Cross correlations in mesoscopic charge detection

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We study a tunnel contact that acts as charge detector for a single-electron transistor (SET) focusing on correlations between the detector current and the current through the SET. This system can be described fully by a Markovian master equation for the SET, while electron tunneling in the charge monitor represents a process with a stochastic rate, which can be solved exactly. It turns out that current monitoring is possible as long as the detector current correlates with the currents through either SET barrier. By contrast, correlations with the effective current according to the Ramo-Shockley theorem are not essential. Moreover, we propose the measurement of the SET barrier capacitances.