Paraxial Theory of Direct Electro-Optic Sampling of the Quantum Vacuum

TL;DR

This paper develops a paraxial quantum theory for ultrafast electro-optic sampling, demonstrating the feasibility of detecting vacuum fluctuations and analyzing sub-cycle quantum electric field properties with realistic experimental parameters.

Contribution

It introduces a new paraxial quantum model for electro-optic sampling of vacuum fluctuations, showing how experimental conditions affect the detection of quantum vacuum properties.

Findings

Vacuum fluctuations can be detected via nonlinear mixing with near-infrared pulses.

Signal variance increases with crystal length, pulse duration, focusing, and photon number.

Sub-cycle noise level below vacuum can be achieved with proper timing and squeezing.

Abstract

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 electro-optic 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.