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 modelling 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.Comment: 16 pages, 7 figure

Investigation of resonant and transient phenomena in Josephson junction flux qubits

We present an analytical and computational study of resonances and transient responses in a classical Josephson junction system. A theoretical basis for resonances in a superconducting loop with three junctions is presented, outlining both the direct relationship between the dynamics of single- and multi-junction systems, and the direct relationships between observations of the classical counterparts to Rabi oscillations, Ramsey fringes, and spin echo oscillations in this class of systems. We show simulations data along with analytical analyses of the classical model, and the results are related to previously reported experiments conducted on three junction loops. We further investigate the effect of off-resonant microwave perturbations to, e.g., the Rabi-type response of the Josephson system, and we relate this response back to the nonlinear and multi-valued resonance behavior previously reported for a single Josephson junction. The close relationships between single and multi-junction behavior demonstrates the underlying dynamical mechanism for a whole class of classical counterparts to expected quantum mechanical observations in a variety of systems; namely the resonant and transient behavior of a particle in an anharmonic potential well with subsequent escape.Comment: 11 pages, seven figure

Classical analysis of phase-locking transients and Rabi-type oscillations in microwave-driven Josephson junctions

We present a classical analysis of the transient response of Josephson junctions perturbed by microwaves and thermal fluctuations. The results include a specific low frequency modulation in phase and amplitude behavior of a junction in its zero-voltage state. This transient modulation frequency is linked directly to an observed variation in the probability for the system to switch to its non-zero voltage state. Complementing previous work on linking classical analysis to the experimental observations of Rabi-oscillations, this expanded perturbation method also provides closed form analytical results for attenuation of the modulations and the Rabi-type oscillation frequency. Results of perturbation analysis are compared directly (and quantitatively) to numerical simulations of the classical model as well as published experimental data, suggesting that transients to phase-locking are closely related to the observed oscillations.Comment: 18 pages total, 8 figures (typos corrected; minor revisions to figures and equations

Inertial amplification of continuous structures: Large band gaps from small masses

Wave motion in a continuous elastic rod with a periodically attached inertial-amplification mechanism is investigated. The mechanism has properties similar to an "inerter" typically used in vehicle suspensions, however here it is constructed and utilized in a manner that alters the intrinsic properties of a continuous structure. The elastodynamic band structure of the hybrid rod-mechanism structure yields band gaps that are exceedingly wide and deep when compared to what can be obtained using standard local resonators, while still being low in frequency. With this concept, a large band gap may be realized with as much as twenty times less added mass compared to what is needed in a standard local resonator configuration. The emerging inertially enhanced continuous structure also exhibits unique qualitative features in its dispersion curves. These include the existence of a characteristic double-peak in the attenuation constant profile within gaps and the possibility of coalescence of two neighbouring gaps creating a large contiguous gap.Comment: Manuscript is under review for journal publicatio

Proton Pump Activity of Mitochondria-rich Cells : The Interpretation of External Proton-concentration Gradients

We have hypothesized that a major role of the apical H+-pump in mitochondria-rich (MR) cells of amphibian skin is to energize active uptake of Cl− via an apical Cl−/HCO3−-exchanger. The activity of the H+ pump was studied by monitoring mucosal [H+]-profiles with a pH-sensitive microelectrode. With gluconate as mucosal anion, pH adjacent to the cornified cell layer was 0.98 ± 0.07 (mean ± SEM) pH-units below that of the lightly buffered bulk solution (pH = 7.40). The average distance at which the pH-gradient is dissipated was 382 ± 18 μm, corresponding to an estimated “unstirred layer” thickness of 329 ± 29 μm. Mucosal acidification was dependent on serosal pCO2, and abolished after depression of cellular energy metabolism, confirming that mucosal acidification results from active transport of H+. The [H+] was practically similar adjacent to all cells and independent of whether the microelectrode tip was positioned near an MR-cell or a principal cell. To evaluate [H+]-profiles created by a multitude of MR-cells, a mathematical model is proposed which assumes that the H+ distribution is governed by steady diffusion from a number of point sources defining a set of particular solutions to Laplace's equation. Model calculations predicted that with a physiological density of MR cells, the [H+] profile would be governed by so many sources that their individual contributions could not be experimentally resolved. The flux equation was integrated to provide a general mathematical expression for an external standing [H+]–gradient in the unstirred layer. This case was treated as free diffusion of protons and proton-loaded buffer molecules carrying away the protons extruded by the pump into the unstirred layer; the expression derived was used for estimating stationary proton-fluxes. The external [H+]-gradient depended on the mucosal anion such as to indicate that base (HCO3−) is excreted in exchange not only for Cl −, but also for Br− and I−, indicating that the active fluxes of these anions can be attributed to mitochondria-rich cells

Phase-Locking of Vortex Lattices Interacting with Periodic Pinning

We examine Shapiro steps for vortex lattices interacting with periodic pinning arrays driven by AC and DC currents. The vortex flow occurs by the motion of the interstitial vortices through the periodic potential generated by the vortices that remain pinned at the pinning sites. Shapiro steps are observed for fields B_{\phi} < B < 2.25B_{\phi} with the most pronouced steps occuring for fields where the interstitial vortex lattice has a high degree of symmetry. The widths of the phase-locked current steps as a function of the magnitude of the AC driving are found to follow a Bessel function in agreement with theory.Comment: 5 pages 5 postscript figure