Absence of skewness in the voltage fluctuations of a tunnel junction in the quantum regime
Current fluctuations in a tunnel junction have a remarkable property: On the one hand, their variance corresponds to vacuum fluctuations at low voltage bias $V$, when the electron energy $eV$ is smaller than the photon detection energy $hf$ . On the other hand, their skewness, i.e. their third moment, is frequency independent, equal to $e^2I$ as if electron transport were simply Poissonian. We address the following question: Could it be that at low voltage, the vacuum fluctuations generated by the junction have a finite skewness, i.e. that the junction generates skewed vacuum ? To answer this question we calculate the effect of an arbitrary electromagnetic environment at zero temperature and show that the bispectrum of third moment of voltage fluctuations of any quantum conductor is always zero at frequencies larger than the voltage. We also show experimental data on tunnel junctions in the quantum regime that agree with our calculation.