We study the zero-temperature phase diagram of the disordered spin-$1$ Bose-Hubbard model in a two-dimensional square lattice. To this aim, we use a mean-field Gutzwiller ansatz and a probabilistic mean-field perturbation theory. The spin interaction induces two different regimes, corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime, the phase diagram differs more from the scalar case. Disorder in the chemical potential can lead to the disappearance of Mott insulator lobes with an odd-integer filling factor and, for sufficiently strong spin coupling, to Bose glass of singlets between even-filling Mott insulator lobes. Disorder in the spinor coupling parameter results in the appearance of a Bose glass phase only between the $n$ and the $n+1$ lobes for $n$ odd. Disorder in the scalar Hubbard interaction inhibits Mott insulator regions for occupation larger than a critical value.

We describe an imbalanced superfluid Fermi gas in three dimensions within the path-integral framework. To allow for the formation of the Fulde-Ferell-Larkin-Ovchinnikov state (FFLO state), a suitable form of the saddle point is chosen, in which the pairs have a finite center-of-mass momentum. To test the correctness of this path-integral description, the zero-temperature phase diagram for an imbalanced Fermi gas in three dimensions is calculated, and compared to recent theoretical results. Subsequently, we investigate two models that describe the effect of imposing a one-dimensional (1D) optical potential on the three-dimensional (3D) imbalanced Fermi gas. We show that this 1D optical potential can greatly enlarge the stability region of the FFLO state, relative to the case of the 3D Fermi gas without 1D periodic modulation. Furthermore, it is shown that there exists a direct connection between the center-of-mass momentum of the FFLO pairs and the wave vector of the optical potential. We propose that this concept can be used experimentally to resonantly enhance the stability region of the FFLO state.

The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential $-r^{-2}$) is a well-known issue in quantum theory. It is closely related to the quantum anomaly, i.e., breaking of the scaling invariance of the respective Hamiltonian by quantization. We demonstrate that the mean-field repulsive nonlinearity prevents the collapse and thus puts forward a solution to the quantum-anomaly problem that differs from that previously developed in the framework of the linear quantum-field theory. This solution may be realized in the 3D or 2D gas of dipolar bosons attracted by a central charge and in the 2D gas of magnetic dipoles attracted by a current filament. In the 3D setting, the dipole-dipole interactions are also taken into regard, in the mean-field approximation, resulting in a redefinition of the scattering length which accounts for the contact repulsion between the bosons. In lieu of the collapse, the cubic nonlinearity creates a 3D ground state (GS), which does not exist in the respective linear Schrödinger equation. The addition of the harmonic trap gives rise to a tristability, in the case when the Schrödinger equation still does not lead to the collapse. In the 2D setting, the cubic nonlinearity is not strong enough to prevent the collapse; however, the quintic term does it, creating the GS, as well as its counterparts carrying the angular momentum (vorticity). Counterintuitively, such self-trapped 2D modes exist even in the case of a weakly repulsive potential $r^{-2}$. The 2D vortical modes avoid the phase singularity at the pivot ($r=0$) by having the amplitude diverging at $r\to 0$ instead of the usual situation with the amplitude of the vortical mode vanishing at $r\to 0$ (the norm of the mode converges despite of the singularity of the amplitude at $r\to 0$). In the presence of the harmonic trap, the 2D quintic model with a weakly repulsive central potential $r^{-2}$ gives rise to three confined modes, the middle one being unstable, spontaneously developing into a breather. In both the 3D and 2D cases, the GS wave functions are found in a numerical form and in the form of an analytical approximation, which is asymptotically exact in the limit of the large norm.

Quantized x-ray phase vortices, namely, screw-type topological defects in the wave fronts of a coherent monochromatic scalar x-ray wave field, may be spontaneously nucleated by x-ray lenses. Phase retrieval is used to reconstruct the phase and amplitude of the complex disturbance created by aberrated gold nanolenses illuminated with hard x rays. A nanoscale quantized x-ray vortex-antivortex dipole is observed, manifest both as a pair of opposite-helicity branch points in the Riemann sheets of the multivalued x-ray phase map of the complex x-ray field and in the vorticity of the associated Poynting vector field.

Wave propagation guided by a dielectric slab inserted in a sculptured nematic thin film (SNTF) was studied theoretically. Two types of guided waves can be identified: (i) surface (Dyakonov–Tamm) waves guided by one or both of the two planar interfaces of the dielectric slab and the SNTF, and (ii) waveguide modes in the dielectric waveguide formed by the slab with the SNTF as the cladding. As the thickness of the dielectric slab is increased, the number of waveguide modes increases. If the slab thickness is less than twice the e-folding distance into the dielectric slab, the Dyakonov–Tamm waves propagate coupled to both interfaces; the coupling decreases and eventually vanishes as the slab thickness increases, so that Dyakonov–Tamm waves are guided by the individual dielectric-SNTF interfaces independently. The chosen structure supports the propagation of Dyakonov–Tamm waves in all directions, in contrast to the restricted range of propagation supported by a single SNTF-dielectric interface. Propagation of both Dyakonov–Tamm waves and waveguide modes should occur in practice with negligible attenuation, in contrast to that of surface-plasmon-polariton waves that are guided when the dielectric slab is replaced by a metal slab.

