Quantum Walks with Non-Orthogonal Position States

Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the non-orthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows to investigate intriguing effects such as the analog of Bloch oscillations.Comment: 5 pages, 4 figure

Self-assembly of the simple cubic lattice with an isotropic potential

Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures (Phys. Rev. Lett. 95, 228301 (2005), Phys. Rev. E 73, 011406 (2006)), we present an isotropic pair potential $V(r)$ for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic (SC) lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.Comment: 16 pages, 12 figures. Accepted for publication in Physical Review

Discerning Aggregation in Homogeneous Ensembles: A General Description of Photon Counting Spectroscopy in Diffusing Systems

In order to discern aggregation in solutions, we present a quantum mechanical analog of the photon statistics from fluorescent molecules diffusing through a focused beam. A generating functional is developed to fully describe the experimental physical system as well as the statistics. Histograms of the measured time delay between photon counts are fit by an analytical solution describing the static as well as diffusing regimes. To determine empirical fitting parameters, fluorescence correlation spectroscopy is used in parallel to the photon counting. For expedient analysis, we find that the distribution's deviation from a single Poisson shows a difference between two single fluor moments or a double fluor aggregate of the same total intensities. Initial studies were performed on fixed-state aggregates limited to dimerization. However preliminary results on reactive species suggest that the method can be used to characterize any aggregating system.Comment: 30 pages, 5 figure

Charge and spin distributions in GaMnAs/GaAs Ferromagnetic Multilayers

A self-consistent electronic structure calculation based on the Luttinger-Kohn model is performed on GaMnAs/GaAs multilayers. The Diluted Magnetic Semiconductor layers are assumed to be metallic and ferromagnetic. The high Mn concentration (considered as 5% in our calculation) makes it possible to assume the density of magnetic moments as a continuous distribution, when treating the magnetic interaction between holes and the localized moment on the Mn(++) sites. Our calculation shows the distribution of heavy holes and light holes in the structure. A strong spin-polarization is observed, and the charge is concentrated mostly on the GaMnAs layers, due to heavy and light holes with their total angular momentum aligned anti-parallel to the average magnetization. The charge and spin distributions are analyzed in terms of their dependence on the number of multilayers, the widths of the GaMnAs and GaAs layers, and the width of lateral GaAs layers at the borders of the structure.Comment: 12 pages,7 figure

Electron-Phonon Coupling in Highly-Screened Graphene

Photoemission studies of graphene have resulted in a long-standing controversy concerning the strength of the experimental electron-phonon interaction in comparison with theoretical calculations. Using high-resolution angle-resolved photoemission spectroscopy we study graphene grown on a copper substrate, where the metallic screening of the substrate substantially reduces the electron-electron interaction, simplifying the comparison of the electron-phonon interaction between theory and experiment. By taking the nonlinear bare bandstructure into account, we are able to show that the strength of the electron-phonon interaction does indeed agree with theoretical calculations. In addition, we observe a significant bandgap at the Dirac point of graphene.Comment: Submitted to Phys. Rev. Lett. on July 20, 201

Quantum walk of a trapped ion in phase space

We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart if we allow the walker/ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, non-classical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach, that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, in principal allowing to scale the quantum walk to several hundreds of steps.Comment: 4 pages, 4 figure

Multi-phonon Raman scattering in semiconductor nanocrystals: importance of non-adiabatic transitions

Multi-phonon Raman scattering in semiconductor nanocrystals is treated taking into account both adiabatic and non-adiabatic phonon-assisted optical transitions. Because phonons of various symmetries are involved in scattering processes, there is a considerable enhancement of intensities of multi-phonon peaks in nanocrystal Raman spectra. Cases of strong and weak band mixing are considered in detail. In the first case, fundamental scattering takes place via internal electron-hole states and is participated by s- and d-phonons, while in the second case, when the intensity of the one-phonon Raman peak is strongly influenced by the interaction of an electron and of a hole with interface imperfections (e. g., with trapped charge), p-phonons are most active. Calculations of Raman scattering spectra for CdSe and PbS nanocrystals give a good quantitative agreement with recent experimental results.Comment: 16 pages, 2 figures, E-mail addresses: [email protected], [email protected], [email protected], accepted for publication in Physical Review

