High frequency third cumulant of current noise : existence of quantum correlations in the zero-point fluctuations of electrons

We have measured the high frequency third cumulant of voltage quantum 

fluctuations  across a tunnel junction in the high frequency regime  

hf » eV » kT. 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. We obtain that the third cumulant of current fluctuations 

is simply given by e^2I, independent of f. 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. We discuss how this result raises 

the problem of how to calculate high order correlators in quantum mechanics for a given experimental setup.