Dynamics of quantum phase transition in an array of Josephson junctions

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point at a finite rate with a quench time tau(Q) induces finite quantum fluctuations of the current around the loop proportional to tau(-1/6)(Q). This scaling could be experimentally verified with an array of weakly coupled Bose-Einstein condensates or superconducting grains.     

Quantum phase transition and Coulomb blockade with one-dimensional SQUID arrays

We report on experiments with one-dimensional (1D) arrays of small-capacitance superconducting quantum interference devices (SQUIDs), where an external magnetic field can be used to tune in situ the Josephson coupling between neighboring superconducting electrodes. We have studied the superconductor–insulator transition in such arrays, and have also used these arrays to bias a single Josephson junction. In the later experiment, we have observed a clear Coulomb blockade of Cooper-pair tunnelling (CBCPT) in the single junction.     

Quantum phase transitions and vortex dynamics in superconducting networks

Josephson-junction arrays are ideal model systems to study a variety of phenomena such as phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on the quantum dynamical properties of low-capacitance Josephson-junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated with the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy needed to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single-electron effects with the Josephson effect. They give rise to (quantum) superconductor–insulator phase transitions that occur when the ratio between the coupling constants is varied or when the external fields are varied. We describe the dependence of the various control parameters on the phase diagram and the transport properties close to the quantum critical points. On the superconducting side of the transition, vortices are the topological excitations. In low-capacitance junction arrays these vortices behave as massive particles that exhibit quantum behavior. We review the various quantum–vortex experiments and theoretical treatments of their quantum dynamics.     

Three-dimensional Josephson-junction arrays in the quantum regime

We study the quantum phase transition properties of a three-dimensional periodic array of Josephson junctions with charging energy that includes both the self and mutual junction capacitances. We use the phase fluctuation algebra between number and phase operators, given by the Euclidean group E2, and we effectively map the problem onto a solvable quantum generalization of the spherical model. We obtain a phase diagram as a function of temperature, Josephson coupling, and charging energy. We also analyze the corresponding fluctuation conductivity and its universal scaling form in the vicinity of the zero-temperature quantum critical point.     

Discontinuous current-phase relations in small one-dimensional Josephson junction arrays

We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase (I-phi) relationships. We present results for a three-junction system in the vicinity of charge-degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I-phi relation at phase pi persist and that, at maximum degeneracy, the problem can be mapped to a tight-binding model providing analytical results for arbitrary system size.     

Josephson Currents and Gap Enhancement in Graph Arrays of Superconductive Islands

Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions.     

Gate-controlled superconductivity in a diffusive multiwalled carbon nanotube

We have investigated electrical transport in a diffusive multiwalled carbon nanotube contacted using superconducting leads made of an Al/Ti sandwich structure. We find proximity-induced superconductivity with measured critical currents up to I(cm)=1.3 nA, tunable by the gate voltage down to 10 pA. The supercurrent branch displays a finite zero bias resistance which varies as R(0) proportional to I(cm){-alpha} with alpha=0.74. Using IV characteristics of junctions with phase diffusion, a good agreement is obtained with the Josephson coupling energy in the long, diffusive junction model of A. D. Zaikin and G. F. Zharkov [Sov. J. Low Temp. Phys. 7, 184 (1981)].     

Effect of an electric field on the deformation of incompressible rubbers: Bifurcation phenomena

