Nonlinear soliton-like excitations in two-dimensional lattices and charge transport

We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation. Adding electrons to the lattice we find solectron bound states and offer computational evidence of how electrons can be controlled and transported by such acoustic waves and how electron-surfing occurs at the nanoscale. We also offer computational evidence of the possibility of long lasting, fast lattice soliton and corresponding supersonic, almost loss-free transfer or transport of electrons bound to such lattice solitons along crystallographic axes.     

Fractional charges in pyrochlore lattices

A pyrochlore lattice is considered where the average electron number of electrons per site is half‐integer, concentrating on the case of exactly half an electron per site. Strong on‐site repulsions are assumed, so that all sites are either empty or singly occupied. When there are in addition strong nearest‐neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge ±e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge ‐e/2, connected by a Heisenberg spin‐chain which carries the electron's spin.     

Resonant charge and spin transport in a $\mathcal T$-stub coupled to a superconductor

We study transport through a single channel T\mathcal T-stub geometry strongly coupled to a superconducting reservoir. In contrast to the standard stub geometry which has both transmission resonances and anti-resonances in the coherent limit, we find that due to the proximity effect, this geometry shows neither a T = 1 resonance (T is the transmission probability for electrons incident on the T\mathcal T-stub) nor a T = 0 anti-resonance as we vary the energy of the incident electron. Instead, we find that there is only one resonant value at T = 1/4, where charge transport vanishes while the spin transport is perfect.     

Effective interactions and charges in58Ni

The structure of the low-lying states of⁵⁸Ni has been calculated in shell model by assuming an inert⁵⁶Ni core plus two valence nucleons in the p_3/2, f_5/2 and p_1/2 orbitals. The two-body matrix elements are first expressed in terms of seven radial matrix elements and these are then parametrized to give best fit between the computed and the observed energies of the levels below 4 MeV. The wave-functions obtained using these two-body matrix elements are used to study the concept of effective charges. It is found that a single effective charge is not sufficient to predict theB(E2) rates equally well for the thirteen known transitions for which experimental values are available. Assumption of state-dependent effective charges gives a far better agreement. An analysis using wavefunctions obtained with Kuo’s two-body matrix elements also gives a similar result.     

Regulating atomic imbalance in double-well lattices

An insulating optical lattice with double-well sites is considered. In the case of the unity filling factor, an effective Hamiltonian in the pseudospin representation is derived. A method is suggested for manipulating the properties of the system by varying the shape of the double-well potential. In particular, it is shown that the atomic imbalance can be varied at will and a kind of the Morse-alphabet sequences can be created.     

Light-induced atomic elevator in optical lattices

It is shown how an atomic elevator that can elevate falling cold atoms in a vertical optical lattice can be created. The effect appears near resonance owing to the nonlinear interaction between the electronic and mechanical degrees of freedom of an atom, which is responsible for its random walk in rigid optical lattices without any modulation and additional action. Numerical experiments involving spontaneous emission demonstrate that random walk of atoms and light-induced atomic elevator can be observed in a real experiment.     

Effective charges in the fp shell

Following the heavy-ion fusion-evaporation reaction 32S+24Mg at 95 MeV beam energy the lifetimes of analogue states in the T(z)=+/-1/2 A=51 mirror nuclei 51Fe and 51Mn have been measured using the Cologne plunger device coupled to the GASP gamma-ray spectrometer. The deduced B(E2;27/2(-)-->23/2(-)) values afford a unique opportunity to probe isoscalar and isovector polarization charges and to derive effective proton and neutron charges, epsilon(p) and epsilon(n), in the fp shell. A comparison between the experimental results and several different large-scale shell-model calculations yields epsilon(p) approximately 1.15e and epsilon(n) approximately 0.80e.     

Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices

We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.     

Effective charges in binary and ternary oxide compounds

Effective charges in non-cubic binary oxide crystals are evaluated on the basis of their transverse and longitudinal optical phonon frequencies. The temperature dependence of the effective charge is reported in quartz, rutile and corundum. Three procedures which allow the determination of effective charges in ternary compounds are presented and applied to halogenate, silicate, aluminate and ABO_n-type crystals, where A is an alkali or alkaline earth and B is a transition-metal element. Results are compared with Phillips's ionicities.     

