Dispersive Response of a Disordered Superconducting Quantum Metamaterial

We consider a disordered quantum metamaterial formed by an array of superconducting flux qubits coupled to microwave photons in a cavity. We map the system on the Tavis-Cummings model accounting for the disorder in frequencies of the qubits. The complex transmittance is calculated with the parameters taken from state-of-the-art experiments. We demonstrate that photon phase shift measurements allow to distinguish individual resonances in the metamaterial with up to 100 qubits, in spite of the decoherence spectral width being remarkably larger than the effective coupling constant. Our simulations are in agreement with the results of the recently reported experiment.Comment: 10 pages, 4 figure

Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions

In this paper we investigate the combinatorial structure of 3-dimensional Minkowski–Voronoi continued fractions. Our main goal is to prove the asymptotic stability of Minkowski–Voronoi complexes in special two-parametric families of rank-1 lattices. In addition we construct explicitly the complexes for the case of White's rank-1 lattices and provide with a hypothetic description in a more complicated setting

Imaging of Microscopic Sources of Resistive and Reactive Nonlinearities in Superconducting Microwave Devices

The technique of low-temperature Laser Scanning Microscopy (LSM) has been applied to the investigation of local microwave properties in operating YBa2Cu3O7/LaAlO3 thin-film resonators patterned into a meandering strip transmission line. By using a modified newly developed procedure of spatially-resolved complex impedance partition, the influence of inhomogeneous current flow on the formation of nonlinear (NL) microwave response in such planar devices is analyzed in terms of the independent impact from resistive and inductive components. The modified procedure developed here is dramatically faster than our previous method. The LSM capability to probe the spatial variations of two-tone, third-order intermodulation currents on micron length scales is used to find the 2D distribution of the local sources of microwave NL. The results show that the dominant sources of microwave NL are strongly localized in the resistive domains.Comment: 4 pages, 6 figures, 2-column format,submitted for the 2006 Applied Superconductivity Conferenc

Spatial and frequency dependencies of local photoresponse of HTS strip-line resonator in regime of two-tone microwave intermodulation excitation

A new phenomenological approach to spatially-resolved research of nonlinear (NL) microwave properties of operating thin-film superconducting resonators is proposed. The approach is based on frequency and spatial singularity of Laser Scanning Microscopy (LSM) images that can be extracted from a set of 2-D patterns representing x-y distribution of the LSM photoresponse, PR(x, y), at fixed third-order intermodulation (IMD) frequencies 2f1-f2 and 2f2-f1 as a result of two-tone resonator microwave excitation at equidistant frequencies f1 and f2 relative to the fundamental resonance, f0. It was shown by us earlier that the total LSM PR(x, y) originates from two independent (resistive, PRR(x, y), and inductive, PRX(x, y)) contributions which can be extracted directly from the LSM images acquired at f1 and f2 by using a method of spatially-resolved complex impedance partition [1]. Here, we show that practically the same manipulation of LSM images at 2f1-f2 and 2f2-f1 can be used to present NL components of IMD LSM PR(x, y) in terms of its independent spatial variations of (i) inductive IMD_IND(x, y) and (ii) resistive IMD_RES(x, y) contributions reflecting the origin of the local sources of microwave NL. [1] A.P. Zhuravel, S.M. Anlage, and A.V. Ustinov, Appl. Phys. Lett., vol. 88, p. 212503, 2006.Comment: 3 pages, 4 figures, submitted to the Seventh International Kharkov Symposium (MSMW'10) Proceeding

Sine-Gordon breathers generation in driven long Josephson junctions

We consider a long Josephson junction excited by a suitable external ac-signal, in order to generate control and detect breathers. Studying the nonlinear supratransmission phenomenon in a nonlinear sine-Gordon chain sinusoidally driven, Geniet and Leon explored the bifurcation of the energy transmitted into the chain and calculated a threshold $A (\omega)$ for the external driving signal amplitude, at which the energy flows into the system by breathers modes. I numerically study the continuous sine-Gordon model, describing the dynamics of the phase difference in a long Josephson junction, in order to deeply investigate the "continuous limit" modifications to this threshold. Wherever the energy flows into the system due to the nonlinear supratransmission, a peculiar breather localization areas appear in a $(A, \omega)$ parameters space. The emergence of these areas depends on the damping parameter value, the bias current, and the waveform of driving external signal. The robustness of generated breathers is checked by introducing into the model a thermal noise source to mimic the environmental fluctuations. Presented results allows one to consider a cryogenic experiment for creation and detection of Josephson breathers.Comment: 8 pages, 3 figure

Spatial correlation of linear and nonlinear electron transport in superconducting microwave resonator: laser scanning microscopy analysis

Spatially-resolved techniques of laser scanning microscopy (LSM) have been used to image simultaneously the spatial variations of (i) rf current flow, J$_RF$(x,y), of (ii) areas of resistive dissipation and (iii) the sources of microwave nonlinearity (NL) in an operating superconducting resonator. The RF power dependent spatial evolution of these linear and NL microwave properties in the meander strip YBCO/LAO superconducting resonator have been LSM probed at different temperatures below Tc. The influence of both topologies of the twin-domain YBCO structure and of J$_RF$(x,y) peaks at the edges of superconducting strip line on its NL properties was analyzed in detail with a micron-scale spatial resolution. Result shows the resistive origin of the dominant sources of microwave NLsComment: 3 pages, 3 figures, submitted to MSMW-07 Symposium Proceeding