  The influence of measurement back action on electro-optic sampling of
electromagnetic quantum fluctuations is investigated. Based on a cascaded
treatment of the nonlinear interaction between a near-infrared coherent probe
and the mid-infrared vacuum, we account for the generated electric-field
contributions that lead to detectable back action. Specifically, we
theoretically address two realistic setups, exploiting one or two probe beams
for the nonlinear interaction with the quantum vacuum, respectively. The setup
parameters at which back action starts to considerably contaminate the measured
noise profiles are determined. Due to the vacuum fluctuations entering at the
beam splitter, the shot noise of two incoming probe pulses in different
channels is uncorrelated. This leads to the absence of the base-level shot
noise in the correlation, while further contributions due to nonlinear
shot-noise enhancement are still present. Ultimately, the regime in which
electro-optic sampling of quantum fields can be considered as effectively
back-action free is found.
