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Quantum electrodynamics predicts that the vacuum must behave as a nonlinearoptical medium: the speed of light should be modified when the vacuum isstressed by intense electromagnetic fields. This optical phenomenon has not yetbeen observed. The DeLLight (Deflection of Light by Light) experiment aims toobserve the optically-induced index change of vacuum, a nonlinear effect whichhas never been explored. The experiment is installed in the LASERIX facility atIJCLab, which delivers ultra-short intense laser pulses (2.5 J per pulse, eachof 30 fs duration, with a 10 Hz repetition rate). The proposal is to measurethe refraction of a probe laser pulse when crossing a transverse vacuum indexgradient, produced by a very intense pump pulse. The refraction induces atransverse shift in the intensity profile of the probe, whose signal isamplified by a Sagnac interferometer. In this article, we describe theexperimental method and setup, and present the complete theoreticalcalculations for the expected signal. With a minimum waist at focus of $5\,\mu$m (corresponding to a maximum intensity of $\sim 3 \times 10^{20}$W/cm$^2$), and with the nonlinear vacuum index derived from QED, the expectedrefraction angle is 0.13 prad. First results of the interferometer prototypeare presented. It is shown that an extinction factor $\mathcal{F} = 0.4 \times10^{-5}$ (corresponding to a signal amplification factor of 250) and a spatialresolution $\sigma_y = 10$ nm are achievable. The expected signal is then about15 pm, and could be observed at a 5-sigma confidence level with about one monthof collected data.

The DeLLight experiment to observe an optically-induced change of the vacuum index