A model of quantum measurement in Josephson junctions

A model for the quantum measurement of the electronic current in a Josephson junction is presented and analyzed. The model is similar to a Stern-Gerlach apparatus, relying on the deflection of a spin-polarized particle beam by the magnetic field created by the Josephson current. The aim is (1) to explore, with the help of a simple model, some general ideas about the nature of the information which can be obtained by measurements upon a quantum system and (2) to find new approaches for obtaining information about the nature of the states of a macroscopic quantum system. In the case of sufficiently strong coupling between the system and the apparatus, we find that the model provides in principle a standard ideal measurement of the value of the instantaneous Josephson current. In the case of weak coupling, where the measurement is not ideal, we show that the scattering of neutrons from a junction can in principle be used to measure the average value of the Josephson current, thereby allowing an experimental distinction to be made between an eigenstate of relative phase and one of relative Cooper pair number. The possibility of the latter type of measurement suggests an experimental approach to answer a question of fundamental interest, namely whether two isolated superconductors (or superfluids) possess a definite relative phase or a definite relative number of superconducting (or super/lowing) particles.     

Classical analogs for Rabi-oscillations,Ramsey-fringes,and spin-echo in Josephson junctions

We investigate the results of recently published experiments on the quantum behavior of Josephson circuits in terms of the classical modeling based on the resistively and capacitively-shunted (RCSJ) junction model. Our analysis shows evidence for a close analogy between the nonlinear behavior of a pulsed microwave-driven Josephson junction at low temperature and low dissipation and the experimental observations reported for the Josephson circuits. Specifically, we demonstrate that Rabi-oscillations, Ramsey-fringes, and spin-echo observations are not phenomena with a unique quantum interpretation. In fact, they are natural consequences of transients to phase-locking in classical nonlinear dynamics and can be observed in a purely classical model of a Josephson junction when the experimental recipe for the application of microwaves is followed and the experimental detection scheme followed. We therefore conclude that classical nonlinear dynamics can contribute to the understanding of relevant experimental observations of Josephson response to various microwave perturbations at very low temperature and low dissipation.     

Quadruple-stacked Nb/Nb_xSi_(1-x)/Nb Josephson junctions for large-scale array application

Large-scale Josephson junction(JJ) arrays are essential in many applications, especially quantum voltage standards application for which hundreds of thousands of junctions are required to realize a high quantum voltage. For almost all applications, high-quality JJ arrays must be realized in a small chip area. This study proposes vertically quadruplestacked Nb/Nb_xSi_(1-x) JJs to increase the integration density of junctions in an array. The current–voltage(I–V)characteristics of a single stack of Nb/Nb_xSi_(1-x) JJs have been measured at 4.2 K. The uniformity of junctions in one stack and the uniformity of several stacks over the entire 2 inches wafer have been analyzed. By optimizing the fabrication parameters, a large-scale quadruple-stacked Nb/Nb_xSi_(1-x) array consisting of 400000 junctions is realized. Good DC I–V characteristics are obtained, indicating the good uniformity of the large-scale array.     

Chaotic diffusion and 1/f-noise of particles in two-dimensional solids

We investigate the classical nonlinear dynamics of a particle moving conservatively in a two-dimensional periodic potential. The particle exhibits diffusive motion in the absence of random forces. In a broad range of energies above the potential barrier, the diffusion process is anomalously accelerated and associated with 1/f-noise in the power spectrum of velocity fluctuations. The analysis of Poincaré surfaces of section and the distribution of free paths indicate that the phenomenon is caused by a trapping of orbits in a self-similar hierarchy of nested cantori. We describe a statistical theory for this mechanism in terms of a renewal process and a random walk on a hierarchical lattice.Work supported by Deutsche Forschungsgemeinschaft     

Decoherence and 1/f noise in Josephson qubits

We propose and study a model of dephasing due to an environment of bistable fluctuators. We apply our analysis to the decoherence of Josephson qubits, induced by background charges present in the substrate, which are also responsible for the 1/f noise. The discrete nature of the environment leads to a number of new features which are mostly pronounced for slowly moving charges. Far away from the degeneracy this model for the dephasing is solved exactly.     

A microscopic model for the intrinsic Josephson tunneling in high- superconductors

A quantitative analysis of a microscopic model for the intrinsic Josephson effect in high-temperature superconductors based on interlayer tunneling is presented both within a mean-field BCS evaluation and a numerically essentially exact Quantum Monte-Carlo study. The pairing correlations in the CuO₂-planes are modelled by a 2D Hubbard model with attractive interaction, a model which accounts well for some of the observed features such as the short planar coherence length. The stack of Hubbard planes is arranged on a torus, which is threaded by a magnetic flux. The current perpendicular to the planes is calculated as a function of applied flux (i.e. the phase), and - after careful elimination of finite-size effects due to single-particle tunneling - found to display a sinusoidal field dependence in accordance with interlayer Josephson tunneling. Studies of the temperature dependence of the supercurrent reveal at best a mild elevation of the Josephson transition temperature compared to the planar Kosterlitz-Thouless temperature. These and other results on the dependence of the model parameters are compared with a standard BCS evaluation. Received: 24 February 1998 / Revised: 28 April 1998 / Accepted: 23 June 1998     

Deterministic chaos in a quantum mechanical system described by a time-independent Hamiltonian: A model of three Josephson junctions in a loop

Quantum mechanical equations of motion are obtained for a system consisting of a very large number of three types of interacting bosons. Under suitable choice of parameters of the Hamiltonian of the system, the equations of motion are those describing three Josephson junctions in a superconducting loop. It is shown numerically that this system is capable of exhibiting deterministic chaos (extreme sensitivity to initial conditions).     

