Coulomb Blockade and Coherent Single-Cooper-Pair Tunneling in Single Josephson Junctions

We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures (T < 0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e^2 = 26 kohm. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.Comment: RevTeX, 4 pages with 6 embedded figure

Josephson junction transmission lines as tunable artificial crystals

We investigate one-dimensional Josephson junction arrays with generalized unit cells as a circuit approach to engineer microwave band gaps. An array described by a lattice with a basis can be designed to have a gap in the electromagnetic spectrum, in full analogy to electronic band gaps in diatomic or many-atomic crystals. We derive the dependence of this gap on the array parameters in the linear regime, and suggest experimentally feasible designs to bring the gap below the single junction plasma frequency. The gap can be tuned in a wide frequency range by applying external flux, and it persists in the presence of small imperfections.Comment: 9 pages, 5 figure

An exact reformulation of the Bose-Hubbard model in terms of a stochastic Gutzwiller ansatz

We extend our exact reformulation of the bosonic many-body problem in terms of a stochastic Hartree ansatz to a stochastic Gutzwiller ansatz for the Bose Hubbard model. This makes the corresponding Monte Carlo method more efficient for strongly correlated bosonic phases like the Mott insulator phase or the Tonks phase. We present a first numerical application of this stochastic method to a system of impenetrable bosons on a 1D lattice showing the transition from the discrete Tonks gas to the Mott phase as the chemical potential is increased

New quantum phases in a one-dimensional Josephson array

We examine the phase diagram of an ordered one-dimensional Josephson array of small grains. The average grain charge in such a system can be tuned by means of gate voltage. At small grain-to-grain conductance, this system is strongly correlated because of the charge discreteness constraint (Coulomb blockade). At the gate voltages in the vicinity of the charge degeneracy points, we find new phases equivalent to a commensurate charge density wave and to a repulsive Luttinger liquid. The existence of these phases can be probed through a special dependence of the Josephson current on the gate voltage.Comment: 4 pages, including 1 eps figur

Phases of the one-dimensional Bose-Hubbard model

The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.Comment: Revised version, 4 pages, 5 figure

Superconductor-Insulator Transition in a Disordered Electronic System

We study an electronic model of a 2D superconductor with onsite randomness using Quantum Monte Carlo simulations. The superfluid density is used to track the destruction of superconductivity in the ground state with increasing disorder. The non-superconducting state is identified as an insulator from the temperature dependence of its d.c. resistivity. The value of $\sigma_{\rm dc}$ at the superconductor-insulator transition appears to be non-universal.Comment: PostScript, 4 pages, figures include

Time dependent mean field theory of the superfluid-insulator phase transition

We develop a time-dependent mean field approach, within the time-dependent variational principle, to describe the Superfluid-Insulator quantum phase transition. We construct the zero temperature phase diagram both of the Bose-Hubbard model (BHM), and of a spin-S Heisenberg model (SHM) with the XXZ anisotropy. The phase diagram of the BHM indicates a phase transition from a Mott insulator to a compressibile superfluid phase, and shows the expected lobe-like structure. The SHM phase diagram displays a quantum phase transition between a paramagnetic and a canted phases showing as well a lobe-like structure. We show how the BHM and Quantum Phase model (QPM) can be rigorously derived from the SHM. Based on such results, the phase boundaries of the SHM are mapped to the BHM ones, while the phase diagram of the QPM is related to that of the SHM. The QPM's phase diagram obtained through the application of our approach to the SHM, describes the known onset of the macroscopic phase coherence from the Coulomb blockade regime for increasing Josephson coupling constant. The BHM and the QPM phase diagrams are in good agreement with Quantum Monte Carlo results, and with the third order strong coupling perturbative expansion.Comment: 15 pages, 8 figures. To be published in Phys. Rev.

Evolution of the Density of States Gap in a Disordered Superconductor

It has only recently been possible to study the superconducting state in the attractive Hubbard Hamiltonian via a direct observation of the formation of a gap in the density of states N(w). Here we determine the effect of random chemical potentials on N(w) and show that at weak coupling, disorder closes the gap concurrently with the destruction of superconductivity. At larger, but still intermediate coupling, a pseudo-gap in N(w) remains even well beyond the point at which off-diagonal long range order vanishes. This change in the elementary excitations of the insulating phase corresponds to a crossover between Fermi- and Bose-Insulators. These calculations represent the first computation of the density of states in a finite dimensional disordered fermion model via the Quantum Monte Carlo and maximum entropy methods.Comment: 4 pages, 4 figure

Impact of culture towards disaster risk reduction

Number of natural disasters has risen sharply worldwide making the risk of disasters a global concern. These disasters have created significant losses and damages to humans, economy and society. Despite the losses and damages created by disasters, some individuals and communities do not attached much significance to natural disasters. Risk perception towards a disaster not only depends on the danger it could create but also the behaviour of the communities and individuals that is governed by their culture. Within this context, this study examines the relationship between culture and disaster risk reduction (DRR). A comprehensive literature review is used for the study to evaluate culture, its components and to analyse a series of case studies related to disaster risk. It was evident from the study that in some situations, culture has become a factor for the survival of the communities from disasters where as in some situations culture has acted as a barrier for effective DRR activities. The study suggests community based DRR activities as a mechanism to integrate with culture to effectively manage disaster risk

Kosterlitz-Thouless Universality in a Fermionic System

A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous calculations in the attractive Hubbard model which were limited to small lattices, the new algorithm is used to study the critical behavior on lattices as large as $128\times 128$. These precise results for the first time show that a fermionic system can undergo a finite temperature phase transition whose critical behavior is well described by the predictions of Kosterlitz and Thouless almost three decades ago. In particular it is confirmed that the spatial winding number susceptibility obeys the well known predictions of finite size scaling for $T<T_c$ and up to logarithmic corrections the pair susceptibility scales as $L^{2-\eta}$ at large volumes with $0\leq\eta\leq 0.25$ for $0\leq T\leq T_c$.Comment: Revtex format; 4 pages, 2 figure