Direct detection of vacuum fluctuations and analysis of sub-cycle quantum properties of the electric field are explored by a paraxial quantum theory of ultrafast electro-optic sampling. The feasibility of such experiments is demonstrated by realistic calculations adopting a thin ZnTe electrooptic crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing of a short near-infrared probe pulse with multi-terahertz vacuum field modes leads to an increase of the signal variance with respect to the shot noise level. The vacuum contribution increases significantly for appropriate length of the nonlinear crystal, short probe pulse durations, tight focusing, and sufficiently large number of photons per probe pulse. If the vacuum input is squeezed, the signal variance depends on the probe delay. Temporal positions with noise level below the pure vacuum may be traced with a sub-cycle accuracy.PACS numbers: 42.50. Ct, 42.50.Lc, 42.65.Re, 78.20.Jq Finite fluctuation amplitudes in the ground state of empty space represent the ultimate hallmark of the quantum nature of the electromagnetic radiation field. These vacuum fluctuations manifest themselves indirectly in a number of phenomena that are accessible to spectroscopy such as the spontaneous decay of excited atomic states as well as the Lamb shift [1] in atoms [2] and in quantummechanical electric circuits [3]. Access to the quantum aspects of electromagnetic radiation is provided by the analysis of photon correlation [4,5] or homodyning [6][7][8][9][10][11] measurements. However, these approaches require amplification of the quantum field under study to finite intensity and averaging of the information over multiple optical cycles.On the other side, precise determination of voltage or electric field amplitude as a function of time represents a fundamental task in science and engineering. Optical techniques have to be applied when detecting electric fields oscillating in the terahertz (THz) range and above. Those approaches involve probing with ultrashort laser pulses of a temporal duration on the order of half an oscillation period at the highest frequencies under study. Far-infrared electric transients [12,13] can be characterized by photoconductive switching [14]. Electro-optic sampling in free space [15][16][17] allows field-resolved detection at high sensitivity in the entire far-and mid-infrared spectral range [18,19]. Direct studies of the complexvalued susceptibilities of materials and the elementary dynamics in condensed matter may be performed with these methods [20,21]. The time integral of near-infrared to visible electric-field wave packets is accessible with attosecond streaking [22]. So far, all those techniques were restricted to the classical field amplitude.In this Letter, we demonstrate theoretically that the quantum properties of light may be accessed directly in the time domain, i.e. with sub-cycle temporal resolution. Our considerations are based on the realistic example of electro-optic detection with zincblende-type materials T...