Realistic Monitoring of a Charge Qubit by a Quantum Tunnellling Device – a Quantum Trajectory Approach

Full text: Recently, we presented a model for continuous DC-biased measurement of a coupled quantum dot (CQD) charge qubit by realistic measurement devices. Modelling realistic measurement devices as ideal detectors embedded in an equivalent measurement circuit (see figure), our aim was to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit, i.e. the measured current. We generalised a recently developed quantum trajectory theory for realistic photodetectors to treat solid-state detectors-primarily a single electron transistor (SET). This method yields stochastic equations whose (numerical) solutions are the 'realistic quantum trajectories' of the conditioned qubit state. Here we present numerical solutions and analysis for the SET equations. The solutions elucidate the regimes in which (Rabi) electron tunnelling between the CQDs can be detected in a realistic measurement. Further to this, the solutions reveal the conditions under which electron tunnelling events through the SET can be observed, which is related to the question of the nature of the back-action noise of the SET. Copyright (2005) Australian Institute of Physics.