In this work we have measured single-electron capture in collisions of ${}^3\mathrm{He}$${}^{2+}$ projectiles incident on a helium target for energies of 13.3–100 keV/amu with the cold-target recoil-ion momentum spectroscopy setup implemented at the Centro Atómico Bariloche. State-selective single-capture cross sections were measured as a function of the impact energy. They were found to agree with previous existing data from the Frankfurt group, starting at the impact energy of 60 keV/amu; as well as with recent data, at 7.5 keV/amu, from the Lanzhou group. The present experimental results are also contrasted to the classical trajectory Monte Carlo method with dynamical screening.

We study the dependence of electromagnetically induced transparency (EIT) resonance amplitudes on the external magnetic field direction in a linearly polarized bichromatic light ($\mathit{lin}\left|\right|\mathit{lin}$) configuration in ${}^{87}\mathrm{Rb}$ vapor. We demonstrate that all seven resolvable EIT resonances exhibit maxima or minima at certain orientations of the laser polarization relative to the wave vector and magnetic field. This effect can be used for the development of a high-precision EIT vector magnetometer.

We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. Finally, by random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of the appearance of quantum and classical correlations for different ranks.

The DiVincenzo criteria for implementing a quantum computer have been seminal in focusing both experimental and theoretical research in quantum-information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. Therefore, the question is what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that, according to this definition, a device is a quantum computer if it obeys the following criteria: Any quantum computer must consist of a quantum memory, with an additional structure that (1) facilitates a controlled quantum evolution of the quantum memory; (2) includes a method for information theoretic cooling of the memory; and (3) provides a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault tolerantly. We discuss various existing quantum computing paradigms and how they fit within this framework. Finally, we present a decision tree for selecting an avenue toward building a quantum computer. This is intended to help experimentalists determine the most natural paradigm given a particular physical implementation.

Storing quantum information for long times without disruptions is a major requirement for most quantum information technologies. A very appealing approach is to use self-correcting Hamiltonians, that is tailoring local interactions among the qubits such that when the system is weakly coupled to a cold bath the thermalization process takes a long time. Here we propose an alternative but more powerful approach in which the coupling to a bath is engineered, so that dissipation protects the encoded qubit against more general kinds of errors. We show that the method can be implemented locally in four-dimensional lattice geometries by means of a toric code and propose a simple two-dimensional setup for proof-of-principle experiments.

We study the geometric measure of entanglement (GM) of pure symmetric states related to rank 1 positive-operator-valued measures (POVMs) and establish a general connection with quantum state estimation theory, especially the maximum likelihood principle. Based on this connection, we provide a method for computing the GM of these states and demonstrate its additivity property under certain conditions. In particular, we prove the additivity of the GM of pure symmetric multiqubit states whose Majorana points under Majorana representation are distributed within a half sphere, including all pure symmetric three-qubit states. We then introduce a family of symmetric states that are generated from mutually unbiased bases and derive an analytical formula for their GM. These states include Dicke states as special cases, which have already been realized in experiments. We also derive the GM of symmetric states generated from symmetric informationally complete POVMs (SIC POVMs) and use it to characterize all inequivalent SIC POVMs in three-dimensional Hilbert space that are covariant with respect to the Heisenberg-Weyl group. Finally, we describe an experimental scheme for creating the symmetric multiqubit states studied in this article and a possible scheme for measuring the permanence of the related Gram matrix.

The nuclear-size effect on the one-loop self-energy and vacuum polarization is evaluated for the $1s$, $2s$, $3s$, $2p_{1/2}$, and $2p_{3/2}$ states of hydrogen-like ions. The calculation is performed to all orders in the nuclear binding strength parameter $Z\alpha$. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter $Z\alpha$. Extrapolation of the all-order numerical results obtained toward $Z=1$ provides results for the radiative nuclear-size effect on the hydrogen Lamb shift.