Experimental simulation and limitations of quantum walks with trapped ions

We examine the prospects of discrete quantum walks (QWs) with trapped ions. In particular, we analyze in detail the limitations of the protocol of Travaglione and Milburn (PRA 2002) that has been implemented by several experimental groups in recent years. Based on the first realization in our group (PRL 2009), we investigate the consequences of leaving the scope of the approximations originally made, such as the Lamb--Dicke approximation. We explain the consequential deviations from the idealized QW for different experimental realizations and an increasing number of steps by taking into account higher-order terms of the quantum evolution. It turns out that these become dominant after a few steps already, which is confirmed by experimental results and is currently limiting the scalability of this approach. Finally, we propose a new scheme using short laser pulses, derived from a protocol from the field of quantum computation. We show that the new scheme is not subject to the above-mentioned restrictions, and analytically and numerically evaluate its limitations, based on a realistic implementation with our specific setup. Implementing the protocol with state-of-the-art techniques should allow for substantially increasing the number of steps to 100 and beyond and should be extendable to higher-dimensional QWs.Comment: 29 pages, 15 figue

Quantum dots and spin qubits in graphene

This is a review on graphene quantum dots and their use as a host for spin qubits. We discuss the advantages but also the challenges to use graphene quantum dots for spin qubits as compared to the more standard materials like GaAs. We start with an overview of this young and fascinating field and will then discuss gate-tunable quantum dots in detail. We calculate the bound states for three different quantum dot architectures where a bulk gap allows for confinement via electrostatic fields: (i) graphene nanoribbons with armchair boundary, (ii) a disc in single-layer graphene, and (iii) a disc in bilayer graphene. In order for graphene quantum dots to be useful in the context of spin qubits, one needs to find reliable ways to break the valley-degeneracy. This is achieved here, either by a specific termination of graphene in (i) or in (ii) and (iii) by a magnetic field, without the need of a specific boundary. We further discuss how to manipulate spin in these quantum dots and explain the mechanism of spin decoherence and relaxation caused by spin-orbit interaction in combination with electron-phonon coupling, and by hyperfine interaction with the nuclear spin system.Comment: 23 pages, 10 figures, topical review prepared for Nanotechnolog

Knee complaints and consequences on work status; a 10-year follow-up survey among floor layers and graphic designers

<p>Abstract</p> <p>Background</p> <p>The purpose of the study was to examine if knee complaints among floor layers predict exclusion from the trade.</p> <p>Methods</p> <p>In 1994/95 self-reported data were obtained from a cohort of floor layers and graphic designers with and without knee straining work activities, respectively. At follow-up in 2005 the questionnaire survey was repeated. The study population consisted of 81 floor layers and 173 graphic designers who were presently working in their trades at baseline (1995). All participants were men aged 36–70 years in 2005.</p> <p>We computed the risk of losing gainful employment in the trade according to occurrence of knee complaints at baseline, using Cox proportional hazard regression adjusted for a number of potential confounding variables. Moreover, the crude and adjusted odds risk ratio for knee complaints according to status of employment in the trade were computed, using graphic designers as reference.</p> <p>Results</p> <p>A positive but non-significant association between knee complaints lasting more than 30 days the past 12 months and exclusion from the trade was found among floor layers (Hazard Ratio = 1.4, 95% CI = 0.6–3.5).</p> <p>The frequency of self-reported knee complaints was lower among floor layers presently at work in the trade in year 2005 (26.3%) compared with baseline in 1995 (41.1%), while the opposite tendency was seen among graphic designers (20.7% vs. 10.7%).</p> <p>Conclusion</p> <p>The study suggests that knee complaints are a risk factor for premature exclusion from a knee demanding trade. However, low power of the study precludes strong conclusions. The study also indicates a healthy worker effect among floor layers and a survivor effect among graphic designers.</p