb}}^{-}$. The lowest $4f^{8}5d6s^{2}6p$ ${\mathrm{Tb}}^{-}$ state is bound relative to the neutral $4f^{9}6s^2$ ground state by $88\mathrm{meV}$, indicating that the ${\mathrm{Tb}}^{-}$ ground state may actually be an attachment to the first excited state of the neutral atom. Revised calculations and analyses of the much simpler ${\mathrm{Lu}}^{-}$, ${\mathrm{La}}^{-}$, and ${\mathrm{Ce}}^{-}$ anions are also presented.

The charge transfer in the collision of ${\mathrm{C}}^{4+}$ ions on 5-halouracil molecules has been studied theoretically by means of ab initio quantum chemistry molecular methods followed by a semiclassical dynamical treatment. The process appears markedly less efficient than the corresponding charge transfer with a uracil target which induces an enhancement of the complementary fragmentation process in agreement with the radio sensitivity of 5-halouracil molecules widely recognized. The mechanism seems to be driven by both electronic and steric effects which induce a lowering of the charge transfer cross sections and favor various orientations of the projectile with respect to the 5-halouracil target considered.

Dynamic features of the guiding of ${\mathrm{Ne}}^{7+}$ ions through nanocapillaries in insulating PET polymers were investigated for incident energies from $3.5\text{to}7\mathrm{keV}$. The deflection angle of the transmitted ${\mathrm{Ne}}^{7+}$ ions shows a few oscillations before approaching an equilibrium value. The experimental results are interpreted in terms of a scenario where the deflection angles of transmitted ions are governed by charge patches formed on the inner wall of the capillary. In addition, the memory effects of different charge patches retained from previous irradiations are studied.

Superpositions of paraxial laser beam modes to generate atom-optical lenses based on the optical dipole force are investigated theoretically. Thin, wide, parabolic, cylindrical, and circular atom lenses with numerical apertures much greater than those reported in the literature to date can be synthesized. This superposition approach promises to make high-quality atom beam imaging and nanodeposition feasible.

Through exact numerical diagonalization, the von Neumann entropy is calculated for the Laughlin and Pfaffian quantum Hall states in rotating interacting Bose gases at zero temperature in the lowest Landau level limit. The particles comprising the states are indistinguishable, so the required spatial bipartitioning is effected by tracing over a subset of single-particle orbitals. The topological entropy is then extracted through a finite-size scaling analysis. The results for the Laughlin and the Pfaffian states are consistent with the expected values of $\ln \sqrt{2}$ and $\ln \sqrt{4}$, respectively.

A perturbation method is developed for calculating the oscillating frequencies of collective modes of trapped superfluid Fermi gases from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensation (BEC). Based on the complete and orthogonal eigenfunction set obtained recently and a series expansion of the equation of state beyond the mean-field approximation, the corrections of eigenfrequencies and eigenfunctions of all collective modes are given systematically, which are valid for various superfluid regimes in the BCS-BEC crossover beyond the mean-field approximation. Expressions of frequency correction of the collective modes for both spherical and axial symmetric traps excited near the BCS, BEC, and unitarity limits are provided explicitly, and their dependence on interatomic interaction strength and anisotropic trapping parameter is also discussed in detail.

We study the stability of singly and doubly quantized vortex states of harmonically trapped dipolar Bose-Einstein condensates (BECs) by calculating the low-lying excitations of these condensates. We map the dynamical stability of these vortices as functions of the dipole-dipole interaction strength and trap geometry by finding where their excitations have purely real energy eigenvalues. In contrast to BECs with purely contact interactions, we find that dipolar BECs in singly quantized vortex states go unstable to modes with an increasing number of angular and radial nodes for more oblate trap aspect ratios, corresponding to local collapse that occurs on a characteristic length scale. Additionally, we find that dipolar BECs in doubly quantized vortex states are unstable to decay into a different topological state (with two singly quantized vortices) for all interaction strengths when the trap geometry is sufficiently prolate to make the dipoles attractive, and in windows of interaction strength when the trap geometry is sufficiently oblate to make the dipoles repulsive.