Temperature and magnetic field variations in the resistance,cos ϕ conductance,and effective capacitance of small Josephson junctions

From direct microwave reflection measurements on very small Pb Josephson junctions, we found a previously unobserved maximum in the small voltage tunneling resistance as the temperature was lowered just below the superconducting transition temperature. In the same range the cos ? amplitude increased to + 1 and then rapidly decreased to ? 1. The effective junction capacitance increased 2–3 times when the magnetic field (for tuning the plasma resonance) was increased, which can be interpreted as evidence for the existence of a phase dependent parametric capacitance.     

Experimental evidence for the Coulomb blockade of Cooper pair tunneling and Bloch oscillations in single Josephson junctions

We report on measurements of the current-voltage characteristics of ultrasmall Josephson junctions. The junctions were made of either Al or Pb alloy, and the leads connecting the junctions to the outside world were high resistance thin film microstrips fabricated on the chip very close to the junction. The high frequency impedance of these leads was sufficiently large to enable the observation in a single Josephson junction of the Coulomb blockade of Cooper pair tunneling, as well as evidence for the time correlation of Cooper pair tunneling (Bloch Oscillations).     

Zurek-Kibble mechanism for the spontaneous vortex formation in Nb-Al/Al(ox)/Nb Josephson tunnel junctions: new theory and experiment

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched Nb-Al/Al(ox)/Nb annular Josephson tunnel junctions (JTJs) as a function of the quench time, tau(Q). The probability f(1) to trap a single defect during the normal-metal-superconductor phase transition clearly follows an allometric dependence on tau(Q) with a scaling exponent sigma = 0.5, as predicted from the Zurek-Kibble mechanism for realistic JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealized model was used that predicted sigma = 0.25, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability.     

A simple model of thin-film point contact in two and three dimensions

We treat a free spinless quantum particle moving on a configuration manifold which consists of two identical parts connected in one point. Most attention is paid to the three-dimensional case when these parts are halfspaces with Neumann condition on the boundary; we also discuss briefly a more general boundary conditions. The class of admissible Hamiltonians is constructed by means of the theory of self-adjoint extensions. Among them, particularly important is a two-parameter family whose elements are invariant with respect to exchange of the halfspaces; we compute the transmission coefficient for each of these extensions. We discuss also the motion on two planes considered in our recent paper, obtaining another characterization of the admissible Hamiltonians. In conclusion, the two situations are compared as models for point-contact spectroscopical experiments in thin metal films.On leave of absence fromNuclear Physics Institute, Czechosl. Acad. Sci., 250 68 e near Prague, Czechoslovakia.On leave of absence fromNuclear Centre, Charles University, V Holeovikách 2, 180 00 Prague 8, Czechoslovakia.     

A thin-film prism as a beam separator for multimode guided waves in integrated optics

We discuss a new application of a thin-film prism as a beam separator for multimode guided waves in integrated optics. For each mode of propagation, the angle of deflection by the thin-film prism is different and each deflected beam can be processed subsequently. Deflection angles for different modes can be predicted by using the concept of effective index of refraction. The thickness and index of refraction of the guiding film are determined simultaneously by measuring the coupling angles of the laser beam and a simple graphical method. Calculated and observed angles of deflection are in good agreement. The thin-film prism is made by using preferential etching technique in order to obtain linear, well defined, tapered edges. Furthermore, silicon is used as the base material for possible future integration of optical and electronic components.     

CPN−1 model: A toy model for QCD?

We examine the CP^N?1₂ models and discuss their relevance as toy models for QCD₄. Specifically, we study the role of instantons, θ vacua, and confinement in the $\text{1}\text{N}$ expansion. Our results, and comparisons with other two-dimensional models, suggest that most of the interesting features of these models are peculiarities of two-dimensional space-time and cannot be expected to reappear in QCD₄.     

A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems

This paper presents a new consistent and stabilized finite-element formulation for fourth-order incompressible flow problems. The formulation is based on the C⁰-interior penalty method, the Galerkin least-square (GLS) scheme, which assures that the formulation is weakly coercive for spaces that fail to satisfy the inf-sup condition, and considers discontinuous pressure interpolations. A stability analysis through a lemma establishes that the proposed formulation satisfies the inf-sup condition, thus confirming the robustness of the method. This lemma indicates that, at the element level, there exists an optimal or quasi-optimal GLS stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, the geometry of the finite element, and the fluid viscosity term. Numerical experiments are carried out to illustrate the ability of the formulation to deal with arbitrary interpolations for velocity and pressure, and to stabilize large pressure gradients.     

A model for l-shell auto-ionization in /gb-decay

The previously proposed model for auto-ionization in the K-shell is extended to the L-shell. The comparison between the calculated and available experimental results is not as straightforward as for the K-shell case, due to complications arising from fluorescence yields and Coster-Kronig vacancy shifting probabilities. However, in cases where comparisons are possible the agreements are encouraging.