Nonlinear dynamics of Josephson Junction Chains and Superconducting Resonators

Abstract: This thesis presents the results of the experimental studies on two kindof Superconducting circuits: one-dimensional Josephson junction chains andsuperconducting coplanar waveguide (CPW) resonators. One-dimensionalJosephson junction chains are constructed by connecting many Superconducting quantum interference devices (SQUIDs) in series. We have studied DC transport properties of the SQUID chains and model their nonlineardynamics with Thermally Activated Phase-Slips (TAPS). Experimental andsimulated results showed qualitative agreement revealing the existence of auniform phase-slipping and phase-sticking process which results in a voltage-independent current on the dissipative branch of the current-voltage char-acteristics (IVC). By modulating the effective Josephson coupling energy ofthe SQUIDs (EJ ) with an external magnetic field, we found that the ratio EJ /EC is a decisive factor in determining the qualitative shape of theIVC. A quantum phase transition between incoherent Quantum Phase Slip, QPS (supercurrent branch with a finite slope) to coherent QPS (IVC withwell-developed Coulomb blockade) via an intermediate state (supercurrentbranch with a remnant of Coulomb blockade) is observed as the EJ /EC ratio is tuned. This transition from incoherent QPS to the intermediate-statehappens around R0 ∼ RQ (RQ = h/4e^2 = 6.45kΩ). We also fabricated structured chains where a SQUID at the middle of the chain (central SQUID) has different junction size and loop area compared to other SQUIDs in the chain. Results showed that with these structured chains it is possible to localize andtune the amplitude of both TAPS and QPS at the central SQUID.The second part of the thesis describes the fabrication process and themeasurement results of superconducting CPW resonators. Resonators withdifferent design parameters were fabricated and measured. The transmissionspectra showed quality factors up to, Q ∼ 5 × 10^5 . We have observed bendingof the resonance curves to the lower frequencies due to existence of a nonlinear kinetic inductance. The origin of the nonlinear kinetic inductance isthe nonlinear relation between supercurrent density, Js, and superfluid veloc-ity, vs , of the charge carriers on the center line of the resonators. A simplemodel based on the Ginzburg-Landau theory is used in order to explain ob-served nonlinear kinetic inductance and estimates using this model showedgood agreement with the experimental results.