One of the most striking nonlinear quantum effect is the production of an electron-positron pair by an electric field in vacuum. The probability of this process was determined by Schwinger in 1951 and shows that the production of electron-positron pairs is exponentially small for electric fields small compared to the Schwinger field. Unfortunately, despite the tremendous progress observed in the development of ultra-intense lasers in the last decades, the electric fields generated by current lasers are many orders weaker than the Schwinger field, so that many effects have exponentially small probabilities and are therefore unobservable. One can nevertheless observe certain nonlinear quantum effects in fields small compared to the Schwinger field by using ultra relativistic particles such that the field amplitude in the rest frame of the particles will be not too small or on the order of the Schwinger field. We intend to show in this presentation three types of QED effects that can nowadays be simulated in OSIRIS-PIC-QED framework:

1) QED-Radiation Reaction: we have incorporate a module which allows real photons emission from an electron (or a positron) according to the nonlinear Compton scattering.
The typical electron energy sufficient to diagnose weak nonlinear quantum effects is around few GeV and such electron beams can now be generated from an all-optical source in an efficient manner: current experimental record for self-injected electrons obtained in a laser wakefield accelerator is 4 GeV.
PIC-QED simulations that allow us to evaluate the influence of quantum emission on the energy spread and the divergence of an electron beam colliding head-on with an intense laser (I~10^21 W/cm2).Maximum attainable energy spread due to quantum stochasticity as a function of mean electron energy and the laser intensity is computed.

2) Seeded QED cascades in ultra-intense counter-propagating lasers: In this configuration, the stimulated pair production is a two-step process: nonlinear Compton scattering (emission of a hard photon) + Breit-Wheeler (decay of a hard photon into a pair). We have investigated the pair cascades seeded by electrons in counter-propagating lasers pulses for ELI parameters. The self-consistent modeling of these scenarios is challenging since some localized regions of ultra-intense field will produce a vast number of pairs that may cause memory overflow during the simulation.  To overcome this issue, we have developed a merging algorithm that allows merging a large number of particles into fewer particles with higher particle weights while conserving local particle distributions. This algorithm is crucial to investigate the laser absorption in self-generated pair plasmas. During the interaction, the laser energy is converted into pairs and photons and the absorption become significant when the plasma density reaches the critical density. With the results of 2D and 3D PIC-QED simulations, we will present the growth rates of the pair cascades and their dependence on the initial intensity of the lasers and on the polarisation. A simple analytical model for pair cascade will be compared with the numerical results. We will additionally show the respective fraction of laser energy transferred into pairs and photons for various configurations. Finally the various mechanisms contributing the laser absorption will be discussed

3) QED vacuum polarisation: Within the framework of QED, the second order process of photon-photon scattering mediated through the exchange of virtual electron-positron pairs leads to a set of corrected Maxwell's equations, effectively creating a non linear polarization and magnetization of the vacuum. To study this interaction, we incorporated a robust solver in the OSIRIS.  We are thus able to self consistently solve the nonlinear Maxwell's equations for a broad set of initial conditions. Our simulations confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field. Our work also shows the generation of high harmonics when two counter-propagating pulses interact. A perturbative analysis yields an exact form for the self consistent fields in this setup which closely agrees with the simulation results obtained.