Quantum Coherence in the Single Cooper Pair Box

This thesis presents measurements of quantum coherence in a single Cooper pair box, where quantum oscillations of charge between a reservoir and a small superconducting island have been observed. The single Cooper pair box (SCB) consists of a small metallic island which is connected to a reservoir via a tunnel junction. In the superconducting state, Cooper pairs are free to tunnel to and from the island, whose potential can be controlled by a gate voltage. A graded gap method was used to prevent quasiparticles from tunneling onto the island. For this purpose, a magnetic field suppressed the superconducting gap in the SCB leads more than in the island. This created an additional energy barrier for quasiparticles to tunnel to the island, making the gate voltage modulation periodic in Cooper pair charge. For a limited range of gate voltage, the SCB was found to behave as a model two-level quantum mechanical system. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with a frequency given by the energy level separation divided by Planck\u27s constant. These oscillations had a longest coherence time of T2=9 ns at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate, ?1. Away from this point, the coherence time was limited by the dephasing rate, ??. Away from the charge degeneracy, the dependence of T2 on gate charge suggested that low frequency fluctuators were the main source of dephasing. The charge of the Cooper pair box was measured by coupling the SCB capacitively to a radio frequency single electron transistor (RF-SET). The RF-SET was used as an electrometer by measuring the amount of reflection from a resonant microwave circuit in which a single electron transistor (SET) was embedded. A best charge sensitivity of 2.3\ub710-6 e/sqrt(Hz) and a 7 MHz bandwidth was reached in an improved setup. Another part of this thesis concerns an investigation of electrical filters for use in single electronics experiments. The characteristics of seven different types of cryogenic filters were evaluated

Noise performance of the radio-frequency single-electron transistor

Measurements were performed on aluminum and multiwalled carbon nanotube radio-frequency single-electron transistors (RF-SETs) and analyzed the results carefully. A detailed noise model based on scattering matrix and noise wave formalisms was developed. The signal-to-noise ratios obtained from the model agree well with the measured charge sensitivities. It was found that, in the setup, the first stage HEMT amplifier was the most inadequate component contributing nearly all of the charge noise

Noise performance of the radio-frequency single-electron transistor

Measurements were performed on aluminum and multiwalled carbon nanotube radio-frequency single-electron transistors (RF-SETs) and analyzed the results carefully. A detailed noise model based on scattering matrix and noise wave formalisms was developed. The signal-to-noise ratios obtained from the model agree well with the measured charge sensitivities. It was found that, in the setup, the first stage HEMT amplifier was the most inadequate component contributing nearly all of the charge noise

Backaction effects of a SSET measuring a qubit spectroscopy and ground State measurement

We investigate the backaction of superconducting single-electron transistor (SSET) continuously measuring a Cooper-pair box. Due to the minimized backaction of the SSET, we observe a 2e periodic Coulomb staircase according to the two-level system Hamiltonian of the Cooper-pair box. We demonstrate that we can control the quantum broadening of the ground state in-situ. We perform spectroscopy measurements and demonstrate that we have full control over the Cooper-pair box Hamiltonian. The ability to reduce the backaction is a necessary condition to use the SSET as a quantum state readout for the CPB as a qubit