Well above their glass transition temperatures, polymers behave like rubber materials. In the rubbery state, the elastic modulus is low enough to allow large deformations. Rubbery materials also deform under the application of an electric field. Rubbers can be referred as electromechanically active elastomers (EMAE) or lightweight materials that convert electrical into mechanical energy and vice versa [H. Xu, Z.-Y. Cheng, D. Olson, T. Mai, Q.M. Zang, G. Kavarnos, Ferroelectric and electromechanical properties of poly(vinylidene-fluoride-trifluoroethylene-chlrotrifluoroethylene) terpolymer, Appl. Phys. Lett. 78 (2001) 2360–2362]. Possible applications include biomedical prostheses, actuators, energy harvesters and robots [R.E. Pelrine, R.D. Kornbluh, J.P. Joseph, Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation, Sens. Actuators, A 64 (1998) 77–85; G. Kofod, W. Wirges, Energy minimization for self-organized structure formation and actuation, Appl. Phys. Lett., 90 (2007) 81916–81918; J.S. Plante, S. Dubowsky, Large-scale failure modes of dielectric elastomer actuators, Int. J. Solids Struct. 43 (2006) 7727–7751].However, although the engineering applications of EMAE are quite recent, the theoretical foundations of continua under simultaneous electrical and mechanical force fields date back the 1960s. In this paper we present the basis of the nonlinear electroelasticity according to the formulation by Dorfmann and Ogden [A. Dorfmann, R.W. Ogden, Nonlinear Electroelastic Deformations, J. Elasticity 82 (2006) 99–127; A. Dorfmann, R.W. Ogden, Nonlinear electroelasticity, Acta Mechanica 174 (2005) 167–183] and discuss the influence of an electrical field on the bifurcation phenomena appearing in some cases of electromechanical deformation in rubber materials.     

Geometrically-frustrated magnetism on triangular and tetrahedral lattices

The combination of simple, nearest neighbor antiferromagnetic interactions and certain lattice symmetries leads to phenomena known broadly as frustration. In such systems, the formation of a collinear magnetic structure cannot occur at low temperature. The material may undergo a phase transition to an unusual magneticallyordered state, or it may not undergo a conventional transition at all-entering a glass-like state as the temperature is lowered.This paper will review recent work, mostly from neutron scattering studies, on three such magnetic materials. CsMnBr₃ and CsCoBr₃ are XY-like and Ising-like stacked-triangular lattice antiferromagnets, respectively. Both undergo magnetic phase transitions with interesting properties due to the presence of geometricalfrustration within the triangular layers. TD₂Mo₂O₇ is a pyrochlore antiferromagnet, in which the magnetic moments reside on a network of corner-sharing tetrahedra. This material enters a magnetic glass-like state at low temperature.This paper reports on work done in collaboration with D.P. Belanger, A.E. Bunker, M.F. Collins, A. Farkas, J.E. Greedan, C. Kallin, J.Z. Larese, T.E. Mason, R.M. Nicklow, J.N. Reimers, R.B. Rogge, Z. Tun, J. Wang, and Y.S. Yang.     

Fabrication of 3D proximity coupled Josephson junction arrays

Experimentally realizable 3D arrays of Josephson junctions have been a goal of researchers since 2D Josephson junctions (JJ) arrays were first introduced. In the past, it has proven to be technically impossible to manufacture 3D proximity-coupled arrays. Recent advancements in etching technology have now made fabrication more feasible. In this paper, we present details of our fabrication process.     

Observation of quantum capacitance in the Cooper-pair transistor

We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, it behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage and has two parts, the geometric capacitance, C(geom), and the quantum capacitance C(Q). The latter is due to the level anticrossing caused by the Josephson coupling and is dual to the Josephson inductance. It depends parametrically on the gate voltage and its magnitude may be substantially larger than C(geom). We have detected C(Q) in our CPT, by measuring the in phase and quadrature rf signal reflected from a resonant circuit in which the CPT is embedded. C(Q) can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit.     

Resistance noise scaling in a dilute two-dimensional hole system in GaAs

We have measured the resistance noise of a two-dimensional (2D) hole system in a high mobility GaAs quantum well, around the 2D metal-insulator transition (MIT) at zero magnetic field. The normalized noise power S(R)/R(2) increases strongly when the hole density p(s) is decreased, increases slightly with temperature (T) at the largest densities, and decreases strongly with T at low p(s). The noise scales with the resistance, S(R)/R(2) approximately R2.4, as for a second order phase transition such as a percolation transition. The p(s) dependence of the conductivity is consistent with a critical behavior for such a transition, near a density p(*) which is lower than the observed MIT critical density p(c).     

Tunneling spectroscopy of two-level systems inside a Josephson junction

We consider a two-level system (TLS) with energy level separation plankvOmega0 inside a Josephson junction. The junction is shunted by a resistor R and is voltage V biased. If the TLS modulates the Josephson energy and/or is optically active, it is Rabi driven by the Josephson oscillations in the running phase regime near the resonance 2eV=plankvOmega0. The Rabi oscillations, in turn, translate into oscillations of current and voltage that can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS's contribution to the decoherence when the junction is used as a qubit.     

