1 9 Fe b 20 03 Scattering Theory of Mesoscopic Detectors

We consider a two-level system coupled to a mesoscopic two-terminal conductor that acts as measuring device. As a convenient description of the conductor we introduce its scattering matrix. We show how its elements can be used to calculate the relaxation and decoherence rates of the two-level system. Special emphasis is laid on the charge screening in the conductor that becomes important in the many-channel limit. Finally we give some examples that illustrate charge screening in different limits. The detection of quantum states by means of mesoscopic detectors is of fundamental importance from the point of view of quantum measurement theory. It is also important due to the recent interest in different schemes of quantum computation for which the read-out process must be a key step [1]. A detector, typically, has a back action [2] on the measured system and thus can also be used to introduce decoherence in a controlled way. Here we are concerned with a simple prototype of a detector that consists of a mesoscopic conductor capacitively coupled to the state of a nearby quantum system (see Fig. (1)). The most basic quantum system is a two state system here taken to be two mesoscopic quantum dots weakly coupled to each other. Recent experiments demonstrated elegantly the effect of a detector on a phase coherent mesoscopic system [3, 4, 5, 6]. Different aspects of weak measurement were addressed in several theoretical discussions: the relation between detector noise and decoherence [7, 8], their connection to measurement 1