Spin-up and spin-down electron transport through a single-atom imperfect metallic wire: An analytical picture

Within a new perspective which includes the consideration of spin-up and spin-down electrons, a quantum-box approach is used to find a closed mathematical expression for the quantized electrical conductance of an imperfect point–metal contact. From this expression, both proper and improper fractions of the fundamental conductance quantum are obtained and discussed in the light of both resonant and off-resonant conduction states. Issues concerning Fermi energy and electrochemical potential are discussed. In addition, essential aspects related to the atom–lead coupling are examined; in particular, a tensor–dyadic formalism is introduced. Our results are found to be in excellent agreement with previous theoretical results and with experimental observations.     

Extended Brueckner–Hartree–Fock theory with pionic correlation in finite nuclei

We formulate a nuclear many-body theory with explicit treatment of the strong tensor correlation caused by the pion-exchange interaction. To do this, we have to extend the Hartree–Fock variational model space to include 2-particle 2-hole (2p–2h) states, which are able to handle the tensor correlation and to contain high momentum components originating from its pseudo-scalar nature of the pion. We take the variational principle of the total energy, and obtain equations of motion for the variational parameters as the Hartree–Fock single particle states and 2p–2h states. As for the short range repulsion, we use the unitary correlation operator method (UCOM) to express the short range correlation in the ground state wave function. We then arrive at an extended Hartree–Fock equation with the inclusion of the effect of the pion exchange and short range repulsive interactions. We find this extended Hartree–Fock equation has a structure of the Brueckner theory. Thus, we name the present theoretical framework as an extended Brueckner–Hartree–Fock (EBHF) theory. We compare the EBHF theory with the Feshbach projection method and the Brueckner–Hartree–Fock theory.     

Vortex–antivortex states in nanostructured superconductor–ferromagnet hybrids

The formation of vortex–antivortex states in a superconducting film with a square array of magnetic dipoles magnetized perpendicularly to the film is investigated in the framework of the time-dependent Ginzburg–Landau equations. It is shown that a possible route to obtain equilibrium states is obtained following an experimentally realizable field-cooling procedure. The states thus obtained demonstrate a rich variety of phases, depending on magnetic moment intensity and dipole array-to-superconducting film distance. For instance, in the region of the phase diagram where each dipoles is able to generate N = 2 vortex–antivortex pairs, the antivortices induced by the negative stray fields of the dipoles undergo two transitions before ultimately merging into doubly-quantized giant antivortices. For N = 4, a state consisting on a three-quanta giant vortex below each dipole and an interstitial vortex–antivortex molecule was observed. Such state is thermodynamically stable and is induced by the fourfold symmetry of the dipole array, similar to symmetry-induced vortex–antivortex molecules found in mesoscopic superconductors.     

Ion–laser interactions: The most complete solution

Trapped ions are considered one of the best candidates to perform quantum information processing. By interacting them with laser beams they are, somehow, easy to manipulate, which makes them an excellent choice for the production of nonclassical states of their vibrational motion, the reconstruction of quasiprobability distribution functions, the production of quantum gates, etc. However, most of these effects have been produced in the so-called low intensity regime, this is, when the Rabi frequency (laser intensity) is much smaller than the trap frequency. Because of the possibility to produce faster quantum gates in other regimes it is of importance to study this system in a more complete manner, which is the motivation for this contribution. We start by studying the way ions are trapped in Paul traps and review the basic mechanisms of trapping. Then we show how the problem may be completely solved for trapping states; i.e., we find (exact) eigenstates of the full Hamiltonian. We show how, in the low intensity regime, Jaynes–Cummings and anti-Jaynes–Cummings interactions may be obtained, without using the rotating wave approximation and analyze the medium and high intensity regimes where dispersive Hamiltonians are produced. The traditional approach (low intensity regime) is also studied and used for the generation of non-classical states of the vibrational wavefunction. In particular, we show how to add and subtract vibrational quanta to an initial state, how to produce specific superpositions of number states and how to generate NOON states for the two-dimensional vibration of the ion. It is also shown how squeezing may be measured. The time dependent problem is studied by using Lewis–Ermakov methods. We give a solution to the problem when the time dependence of the trap is considered and also analyze a specific (artificial) time dependence that produces squeezing of the initial vibrational wave function. A way to mimic the ion–laser interaction via classical optics is also introduced.     

Action–angle variables,ladder operators and coherent states

This Letter is devoted to the building of coherent states from arguments based on classical action–angle variables. First, we show how these classical variables are associated to an algebraic structure in terms of Poisson brackets. In the quantum context these considerations are implemented by ladder type operators and a structure known as spectrum generating algebra. All this allows to generate coherent states and thereby the correspondence of classical–quantum properties by means of the aforementioned underlying structure. This approach is illustrated with the example of the one-dimensional Pöschl–Teller potential system.     