Abrupt change of josephson plasma frequency at the phase boundary of the bragg glass in Bi(2)Sr(2)CaCu(2)O(8+delta)

We report the first detailed and quantitative study of the Josephson coupling energy in the vortex liquid, Bragg glass, and vortex glass phases of Bi(2)Sr(2)CaCu(2)O(8+delta) by the Josephson plasma resonance. The measurements revealed distinct features in the T and H dependencies of the plasma frequency omega(pl) for each of these three vortex phases. When going across either the Bragg-to-vortex glass or the Bragg-to-liquid transition line, omega(pl) shows a dramatic change. We provide a quantitative discussion on the properties of these phase transitions, including the first order nature of the Bragg-to-vortex glass transition.     

Sigma Terms and Strangeness Contents of Baryon Octet in Modified Chiral Perturbation Theory

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Chaotic behavior of a stack of intrinsic Josephson junctions at the transition to branching for overcritical currents

Phase dynamics of a stack of coupled intrinsic Josephson junctions was investigated in the framework of capacitively coupled Josephson junctions with diffusion current model. We study the transition from the current-voltage characteristic specific to Josephson junctions arrays with small dissipation and weak coupling between the junctions to the arrays with strong coupling between the junctions and high dissipation. Low dissipative arrays of Josephson junctions are characterized by the absence of branching for overcritical currents which appears for highly dissipative arrays. Described branching appears due to charging on the superconducting layers and charge traveling waves generation. Arrays of Josephson junctions with intermediate values of coupling and dissipation parameters are characterized by the chaotic behavior, confirmed by positive Lyapunov exponent, and branching on the current voltage characteristic for both sub- and overcritical currents.     

Collective Cooper-pair transport in the insulating state of Josephson-junction arrays

We investigate collective Cooper-pair transport of one- and two-dimensional Josephson-junction arrays. We derive an analytical expression for the current-voltage characteristic revealing thermally activated conductivity at small voltages and threshold voltage depinning. The activation energy and the related depinning voltage represent a dynamic Coulomb barrier for collective charge transfer over the whole system and scale with the system size. We show that both quantities are nonmonotonic functions of the magnetic field. We propose that formation of the dynamic Coulomb barrier and its size scaling are consequences of the mutual Josephson phase synchronization across the system. We apply the results for interpretation of experimental data in disordered films near the superconductor-insulator transition.     

Coulomb-blockade-induced bound quasiparticle states in a double-island structure

We determine the low temperature shape of the Coulomb-blockade staircase in a superconducting double-island device. For an odd number of electrons, in the ground state the intrinsic quasiparticle is bound to the tunneling contact. For a single channel contact the gap between the ground state and the continuum of excited states is of the order of the Josephson energy E(J). The temperature dependence of the Coulomb-blockade step width is nonmonotonic, with the minimal width occurring at T(i) approximately E(J)/ln(square root DeltaE(J)/delta), where Delta and delta are, respectively, the superconducting gap and mean level spacing in the island. For an even number of electrons, the Coulomb enhancement of the Josephson energy is shown to be significantly stronger than that for a single grain coupled to a lead. If the electrostatic energy favors a single broken Cooper pair, the resulting quasiparticles are bound to the contact at T=0.     

Determination of the short-wavelength propagation threshold in the collective excitations of liquid ammonia

The dynamics structure factor S(Q,E) of liquid ammonia l-NH3 at T = 200 K and at its vapor pressure has been measured by inelastic x-ray scattering (IXS) in the 1-15 nm(-1) momentum transfer ( Q) range. Contrary to previous IXS studies on other associated liquids and glasses, in l-NH3 a large inelastic signal is observed up to Q = 15 nm(-1). This, enabling S(Q,E) measurements as a function of Q at constant E transfer, allows us to demonstrate experimentally the transition from a propagating dynamics regime, where the acoustic excitation energy linearly disperses with Q, to a high-Q regime, where it is no longer possible to observe a dominant excitation in the S(Q,E).