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Electric field correlation measurements on the electromagnetic vacuum state


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 shift2,3,4, the Casimir force between close conductors5,6,7 or spontaneous emission1,8. 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 field10,11 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.

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Fig. 1: Experimental setup for the temporal and spatial electro-optic field correlation on vacuum and thermal fields.
Fig. 2: Mean photon occupation number per mode, coherence length and electric field transmission of THz radiation.
Fig. 3: Electro-optic field correlation results at 300 K and 4 K.
Fig. 4: Electro-optic field correlation result of thermal radiation at 45 K.

Data availability

The raw data associated with Figs. 2b, c, 3a–e and 4a, b are provided with the manuscript. Other data that support the findings of this study are available from the corresponding author on reasonable request.


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This work was funded by the European Research Council (Advanced Grant, Quantum Metamaterials in the Ultra Strong Coupling Regime) and the Swiss National Science Foundation (grant 165639). We acknowledge the mechanical workshop at ETHZ. We acknowledge the contribution of M. Ernzer to the noise analysis tools, E. Mavrona to the design of opto-mechanical components and the extraction of the refractive index of ZnTe, and A. Imamoglu for discussions.

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Authors and Affiliations



I.-C.B.-C. and J.F. conceived and designed the experiments. I.-C.B.-C., F.F.S and G.S. built the experimental setup. I.-C.B.-C. developed the data acquisition system and noise suppression protocols. I.-C.B.-C. and F.F.S. performed the measurements. I.-C.B.-C., F.F.S. and J.F. analysed and interpreted the data. I.-C.B.-C., F.F.S. and J.F. derived the theory. J.F. was the scientific supervisor of this work. All authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to Ileana-Cristina Benea-Chelmus or Jérôme Faist.

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The authors declare no competing interests.

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Benea-Chelmus, IC., Settembrini, F.F., Scalari, G. et al. Electric field correlation measurements on the electromagnetic vacuum state. Nature 568, 202–206 (2019).

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