Efficient scheme for three-photon Greenberger–Horne–Zeilinger state generation

We propose an efficient scheme for the generation of three-photon Greenberger–Horne–Zeilinger (GHZ) state with linear optics, nonlinear optics and postselection. Several devices are designed and a two-mode quantum nondemolition detection is introduced to obtain the desired state. It is worth noting that the states which have entanglement in both polarization and spatial degrees of freedom are created in one of the designed setups. The method described in the present scheme can create a large number of three-photon GHZ states in principle. We also discuss an approach to generate the desired GHZ state in the presence of channel noise.     

Spin–triplet current in half metal/conical helimagnet/superconductor heterojunctions

The BTK theory is extended to investigate spin–triplet current and differential conductance spectrum in the half metal/conical helimagnet (Holmium)/s-wave superconductor heterojunctions. We show that the effective spin–split and spin–flip scatterings of the Holmium layer control the conversion efficiency between the spin–singlet and equal-spin triplet pair correlations, leading to a tunneling current oscillation with the thickness of the Holmium layer. This can provide qualitative explanations on the current oscillation in Ho/Co/Ho-based Josephson junction experiment. The differential conductance spectrum confirms spin–flip Andreev reflection induced long-ranged equal-spin triplet pair correlations.     

Efficient numerical methods for computing ground states and dynamics of dipolar Bose–Einstein condensates

New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose–Einstein condensates (BECs) described by a three-dimensional (3D) Gross–Pitaevskii equation (GPE) with a dipolar interaction potential. Due to the high singularity in the dipolar interaction potential, it brings significant difficulties in mathematical analysis and numerical simulations of dipolar BECs. In this paper, by decoupling the two-body dipolar interaction potential into short-range (or local) and long-range interactions (or repulsive and attractive interactions), the GPE for dipolar BECs is reformulated as a Gross–Pitaevskii–Poisson type system. Based on this new mathematical formulation, we prove rigorously existence and uniqueness as well as nonexistence of the ground states, and discuss the existence of global weak solution and finite time blow-up of the dynamics in different parameter regimes of dipolar BECs. In addition, a backward Euler sine pseudospectral method is presented for computing the ground states and a time-splitting sine pseudospectral method is proposed for computing the dynamics of dipolar BECs. Due to the adoption of new mathematical formulation, our new numerical methods avoid evaluating integrals with high singularity and thus they are more efficient and accurate than those numerical methods currently used in the literatures for solving the problem. Extensive numerical examples in 3D are reported to demonstrate the efficiency and accuracy of our new numerical methods for computing the ground states and dynamics of dipolar BECs.     

Fermionic solutions of chiral Gross–Neveu and Bogoliubov–de Gennes systems in nonlinear Schrödinger hierarchy

The chiral Gross–Neveu model or equivalently the linearized Bogoliubov–de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz–Kaup–Newell–Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n  -th NLS hierarchy generally has n+1$n+1$ gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.     

Effect of electron–phonon interaction on surface states in wurtzite nitride semiconductors under pressure

A variational theory is proposed to study the electronic surface states in semi-infinite wurtzite nitride semiconductors under the hydrostatic pressure. The electronic surface state energy level is calculated, by taking the effects of the electron–Surface–Optical–phonon interaction, structural anisotropy and the hydrostatic pressure into account. The numerical computation has been performed for the electronic surface state energy levels, coupling constants and the average penetrating depths of the electronic surface state wave functions under the hydrostatic pressure for wurtzite GaN, AlN and InN, respectively. The results show that electron–Surface–Optical–phonon interaction lowers the electronic surface state energy levels. It is also found that the electronic surface state energy levels decrease with the hydrostatic pressure in wurtzite GaN and AlN. But for wurtzite InN, the case is contrary. It is shown that the hydrostatic pressure raised the influence of electron–phonon interaction on the electronic surface states obviously. The effect of electron–Surface–Optical–phonon interaction under the hydrostatic pressure on the electronic surface states cannot be neglected, in specially, for materials with strong electron–phonon coupling and wide band gap.     

Effects of Rashba spin–orbit coupling and a magnetic field on a polygonal quantum ring

Using standard quantum network method, we analytically investigate the effect of Rashba spin–orbit coupling (RSOC) and a magnetic field on the spin transport properties of a polygonal quantum ring. Using Landauer–Büttiker formula, we have found that the polarization direction and phase of transmitted electrons can be controlled by both the magnetic field and RSOC. A device to generate a spin-polarized conductance in a polygon with an arbitrary number of sides is discussed. This device would permit precise control of spin and selectively provide spin filtering for either spin up or spin down simply by interchanging the source and drain.     

