Measurements of the third cumulant in quantum shot noise at high frequency

We propose to measure the high frequency third cumulant of voltage quantum fluctuations across a tunnel junction in the high frequency regime ħω ≫ eV ≫ k_BT. This quantity is obtained by correlating the fluctuations of the high frequency noise power with the low frequency part of the fluctuating voltage. In this regime, the high frequency voltage/current fluctuations are due to zero point motion of electrons. It has been predicted that the third cumulant of current fluctuations is simply given by e²I, independent of ω. Despite its classical look, this result expresses that the fluctuations of the square of the high frequency current due to vacuum fluctuations are correlated with the low frequency fluctuating current. It raises the problem of how to calculate high order correlators of a quantum signal for a given experimental setup.