The Single Cooper Pair Box - a Quantum-Mechanical Electronic Circuit
Doctoral thesis, 2005
In this thesis the single Cooper pair box (SCB) is investigated with a radio frequency single electron transistor (RF-SET). The RF-SET is used as an electrometer to detect the charge of the SCB. The SCB can be regarded as a quantum two-level system and could therefore be a possible qubit. Both the SCB and the RF-SET have been fabricated with e-beam lithography followed by two-angle shadow evaporation of aluminium. The system has been measured in a dilution refrigerator at temperatures of ~30 mK.
A charge sensitivity of 2.3 μe/square root of Hz was measured for an optimized RF-SET with a bandwidth of 7 MHz, operated in the superconducting state. In a phase sensitive measurement of the RF-SET reflected signal, the gate dependence of the quantum capacitance, due to avoided level crossing, was detected in a superconducting SET.
Coulomb staircases for the SCB were obtained by changing the charge of the SCB by ramping a gate voltage and continuously measuring the charge with the RF-SET. To prevent quasiparticle poisoning of the SCB island, we have used a method of graded gaps. Here we exploit the greater reduction of the superconducting gap for the connecting leads with an external magnetic field applied, resulting in a higher gap for the island. This creates an effective barrier against quasiparticle tunnelling.
The charging energy and the Josephson coupling energy of the SCB were measured with microwave spectroscopy. The SCBs were fabricated in a SQUID geometry, which made it possible to tune the Josephson coupling energy of the box. This tuning was verified through microwave spectroscopy. The effect of tuning could also be seen in the pure 2e Coulomb staircase, as a predicted smearing of the staircase, which was in excellent agreement with the independent spectroscopy data.
Coherent quantum oscillation of the SCB charge state was measured by applying nonadiabatic DC-pulses to the SCB gate. The measured amplitude of the charge oscillations was higher than 70%. The deviation from 100% can be explained by the initial charge state purity and the finite rise time of the pulses.
The longest decoherence time of the charge oscillations was T2 = 9 ns at the charge degeneracy point. It was found to be limited by relaxation. Away from the degeneracy point the decoherence time was limited by pure dephasing, due to low frequency charge fluctuators.
single Cooper-pair box
macroscopic quantum coherence