Stability of networks of delay-coupled delay oscillators

Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When the local dynamical stability of the network is plotted as a function of the two delays then a pattern of tongues is revealed. Exploiting a link between structure and dynamics, we identify conditions under which perturbations of the topology have a strong impact on the stability. If these critical regions are avoided the local stability of large random networks can be well approximated analytically

Microscopy of a scalable superatom

Strong interactions can amplify quantum effects such that they become important on macroscopic scales. Controlling these coherently on a single particle level is essential for the tailored preparation of strongly correlated quantum systems and opens up new prospects for quantum technologies. Rydberg atoms offer such strong interactions which lead to extreme nonlinearities in laser coupled atomic ensembles. As a result, multiple excitation of a Micrometer sized cloud can be blocked while the light-matter coupling becomes collectively enhanced. The resulting two-level system, often called "superatom", is a valuable resource for quantum information, providing a collective Qubit. Here we report on the preparation of two orders of magnitude scalable superatoms utilizing the large interaction strength provided by Rydberg atoms combined with precise control of an ensemble of ultracold atoms in an optical lattice. The latter is achieved with sub shot noise precision by local manipulation of a two-dimensional Mott insulator. We microscopically confirm the superatom picture by in-situ detection of the Rydberg excitations and observe the characteristic square root scaling of the optical coupling with the number of atoms. Furthermore, we verify the presence of entanglement in the prepared states and demonstrate the coherent manipulation of the superatom. Finally, we investigate the breakdown of the superatom picture when two Rydberg excitations are present in the system, which leads to dephasing and a loss of coherence.Comment: 7 pages, 5 figure

Quantum Fiel Theoretic Treatment of the Non-Forward Compton Amplitude in the Generalized Bjorken Region

A quantum field theoretic treatment of the leading light-cone part of the virtual Compton amplitude is presented. The twist-decomposition of the operators is performed by a group-theoretic procedure respecting the Lorentz group O(3,1). The twist-2 contributions to the Compton amplitude are calculated and it is shown that the electromagnetic current is conserved for these terms. Relations between the amplitude functions associated to the symmetric and asymmetric part of the Compton amplitude are derived. These relations generalize the Callan-Gross and Wandzura-Wilczek relations of forward scattering for the non-forward Compton amplitude.Comment: 7 pages LATEX, 1 style file, DESY 00-045, Contribution to the Proceedings of `Loops and Legs in Quantum Field Theory', Bastei, Germany, April 2000, Nucl. Phys. B (Proc. Suppl.) (2000) to appea

Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain

Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain.Comment: 6 pages, 4 figure

Coherent many-body spin dynamics in a long-range interacting Ising chain

Coherent many-body quantum dynamics lies at the heart of quantum simulation and quantum computation. Both require coherent evolution in the exponentially large Hilbert space of an interacting many-body system. To date, trapped ions have defined the state of the art in terms of achievable coherence times in interacting spin chains. Here, we establish an alternative platform by reporting on the observation of coherent, fully interaction-driven quantum revivals of the magnetization in Rydberg-dressed Ising spin chains of atoms trapped in an optical lattice. We identify partial many-body revivals at up to about ten times the characteristic time scale set by the interactions. At the same time, single-site-resolved correlation measurements link the magnetization dynamics with inter-spin correlations appearing at different distances during the evolution. These results mark an enabling step towards the implementation of Rydberg atom based quantum annealers, quantum simulations of higher dimensional complex magnetic Hamiltonians, and itinerant long-range interacting quantum matter.Comment: 11 pages, 9 figure

HOW DO UNIVERSITY STUDENTS SELECT AND USE THEIR LEARNING TOOLS? A MIXED-METHOD STUDY ON PERSONALISED LEARNING (21)

Universities often blend traditional learning and e-learning by providing software licenses, electronic learning materials, and access to Learning Management Systems. Following the idea of personalised learning in higher education, students are free to choose between a wide range of learning tools constructing their Personalised Learning Environment. However, the characteristics of the chosen tools need to match the characteristics of the learning tasks to support students adequately. In the present paper, a mixed-method approach is used to analyse which types of tools are used in practice and which types of learning tasks are performed using these learning tools. Furthermore, important factors influencing the decision to select learning tools are identified. This study shows that a wide array of learning tools is used in practice. Although students consider individual factors (such as perceived ease of use and task-technology fit) to be most important when selecting their tools, several exogenous factors such as the lecturers’ targeted pedagogy, social norm and the occurrence of higher order thinking skills limit the range of adequate learning tools