Reading out a qubit through an harmonic oscillator, Simulating the driven Jaynes-Cummings Hamiltonian with dissipation

Abstract

In this thesis we investigate the properties of a circuit proposed for reading out the state of a superconducting Cooper-pair box (SCB). The circuit consists of an LC-circuit capacatively coupled to the SCB. By probing the LC-circuit the state of the qubit can be determined. The Hamiltonian for the circuit is derived and found to be the well-known Jaynes-Cummings Hamiltonian. Using the properties of this we can understand why the proposal in question is a good candidate for doing a quantum non-demolition measurement. To model and understand the read-out process we have simulated the open system, including the enviroment. The susceptibility of the circuit is calculated. In an actual experimental situation, microwaves are used to probe the oscillator. Here we model these as quantum mechanical coherent states. Properties of coherent states are then used to device a simple model for calculating the measurement-time. To understand and model the decoherence induced by the measurement we have made numerical simulations of the driven system. These can be used to study the mixing and dephasing of the qubit as function of time and temperature.