Electric field correlation measurements on the electromagnetic vacuum state

Quantum mechanics ascribes to the ground state of the electromagnetic radiation 1 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 detection 9 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. Electro-optic detection in a nonlinear crystal is used to measure coherence properties of vacuum fluctuations of the electromagnetic field and deduce the spectrum of the ground state of electromagnetic radiation.