Fast dynamics and measurements of single-charge devices

Doctoral thesis, 2010

In this thesis we present measurements on several different devices, including the single-Cooper-pair box (SCB), the single-electron box, tunable superconducting resonators and so called transmon qubits. By exploiting the quantum capacitance of the SCB, its state was measured by embedding the box in a radio-frequency resonator. The state dependent change in the quantum capacitance then leads to a measurable shift in the resonator’s frequency. On-chip, lumped-element resonators, optimized for speed, were fabricated together with the SCB, which allowed for very fast measurements of the state. We have performed pulsed measurements, and were able to show that the state of the SCB can be measured in approximately 50 ns. The normal state of the box was also measured. We observed a gate dependent absorption in the single-electron box, centered around its degeneracy points, when it was driven by an radio-frequency signal. The internal dynamics of the system was analyzed by solving a two-level master equation. We model the dissipation in the box by defining an effective resistance, which we name the “Sisyphus resistance”. With the developed model, we were able to very accurately reproduce the measured response over a wide range of RF amplitudes and temperatures. Measurements on a strongly driven SCB are presented. The response of the driven SCB is explained in terms of longitudinal dressed states, defining an effective two-level system. The coherence times of the dressed two-level system are extracted. Relaxation and dephasing in the dressed basis was analyzed. We analyze the possibility of using tunable superconducting resonators for coupling qubits. The resonance frequency is changed by modifying the inductance of a superconducting quantum interference device incorporated into the resonator. The tunability and tuning speed are investigated. We also present measurements on transmon qubits coupled to the tunable cavity. We show Rabi oscillations and observe coherent interaction between two coupled transmon qubits.