Optical absorption in asymmetric double quantum wells driven by two intense terahertz fields

Optical absorption is investigated for asymmetric double quantum wells driven by a resonant terahertz field and a varied terahertz field both polarized along the growth direction. Rich nonlinear dynamics of the replica peak and the Autler-Townes splitting of various dressed states are systematically studied in undoped asymmetric double quantum wells by taking account of multiple factors, such as the frequency of the varied terahertz field and the strength of the resonant terahertz field. Each electron subband splits into two dressed states when the resonant terahertz field is applied in the absence of the varied terahertz field, the optical absorption spectrum shows the first order Autler-Townes splitting of the electron subbands. When a varied terahertz field is added into the resonant system, the replica peak and the second order Autler-Townes splitting of the dressed states near the band edge respectively emerge when the varied terahertz field is non-resonant and resonant with these dressed states. When the strength of the resonant terahertz field is increased, the first order Autler-Townes double peaks and the replica peak in the optical absorption spectrum shift with the shifts of the dressed states. The presented results have potential applications in electro-optical devices.     

Relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Coulomb-like potential induced by the Lorentz symmetry breaking effects

In this work, we discuss the relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that the criterion for studying the violation of Lorentz symmetry is preserving the gauge symmetry.     

Exotic electron states and tunable magneto-transport in a fractal Aharonov–Bohm interferometer

A Sierpinski gasket fractal network model is studied in respect of its electronic spectrum and magneto-transport when each ‘arm’ of the gasket is replaced by a diamond shaped Aharonov–Bohm interferometer, threaded by a uniform magnetic flux. Within the framework of a tight binding model for non-interacting, spinless electrons and a real space renormalization group method we unravel a class of extended and localized electronic states. In particular, we demonstrate the existence of extreme localization of electronic states at a special finite set of energy eigenvalues, and an infinite set of energy eigenvalues where the localization gets ‘delayed’ in space (staggered localization). These eigenstates exhibit a multitude of localization areas. The two terminal transmission coefficient and its dependence on the magnetic flux threading each basic Aharonov–Bohm interferometer is studied in details. Sharp switch on–switch off effects that can be tuned by controlling the flux from outside, are discussed. Our results are analytically exact.     

Approximate solutions for half-dark solitons in spinor non-equilibrium Polariton condensates

In this work I generalize and apply an analytical approximation to analyze 1D states of non-equilibrium spinor polariton Bose–Einstein condensates (BEC). Solutions for the condensate wave functions carrying black solitons and half-dark solitons are presented. The derivation is based on the non-conservative Lagrangian formalism for complex Ginzburg–Landau type equations (cGLE), which provides ordinary differential equations for the parameters of the dark soliton solutions in their dynamic environment. Explicit expressions for the stationary dark soliton solution are stated. Subsequently the method is extended to spin sensitive polariton condensates, which yields ordinary differential equations for the parameters of half-dark solitons. Finally a stationary case with explicit expressions for half-dark solitons is presented.     

Rashba spin–orbit coupling effect on a diluted magnetic semiconductor cylinder surface and ballistic transport

We have studied the Rashba spin–orbital effect on a diluted magnetic semiconductor (DMS) cylinder surface in the presence of a magnetic field parallel to the cylinder axis, taking into account the Zeeman coupling and the s–d exchange interaction between the carriers and the magnetic ions. We have obtained an analytical expression for the electron energy spectrum, which depends on the magnetic ion concentration, temperature and strength of magnetic field. The results are used to obtain the conductance of the cylinder at finite temperature. It is shown that the presence of additional local extremum points in the subbands of the electronic spectrum leads to a nonmonotonic dependence of the ballistic conductance of the system on the chemical potential and magnetic field. In the presence of anomalous Zeeman terms with taking into account the Rashba splitting, each minimum of subband contributes _G0/2$G_0/2$ to conductance and each local maxima in the subband, actually reduce the conductance by _G0/2$G_0/2$ compared with the value _G0$G_0$, without the anomalous Zeeman splitting. The effect of finite temperature on the DMS cylinder conductance is a smearing out the sharp steps in the zero-temperature conductance, and shifting the peaks due to the temperature dependence of the s–d exchange interaction term.     

Influence of the spin–orbit interaction in the impurity-band states of n-doped semiconductors

We study numerically the effects of an extrinsic spin–orbit interaction on the model of electrons in n-doped semiconductors of Matsubara and Toyozawa (MT). We focus on the analysis of the density of states (DOS) and the inverse participation ratio (IPR) of the spin–orbit perturbed states in the MT set of energy eigenstates in order to characterize the eigenstates with respect to their extended or localized nature. The finite sizes that we are able to consider necessitate an enhancement of the spin–orbit coupling strength in order to obtain a meaningful perturbation. The IPR and DOS are then studied as a function of the enhancement parameter.     

Revised molecular constants and term values for the XΣ and AΠ states of NH

The vibration–rotation spectra of NH have been reinvestigated using laboratory spectra and infrared solar spectra recorded from orbit by the ACE and ATMOS instruments. In addition to identifying the previously unobserved 6–5 vibration–rotation band in the laboratory spectra, many additional high N rotational lines have been observed. By combining the new observations with the previously published data and recent far infrared data, an improved set of molecular constants and term values have been derived for the X³Σ⁻ and A³Π states.