The theory of transfer ionization in fast ion-atom collisions is investigated within the four-body distorted-wave formalism. The four-body Born distorted-wave (BDW-4B) method, which was originally introduced for double electron capture, is presently extended to transfer ionization. In the entrance and exit channel, the BDW-4B method coincides with the four-body versions of the boundary-corrected first Born and the continuum distorted wave approximations, respectively. An illustrative application of the present method is performed for the previously most studied case of transfer ionization in proton-helium collisions at intermediate and high energies (0.3–10 MeV). The obtained total cross sections are compared with all the available experimental data. Overall, very good agreement is found, particularly at high impact energies that are within the expected region of validity of the BDW-4B approximation.

Much effort has been devoted to removing differential Stark shifts for atoms trapped in specially tailored “magic” optical lattices, but thus far work has focused on a single trapped atomic species. In this work, we extend these ideas to include two atomic species sharing the same optical lattice. We show qualitatively that, in particular, scalar $J=0$ divalent atoms paired with nonscalar state atoms have the necessary characteristics to achieve such Stark shift cancellation. We then present numerical results on “magic” trapping conditions for ${}^{27}\mathrm{Al}$ paired with ${}^{87}\mathrm{Sr}$, as well as several other divalent atoms.

Shor’s factoring algorithm illustrates the potential power of quantum computation. Here, we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network by exploiting the potential of fully coherent electron transport assisted by the surface acoustic waves. Specifically, a nonstandard approach is used to implement, in a simple form, the quantum circuits of the modular exponentiation execution for the simplest instance of Shor’s algorithm, that is, the factorization of $N=15$. The numerical procedure is based on a time-dependent solution of the multiparticle Schrödinger equation. The near-ideal algorithm performance and the large estimated fidelity indicate the efficiency of the protocol implemented, which also is almost insensitive to small destabilizing effects during quantum computation.

A scheme for separating optical precursors from a square-modulated laser pulse through an asymmetric double ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}$As/GaAs quantum-well structure via resonant tunneling is proposed. Destructive interference inhibits linear absorption, and a tunneling-induced transparency (TIT) window appears with normal dispersion, which delays the main pulse; then optical precursors are obtained. Due to resonant tunneling, constructive interference for nonlinear susceptibility is created. The enhanced dispersion in a narrow TIT window is about one order of magnitude larger than that of the linear case. In this case, the main pulse is much delayed and the precursor signals are easier to obtain. Moreover, the main pulse builds up due to the gain introduced by the enhanced cross-nonlinearity.

The operator-sum decomposition of a map from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the map of the density matrix in terms of the polarization vector representation. This has been thoroughly explored for qubits since the components of the polarization vector are measurable quantities (corresponding to expectation values of Hermitian operators) and also because it enables the description of map domains geometrically. Here we extend the operator-sum–affine-map correspondence to qudits, briefly discuss general properties of the map and the form for some particular cases, and provide several explicit results for qutrit maps. We use the affine map and a singular-value-like decomposition to find positivity constraints that provide a symmetry for small polarization vector magnitudes (states which are closer to the maximally mixed state), which is broken as the polarization vector increases in magnitude (a state becomes more pure). The dependence of this symmetry on the magnitude of the polarization vector implies the polar decomposition of the map cannot be used as it can for the qubit case. However, it still leads us to a connection between positivity and purity for general $d$-state systems.

Electron-impact dissociation of CS${}_2$ has been studied by observation of the atomic spectral emission features in the range 115–170 nm. Absolute photoemission cross sections are presented over the complete wavelength range for an incident electron energy of 100 eV. As an example, the measured cross section of the strong C i emission at 165.7 nm, which is a prominent feature in many solar and other extraterrestrial spectra, is ($1.45\pm 0.19)\times {10}^{-18}$ cm${}^2$. Comparison with earlier cross-sectional measurements suggest that these were too high by a factor of more than three. Excitation functions of the dominant C i (156.1 nm) and S i (147.4 nm) emission lines have been measured for electron-impact energies from threshold to 360 eV. From appearance energy measurements in the near-threshold region, likely fragmentation channels are identified which involve both two-fragment breakup and total fragmentation of the parent CS${}_2$.

In this work, the effects of quantum interference and spontaneously generated coherence (SGC) are theoretically analyzed in a four-level system of a ${}^{87}\mathrm{Rb}$ atom. For the effects of SGC, we find that a new kind of electromagnetically induced transparency channel can be induced due to destructive interference, and the nonlinear Kerr absorption can be coherently narrowed or eliminated under different strengths of the coupling and switching fields.

Recently, the presence of noise has been found to play a key role in assisting the transport of energy and information in complex quantum networks and even in biomolecular systems. Here we propose an experimentally realizable optical network scheme for the demonstration of the basic mechanisms underlying noise-assisted transport. The proposed system consists of a network of coupled quantum-optical cavities, injected with a single photon, whose transmission efficiency can be measured. Introducing dephasing in the photon path, this system exhibits a characteristic enhancement of the transport efficiency that can be observed with presently available technology.