Inverse Cotton-Mouton effect of the Vacuum and of atomic systems

In this letter we calculate the Inverse Cotton-Mouton Effect (ICME) for the vacuum following the predictions of Quantum ElectroDynamics. We compare the value of this effect for the vacuum with the one expected for atomic systems. We finally show that ICME could be measured for the first time for noble gases using state-of-the-art laser systems and for the quantum vacuum with near-future laser facilities like ELI and HiPER, providing in particular a test of the nonlinear behaviour of quantum vacuum at intensities below the Schwinger limit of 4.5 × 10 W/m. The advent of laser sources in the 1960s has opened the way to non-linear optics thanks to the rapid increase in the light intensities which reached 10W/m in the 1980s, and that can be nowadays as high as 10W/m [1]. Near-future laser facilities like the Extreme Light Infrastructure (ELI) [2] and the High Power laser Energy Research system (HiPER) [3] should deliver 10W/m approaching the Schwinger limit of 4.5 × 10W/m [1]. At this intensity optical nonlinearities of quantum vacuum should be experimentally accessible and quantum vacuum studies are one of the main motivations to further increase laser intensity [4]. In 1999 measurements of quantum electrodynamics processes in an intense electromagnetic wave, have been reported by Bamber et al. [5]. Nonlinear Compton scattering and electron-positron pair production have been observed in collisions between a laser beam of intensity up to 5×10W/m and electrons of energy close to 50 GeV. The electric field strength of the laser in the electron rest frame corresponded to a few percents of the Schwinger limit. Recently, an experiment coupling a very intense transverse pulsed magnetic field with an intense laser source has been performed [6]. The goal was to detect a possible oscillation of photons into massive particles. The maximum value of the pulsed magnetic field was about 10T over 0.36m, pulse duration was a few milliseconds. The laser source intensity was about 10W/m, corresponding to about 1500 J, over 5 ns focussed on a spot of 100μm diameter. These two pulsed facilities proved to work ideally together, opening new possibilities for studies of non linear optics effects where a strong magnetic field and a powerful light source are necessary. One of these effects is the inverse Cotton-Mouton effect (ICME in the following), a non linear optical effect that in principle exists in any medium. In the presence of a transverse magnetic field, a linearly polarized light induces a magnetization in the medium in which it propagates [7]. The optically induced magnetization depends linearly on the transverse magnetic field amplitude. ICME, as its name indicates, is related to the much more studied Cotton-Mouton effect (CME in the following) i.e. the linear birefringence induced by a transverse magnetic field [8] in a similar fashion as the Faraday effect and the inverse Faraday effect are related [7]. ICME and CME can be explained as a mixing of four waves, two static fields, and two photonic fields. The CME depends on the square of the amplitude of the transverse magnetic field. To measure it, intense magnetic fields are necessary. ICME depends on the transverse magnetic field amplitude, and to the light intensity. To measure such an effect one needs to couple a powerful laser beam to an intense magnetic field transverse with respect to the light