  A new theoretical framework to describe the experimental advances in
electro-optic detection of broadband quantum states, specifically the quantum
vacuum, is devised. By making use of fundamental concepts from quantum field
theory on spacetime metrics, the nonlinear interaction behind the electro-optic
effect can be reformulated in terms of an Unruh-DeWitt detector coupled to a
conjugate field during a very short time interval. When the coupling lasts for
a time interval comparable to the oscillation periods of the detected field
mode (i.e. the subcycle regime), virtual particles inhabiting the field vacuum
are transferred to the detector in the form of real excitations. We demonstrate
that this behavior can be rigorously translated to the scenario of
electro-optic sampling of the quantum vacuum, in which the (spectrally
filtered) probe works as an Unruh-DeWitt detector, with its
interaction-generated photons arising from virtual particles inhabiting the
electromagnetic vacuum. We discuss the specific working regime of such
processes, and the consequences through characterization of the quantum light
involved in the detection.
