Observation of magneto-electric non-reciprocity in molecular nitrogen gas

We report the direct observation of the non-reciprocity of the velocity of light, induced in a gas by electric and magnetic fields. This bilinear magneto-electro-optical phenomenon appears in the presence of crossed electric and magnetic fields perpendicular to the light wavevector, as a refractive index difference between two counterpropagating directions. Using a high finesse ring cavity, we have measured this magneto-electric non-reciprocity in molecular Nitrogen at ambient temperature and atmospheric pressure; for light polarized parallel to the magnetic field it is $2\eta_{\parallel \;{\mathrm{exp}}}(\mathrm{N_2})= (4.7\pm 1)\times 10^{-23}\;{m.V}^{-1}{.T}^{-1}$ for $\lambda =1064\;$nm, in agreement with the expected order of magnitude. Our measurement opens the way to a deeper insight into light-matter interaction, since bilinear magneto-electric effects correspond to a coupling beyond the electric dipole approximation. We were able to measure a magneto-electric non-reciprocity as small as $\Delta n = (5\pm 2) \times 10^{-18}$, which makes its observation in quantum vacuum a conceivable challenge.