Superconductor-insulator transition in nanowires and nanowire arrays

Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip processes replacing the tunneling of Cooper pairs. When the quantum phase-slip amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can be tuned by a homogeneous magnetic frustration.Comment: 15 pages, 10 figure

The merger of vertically offset quasi-geostrophic vortices

We examine the critical merging distance between two equal-volume, equal-potential-vorticity quasi-geostrophic vortices. We focus on how this distance depends on the vertical offset between the two vortices, each having a unit mean height-to-width aspect ratio. The vertical direction is special in the quasi-geostrophic model (used to capture the leading-order dynamical features of stably stratified and rapidly rotating geophysical flows) since vertical advection is absent. Nevertheless vortex merger may still occur by horizontal advection. In this paper, we first investigate the equilibrium states for the two vortices as a function of their vertical and horizontal separation. We examine their basic properties together with their linear stability. These findings are next compared to numerical simulations of the nonlinear evolution of two spheres of potential vorticity. Three different regimes of interaction are identified, depending on the vertical offset. For a small offset, the interaction differs little from the case when the two vortices are horizontally aligned. On the other hand, when the vertical offset is comparable to the mean vortex radius, strong interaction occurs for greater horizontal gaps than in the horizontally aligned case, and therefore at significantly greater full separation distances. This perhaps surprising result is consistent with the linear stability analysis and appears to be a consequence of the anisotropy of the quasi-geostrophic equations. Finally, for large vertical offsets, vortex merger results in the formation of a metastable tilted dumbbell vortex.Publisher PDFPeer reviewe

Quantum state transfer in arrays of flux qubits

In this work, we describe a possible experimental realization of Bose's idea to use spin chains for short distance quantum communication [S. Bose, {\it Phys. Rev. Lett.} {\bf 91} 207901]. Josephson arrays have been proposed and analyzed as transmission channels for systems of superconducting charge qubits. Here, we consider a chain of persistent current qubits, that is appropriate for state transfer with high fidelity in systems containing flux qubits. We calculate the fidelity of state transfer for this system. In general, the Hamiltonian of this system is not of XXZ-type, and we analyze the magnitude and the effect of the terms that don't conserve the z-component of the total spin.Comment: 10 pages, 8 figure

Correlated electron states and transport in triangular arrays

We study correlated electron states in frustrated geometry of a triangular lattice. The interplay of long range interactions and finite residual entropy of a classical system gives rise to unusual effects in equilibrium ordering as well as in transport. A novel correlated fluid phase is identified in a wide range of densities and temperatures above freezing into commensurate solid phases. The charge dynamics in the correlated phase is described in terms of a height field, its fluctuations, and topological defects. We demonstrate that the height field fluctuations give rise to a ``free'' charge flow and finite dc conductivity. We show that freezing into the solid phase, controlled by the long range interactions, manifests itself in singularities of transport properties.Comment: 19 pages, 10 figure

Aluminium-oxide wires for superconducting high kinetic inductance circuits

We investigate thin films of conducting aluminium-oxide, also known as granular aluminium, as a material for superconducting high quality, high kinetic inductance circuits. The films are deposited by an optimised reactive DC magnetron sputter process and characterised using microwave measurement techniques at milli-Kelvin temperatures. We show that, by precise control of the reactive sputter conditions, a high room temperature sheet resistance and therefore high kinetic inductance at low temperatures can be obtained. For a coplanar waveguide resonator with 1.5\,k$\Omega$ sheet resistance and a kinetic inductance fraction close to unity, we measure a quality factor in the order of 700\,000 at 20\,mK. Furthermore, we observe a sheet resistance reduction by gentle heat treatment in air. This behaviour is exploited to study the kinetic inductance change using the microwave response of a coplanar wave guide resonator. We find the correlation between the kinetic inductance and the sheet resistance to be in good agreement with theoretical expectations.Comment: 16 pages, 7 figure

Role of relaxation in the quantum measurement of a superconducting qubit using a nonlinear oscillator

We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum non-demolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model to characterize the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator.Comment: 4 pages, 4 figure

Quantum Phase Transition in Skyrmion Lattices

We investigate the ground state of 2D electron gas in Quantum Hall regime at the filling factor slightly deviating from unity, that can be viewed as a sparse lattice of skyrmions. We have found that in the low density limit skyrmions are bound in pairs, those forming the actual lattice. We have shown that at further density increase the lattice undergoes a quantum phase transition, an analogue of superconducting phase transition in Josephson junction arrays.Comment: 4 pages REVTEX, 3 Postscript figure

Quantum interference and Coulomb interaction in arrays of tunnel junctions

We study the electronic properties of an array of small metallic grains connected by tunnel junctions. Such an array serves as a model for a granular metal. Previous theoretical studies of junction arrays were based on models of quantum dissipation which did not take into account the diffusive motion of electrons within the grains. We demonstrate that these models break down at sufficiently low temperatures: for a correct description of the screening properties of a granular metal at low energies the diffusive nature of the electronic motion within the grains is crucial. We present both a diagrammatic and a functional integral approach to analyse the properties of junction arrays. In particular, a new effective action is obtained which enables us to describe the array at arbitrary temperature. In the low temperature limit, our theory yields the correct, dynamically screened Coulomb interaction of a normal metal, whereas at high temperatures the standard description in terms of quantum dissipation is recovered.Comment: 14 pages, 7 figure

Method for direct observation of coherent quantum oscillations in a superconducting phase qubit

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems were so far restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a new method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high quality resonant tank circuit, inductively coupled to the phase qubit. Detailed calculation for zero and non-zero temperature are made for the case of persistent current qubit. According to the estimates for dephasing and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in MHz range.Comment: 5 pages, 1 figure, to appear in Phys.Rev.

Effect of thermal phase fluctuations on the superfluid density of two-dimensional superconducting films

High precision measurements of the complex sheet conductivity of superconducting Mo77Ge23 thin films have been made from 0.4 K through Tc. A sharp drop in the inverse sheet inductance, 1/L(T), is observed at a temperature, Tc, which lies below the mean-field transition temperature, Tco. Just below Tc, the suppression of 1/L(T) below its mean-field value indicates that longitudinal phase fluctuations have nearly their full classical amplitude, but they disappear rapidly as T decreases. We argue that there is a quantum crossover at about 0.94 Tco, below which classical phase fluctuations are suppressed.Comment: 14 pages, 3 figures. Subm. to PR