Observation of vacuum electric field correlations outside the light cone

According to quantum field theory, empty space is permeated by quantum-vacuum fluctuations. Their presence lead to a series of measurable phenomena such as the Casimir force. A counter-intuitive feature of these fluctuating fields, shown theoretically, is the fact that they exhibit correlations between space-time points which are causally disconnected according to special relativity[1]. Using electro-optic sampling correlation measurements on vacuum[2], we have proved experimentally the existence of correlations of the vacuum fields for non-causally connected space-time points. This result is obtained by using  two 195 fs laser pulses separated by a time of flight of 490 fs which propagate through a nonlinear crystal. Our theory enables to attribute the vast majority of the correlations as stemming from space-time points outside the light cone.  

[1]    A. Valentini, "Non-local correlations in quantum electrodynamics," Physics Letters A, vol. 153, no. 6-7, pp. 321-325, 1991, doi: 10.1016/0375-9601(91)90952-5.

[2]    I.-C. Benea-Chelmus, F. F. Settembrini, G. Scalari, and J. Faist, "Electric field correlation measurements on the electromagnetic vacuum state," Nature, vol. 568, no. 7751, pp. 202-206, Apr 03 2019, doi: 10.1038/s41586-019-1083-9.