Nonlinear backreaction in a quantum mechanical SQUID

In this paper we discuss the coupling between a quantum mechanical superconducting quantum interference device (SQUID) and an applied static magnetic field. We demonstrate that the backreaction of a SQUID on the applied field can interfere with the ability to bias the SQUID at values of the static (DC) magnetic flux at, or near to, transitions in the quantum mechanical SQUID.Comment: 9 pages, to be published in Phys. Rev.

Cool for Cats

The iconic Schr\"odinger's cat state describes a system that may be in a superposition of two macroscopically distinct states, for example two clearly separated oscillator coherent states. Quite apart from their role in understanding the quantum classical boundary, such states have been suggested as offering a quantum advantage for quantum metrology, quantum communication and quantum computation. As is well known these applications have to face the difficulty that the irreversible interaction with an environment causes the superposition to rapidly evolve to a mixture of the component states in the case that the environment is not monitored. Here we show that by engineering the interaction with the environment there exists a large class of systems that can evolve irreversibly to a cat state. To be precise we show that it is possible to engineer an irreversible process so that the steady state is close to a pure Schr\"odinger's cat state by using double well systems and an environment comprising two-photon (or phonon) absorbers. We also show that it should be possible to prolong the lifetime of a Schr\"odinger's cat state exposed to the destructive effects of a conventional single-photon decohering environment. Our protocol should make it easier to prepare and maintain Schr\"odinger cat states which would be useful in applications of quantum metrology and information processing as well as being of interest to those probing the quantum to classical transition.Comment: 10 pages, 7 figures. Significantly updated version with supplementary informatio

Fast algorithm for detecting community structure in networks

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for detecting such structure. These algorithms however are computationally demanding, which limits their application to small networks. Here we describe a new algorithm which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster than previous algorithms. We give several example applications, including one to a collaboration network of more than 50000 physicists.Comment: 5 pages, 4 figure

Non-linear dynamics, entanglement and the quantum-classical crossover of two coupled SQUID rings

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.Comment: 9 pages, 4 figures. Published as part of the proceedings of the 32nd International Workshop on Condensed Matter Theories (CMT32) Loughborough University, 2008 (invited paper