Finite-frequency noise cross correlations of a mesoscopic circuit:: A measurement method using a resonant circuit

The measurement of finite frequency cross correlations noise represents an experimental challenge in mesoscopic physics. Here we propose a generalization of the resonant LC circuit setup of Lesovik and Loosen which allow one to probe directly such cross correlations by measuring the charge fluctuations on the plates of a capacitor. The measuring circuit collects noise contributions at the resonant frequency of the LC circuit. Autocorrelation noise can be canceled out by switching the wires and making two distinct measurements. The measured cross correlations then depend on four nonsymmetrized correlators. This detection method is applied to a normal metal three terminal device. We subsequently discuss to what extent the measurement circuit can detect electron antibunching and what singularities appear in the spectral density of cross-correlations noise.