Electric field correlation measurements on the electromagnetic vacuum state

Abstract

Quantum mechanics ascribes to the ground state of the electromagnetic radiation¹ zero-point electric field fluctuations that permeate empty space at all frequencies. No energy can be extracted from the ground state of a system, and therefore these fluctuations cannot be measured directly with an intensity detector. The experimental proof of their existence therefore came from more indirect evidence, such as the Lamb shift^2,3,4, the Casimir force between close conductors^5,6,7 or spontaneous emission^1,8. A direct method of determining the spectral characteristics of vacuum field fluctuations has so far been missing. Here we perform a direct measurement of the field correlation on these fluctuations in the terahertz frequency range by using electro-optic detection⁹ in a nonlinear crystal placed in a cryogenic environment. We investigate their temporal and spatial coherence, which, at zero time delay and spatial distance, has a peak value of 6.2 × 10^-2 volts squared per square metre, corresponding to a fluctuating vacuum field^10,11 of 0.25 volts per metre. With this measurement, we determine the spectral components of the ground state of electromagnetic radiation within the bandwidth of our electro-optic detection.