Dynamics of a charge qubit coupled with a double-dot detector

We investigate theoretically the dynamics of a charge qubit (double quantum dot system) coupled electrostatically with the double-dot detector. The qubit charge oscillations and the detector current are calculated using the equation of motion method for appropriate correlation functions. In order to find the best detector performance (i.e. the detector current signal follows as well as possible the qubit charge oscillations) we consider different qubit-detector geometries. The optimal setup was found for the qubit lying parallel to the detector quantum dots for which we observed very good detector performance together with weak decoherence of the system. It is also shown that the asymptotic detector current (flowing in response to the limited in time qubit-detector interaction) fully reproduces the qubit dynamics.