Magnetism and electrical transport in Kondo lattices

The Anderson lattice model is studied via time ordered perturbation theory in order to derive approximate results for dynamical susceptibility and electrical conductivity in the Kondo regime. A classification of processes on the lattice contributing to the susceptibility leads to expressions containing renormalized band Green's functions and local vertex parts. These quantities are determined by integral equations. Explicit results are obtained via a decoupling procedure for the local parts, which can be motivated in physical terms. It is shown that the formation of the Abrikosov-Suhl resonance near the Fermi level works against, and may actually suppress the tendency towards formation of a magnetic phase. Using a simple, but well founded form for the temperature dependent self energy of band electrons near the Fermi level the influence of coherence on the electrical conductivity at low temperatures can be demonstrated.Dedicated to B. Mühlschlegel on the occasion of the 60th birthday     

Rayleigh scattering and atomic dynamics in dissipative optical lattices

We investigate Rayleigh scattering in dissipative optical lattices. In particular, following recent proposals [S. Guibal, Phys. Rev. Lett. 78, 4709 (1997)]; C. Jurczak, Phys. Rev. Lett. 77, 1727 (1996)]], we study whether the Rayleigh resonance originates from the diffraction on a density grating and is therefore a probe of transport of atoms in optical lattices. It turns out that this is not the case: the Rayleigh line is instead a measure of the cooling rate, while spatial diffusion contributes to the scattering spectrum with a much broader resonance.     

Molecular transport in pulsed optical lattices

This paper presents an overview of our recent theoretical and experimental work investigating the application of deep, periodic optical dipole potentials (optical lattices) produced by intense pulsed optical fields for the transport of neutral molecular gases. Our review outlines the deceleration of molecules in a molecular beam to create slow cold molecules and also acceleration for production of hyperthermal molecular beams with velocities in excess of 10 km/s for material processing. We describe how bulk motion can be induced in a gas by a traveling optical lattice, even when the gas is not fully trapped by the lattice. In all these cases energy and momentum can be deposited from laser radiation that is not resonant with any internal states. When significant numbers of gas collisions occur during the lattice/laser pulse, gas heating accompanied by the formation of gas jets in free space and bulk drift in a capillary can be induced. Finally, we describe a new nonintrusive laser diagnostic method for measurement of gas properties based on analysis of light scattered from density perturbations induced by lattices. PACS 32.80.Lg; 42.50.Vk; 51.10.+y; 42.65.Es; 33.20.Fb     

Multi-soliton energy transport in anharmonic lattices

We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons (see Phys. Rev. Lett. 83 (1999) 296), our analysis reveals a novel physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-component nonlinear models.     

Effective charges for radiative and Auger transition probabilities

Analyses of higher-order resonant, atomic collision processes require many accurate radiative and Auger transition probabilities, A_r and A_a. Numerical evaluation of these probabilities for high Rydberg states and for large angular momenta is difficult. We develop here Coulombic expressions for A_r and A_a, with effective charges for the individual orbitals involved. Simple formulas for the effective charge are proposed and tested against the more accurate data obtained with Hartree—Fock wave functions.     

Optical flux lattices for ultracold atomic gases

We show that simple laser configurations can give rise to "optical flux lattices," in which optically dressed atoms experience a periodic effective magnetic flux with high mean density. These potentials lead to narrow energy bands with nonzero Chern numbers. Optical flux lattices will greatly facilitate the achievement of the quantum Hall regime for ultracold atomic gases.     

Semiclassical theory of transport in antidot lattices

Motivated by a recent experiment by Weiss et al. [Phys. Rev. Lett. 70, 4118 (1993)], we present a detailed study of quantum transport in large antidot arrays whose classical dynamics is chaotic. We calculate the longitudinal and Hall conductivities semiclassically starting from the Kubo formula. The leading contribution reproduces the classical conductivity. In addition, we find oscillatory quantum corrections to the classical conductivity which are given in terms of the periodic orbits of the system. These periodic-orbit contributions provide a consistent explanation of the quantum oscillations in the magnetoconductivity observed by Weiss et al. We find that the phase of the oscillations with Fermi energy and magnetic field is given by the classical action of the periodic orbit. The amplitude is determined by the stability and the velocity correlations of the orbit. The amplitude also decreases exponentially with temperature on the scale of the inverse orbit traversal time/T . The Zeeman splitting leads to beating of the amplitude with magnetic field. We also present an analogous semiclassical derivation of Shubnikov-de Haas oscillations where the corresponding classical motion is integrable. We show that the quantum oscillations in antidot lattices and the Shubnikov-de Haas oscillations are closely related. Observation of both effects requires that the elastic and inelastic scattering lengths be larger than the lengths of the relevant periodic orbits. The amplitude of the quantum oscillations in antidot lattices is of a higher power in Planck's constant and hence smaller than that of Shubnikov-de Haas oscillations. In this sense, the quantum oscillations in the conductivity are a sensitive probe of chaos.This paper is dedicated to Prof. H. Wagner on the occasion of his 60th birthday