3 Negative result measurements in mesoscopic systems

We investigate measurement of electron transport in quantum dot systems by using single-electron transistor as a noninvasive detector. It is demonstrated that such a detector can operate in the " negative-result measurement " regime. In this case the measured current is not distorted, providing that it is a non-coherent one. For a coherent transport, however, the possibility of observing a particular state out of coherent superposition leads to distortion of a measured current even in the " negative-result measurement " regime. The corresponding decoherence rate is obtained in the framework of quantum rate equations. Rapid progress in nanoscale devices made it possible to produce new type of detectors like the quantum point-contact and the single electron transistor (SET), which have been already used in different quantum measurements [1–4]. These devices have been considered also as possible detectors for a single two level system (q-bit) [5–7]. It is of a great advantage that these detectors can be treated entirely quantum mechanically, so that the related measurement process can be investigated in great details. In particular, one can study quantum mechanical mechanism of decoherence and its influence on a measured system. In this letter we consider a measurement of electron current in quantum dots by using SET in close proximity of a measured system, so it monitors the movement of single electrons inside the system [2,4]. We demonstrate that varying parameters of SET one can put 1