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arXiv:1302.4364

A Dynamical Cross-over Regime in the Transmission and Reflection Spectra of Evanescent Waves with 2D Arrays of Josephson Junctions

Laura Adams

Published Feb 18, 2013• 0 citations
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Abstract

A dynamical cross-over regime is revealed when exposing a classical two-dimensional ordered Josephson junction (JJ) array to evanescent waves and tuning the incident microwave power. At the lowest possible temperature for these experiments, 1.1 K, and at the lowest power setting, -55 dBm, evanescent waves are transmitted without loss and the resonance exhibits a quality factor of ~ 4200. A second, smaller resonance, which evolves with increasing power from the main resonance, is also investigated. In contrast to the behavior of the main resonance, this second peak grows as the incident power is increased and does not maintain a fixed resonant frequency for temperatures less than the superconducting critical temperature of niobium. The tunability of both resonances is studied as a function of temperature and microwave power. Finally we speculate that this dynamical crossover regime is evidence of a transition between two states of phase coherence where at low microwave power the JJ arrays are phase locked and at high microwave power the JJ arrays are unlocked.

DOI
10.48550/arxiv.1302.4364

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A dynamical cross-over regime is revealed when exposing a classical two-dimensional ordered Josephson junction (JJ) array to evanescent waves and tuning the incident microwave power. At the lowest possible temperature for these experiments, 1.1 K, and at the lowest power setting, -55 dBm, evanescent waves are transmitted without loss and the resonance exhibits a quality factor of ~ 4200. A second, smaller resonance, which evolves with increasing power from the main resonance, is also investigated. In contrast to the behavior of the main resonance, this second peak grows as the incident power is increased and does not maintain a fixed resonant frequency for temperatures less than the superconducting critical temperature of niobium. The tunability of both resonances is studied as a function of temperature and microwave power. Finally we speculate that this dynamical crossover regime is evidence of a transition between two states of phase coherence where at low microwave power the JJ arrays are phase locked and at high microwave power the JJ arrays are unlocked.
\n\nA dynamical crossover regime is revealed when exposing a classical two-dimensional–ordered Josephson junction (JJ) array to evanescent waves and tuning the incident microwave power. At the lowest possible temperature for these experiments, 1.1 K, and at the lowest power setting, −55textdBm-55\\ \\text{dBm}−55textdBm , evanescent waves are transmitted without loss and the resonance exhibits a quality factor of sim4200{\\sim}4200sim4200 . A second, smaller resonance, which evolves with increasing power from the main resonance, is also investigated. In contrast to the behavior of the main resonance, this second peak grows as the incident power is increased and does not maintain a fixed resonant frequency for temperatures less than the superconducting critical temperature of niobium. The tunability of both resonances is studied as a function of temperature and microwave power. Finally, we speculate that this dynamical crossover regime is evidence of a transition between two states of phase coherence where at low microwave power the JJ arrays are phase locked and at high microwave power the JJ arrays are unlocked.\n
We report low temperature, microwave transmission measurements on a new switchable and tunable class of nonlinear metamaterials. A wireless two dimensional array of Josephson junctions (JJ) is probed as a metamaterial where each plaquette in the array is considered as a meta-atom. In the presence of microwaves, this compact metamaterial of 30,000 connected meta-atoms synchronizes the flow of Cooper pairs to yield a single robust resonant signal with a quality factor of 2800 at the lowest temperature for our measurements. The transmission signal is switched on and off and its amplitude and frequency are tuned with either temperature, incident rf power or dc magnetic field. Surprisingly, increasing the incident rf power above a threshold causes the resonance to split into multiple discrete resonances that extend over a range of 240 MHz for a wide temperature window. We posit that this effect is a new incarnation of the inverse ac Josephson effect where the Josephson plasma frequency locks to the rf drive frequency generating quantized frequency steps, instead of voltage steps, in the absence of a dc bias.
We discuss the dynamics of two-dimensional arrays of Josephson junctions in the overdamped regime. Our discussion is restricted to “classical” arrays, where the Josephson coupling energy is much larger than the charging energy. Such arrays represent a highly controllable system to study the dynamics of vortices. Furthermore, they are promising for applications like, e.g., a coherent microwave source. The experiments have been performed with arrays of Nb/AlOx/Nb-tunnel junctions allowing a high degree of junction uniformity across the array. The typical array size is 10×10 junctions. We show spatially resolved measurement results obtained by low-temperature scanning electron microscopy, and demonstrate the merit of these investigations for the clarification of complex regimes of vortex dynamics as well as for the optimization of coherent microwave sources. In the case of external microwave irradiation with increasing power, a continuous transition from a non-locked to a completely locked oscillation state is presented. In addition, we report on the quantitative measurement of the emitted microwave power from the arrays.
We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of EJ∕kB{E}_{J}∕{k}_{B}EJ​∕kB​ with the Josephson coupling strength EJ{E}_{J}EJ​), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent z=2.0z=2.0z=2.0 in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.
We have studied via computer simulations the dynamical properties of a circuit consisting of two arrays of Josephson junctions closed into a superconducting loop. Due to an internal circuit resonance the phase locking of Josephson junctions is enhanced, which makes possible the application of such a circuit as a source of coherent microwave radiation. The optimal circuit parameters and the influence of thermal noise are discussed. It is shown that the critical spread in junction parameters is about twice that of linear Josephson junction arrays. The possibility of tuning such a device is demonstrated.