Anderson localization in generalized discrete time quantum walks

We study Anderson localization in a generalized discrete time quantum walk - a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and kinetic energy, and external and internal synthetic flux. Such quantum coins can be engineered with microwave pulses in qubit chains. The ordered case yields a two-band eigenvalue structure on the unit circle which becomes completely flat in the limit of vanishing kinetic energy. Disorder in the external magnetic field does not impact localization. Disorder in all the remaining angles yields Anderson localization. In particular, kinetic energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. Strong disorder in potential and internal magnetic field energies allows to obtain analytical expressions for spectrally independent localization length which is highly useful for various applications.Comment: 11 pages, 14 figure

Almost compact moving breathers with fine-tuned discrete time quantum walks

Discrete time quantum walks are unitary maps defined on the Hilbert space of coupled two-level systems. We study the dynamics of excitations in a nonlinear discrete time quantum walk, whose fine-tuned linear counterpart has a flat band structure. The linear counterpart is, therefore, lacking transport, with exact solutions being compactly localized. A solitary entity of the nonlinear walk moving at velocity $v$ would therefore not suffer from resonances with small amplitude plane waves with identical phase velocity, due to the absence of the latter. That solitary excitation would also have to be localized stronger than exponential, due to the absence of a linear dispersion. We report on the existence of a set of stationary and moving breathers with almost compact superexponential spatial tails. At the limit of the largest velocity $v=1$ the moving breather turns into a completely compact bullet.Comment: 8 pages, 8 figure

Two-tone spectroscopy of a SQUID metamaterial in the nonlinear regime

Compact microwave resonantors made of superconducting rings containing Josephson junctions (SQUIDs) are attractive candidates for building frequency tunable metamaterials with low losses and pronounced nonlinear properties. We explore the nonlinearity of a SQUID metamaterial by performing a two-tone resonant spectroscopy. The small-amplitude response of the metamaterial under strong driving by a microwave pump tone is investigated experimentally and theoretically. The transmission coefficient $S_{21}$ of a weak probe signal is measured in the presence of the pump tone. Increasing the power of the pump, we observe pronounced oscillations of the SQUID's resonance frequency $f_{\textrm{res}}$. The shape of these oscillations varies significantly with the frequency of the pump tone $f_{\textrm{dr}}$. The response to the probe signal displays instabilities and sidebands. A state with strong second harmonic generation is observed. We provide a theoretical analysis of these observations, which is in good agreement with the experimental results

Fiske Steps and Abrikosov Vortices in Josephson Tunnel Junctions

We present a theoretical and experimental study of the Fiske resonances in the current-voltage characteristics of "small" Josephson junctions with randomly distributed misaligned Abrikosov vortices. We obtained that in the presence of Abrikosov vortices the resonant interaction of electromagnetic waves, excited inside a junction, with the ac Josephson current manifests itself by Fiske steps in a current-voltage characteristics even in the absence of external magnetic field. We found that the voltage positions of the Fiske steps are determined by a junction size, but the Fiske step magnitudes depend both on the density of trapped Abrikosov vortices and on their misalignment parameter. We measured the magnetic field dependence of both the amplitude of the first Fiske step and the Josephson critical current of low-dissipative small $Nb$ based Josephson tunnel junctions with artificially introduced Abrikosov vortices. A strong decay of the Josephson critical current and a weak non-monotonic decrease of the first Fiske step amplitude on the Abrikosov vortex density were observed. The experimentally observed dependencies are well described by the developed theory.Comment: 21 pages, 7 figures, submitted to Physical Review

Wave scattering by discrete breathers

We present a theoretical study of linear wave scattering in one-dimensional nonlinear lattices by intrinsic spatially localized dynamic excitations or discrete breathers. These states appear in various nonlinear systems and present a time-periodic localized scattering potential for plane waves. We consider the case of elastic one-channel scattering, when the frequencies of incoming and transmitted waves coincide, but the breather provides with additional spatially localized ac channels whose presence may lead to various interference patterns. The dependence of the transmission coefficient on the wave number q and the breather frequency Omega_b is studied for different types of breathers: acoustic and optical breathers, and rotobreathers. We identify several typical scattering setups where the internal time dependence of the breather is of crucial importance for the observed transmission properties.Comment: 17 pages, 19 figures, submitted to CHAOS (Focus Issue

Collective transport in the insulating state of Josephson junction arrays

We investigate collective Cooper-pair transport of one- and two-dimensional Josephson junction arrays in the insulating state. We derive an analytical expression for the current-voltage characteristic revealing thermally activated conductivity at small voltages and threshold voltage depinning. The activation energy and the related depinning voltage represent a dynamic Coulomb barrier for collective charge transfer over the whole system and scale with the system size. We show that both quantities are non-monotonic functions of magnetic field. We propose that formation of the dynamic Coulomb barrier as well as the size scaling of the activation energy and the depinning threshold voltage, are consequences of the mutual phase synchronization. We apply the results for interpretation of experimental data in disordered films near the superconductor-insulator transition.Comment: 4 pages, 2 figures; typos corrected, new figures, an improved fit to experimental dat

Multiphoton antiresonance

We show that nonlinear response of a quantum oscillator displays antiresonant dips and resonant peaks with varying frequency of the driving field. The effect is a consequence of special symmetry and is related to resonant multiphoton mixing of several pairs of oscillator states at a time. We discuss the possibility to observe the antiresonance and the associated multiphoton Rabi oscillations in Josephson junctions.Comment: 4 pages, 3 figures; corrected referenc

Physical properties of Ce3-xTe4 below room temperature

The physical properties of polycrystalline Ce3-xTe4 were investigated by measurements of the thermoelectric properties, Hall coefficient, heat capacity, and magnetization. The fully-filled, metallic x=0 compound displays a soft ferromagnetic transition near 4K, and analysis of the corresponding heat capacity anomaly suggests a doublet ground state for Ce^{3+}. The transition is suppressed to below 2K in the insulating x=0.33 composition, revealing that magnetic order in Ce3-xTe4 is driven by an RKKY-type interaction. The thermoelectric properties trend with composition as expected from simple electron counting, and the transport properties in Ce3Te4 are observed to be similar to those in La3Te4. Trends in the low temperature thermal conductivity data reveal that the phonons are efficiently scattered by electrons, while all compositions examined have a lattice thermal conductivity near 1.2W/m/K at 200K.Comment: Submitted to Phys. Rev.