Photon-dark photon conversions in extreme background electromagnetic fields

The mixing of photons with light pseudoscalars in the presence of external electromagnetic fields has been used extensively to search for axion-like-particles. A similar effect for dark photon propagating states is usually not considered due to the Landau-Yang theorem. We point out that mixing between photon and dark photon propagating states in background electromagnetic fields can indeed occur, in non-linear QED, through a four-photon vertex by integrating out the electron box diagram. Starting from the Schwinger Lagrangian, we derive the equations of motion for dark photons interacting with the Standard Model photon through gauge kinetic terms. We provide expressions for the perpendicular and parallel refractive indices in series expansions in the critical field strength, valid both in the strong and weak background field limits. We then consider mixing between the photon-dark photon propagating system in the presence of pure electric and magnetic background fields, and work out the probability of conversion when the background fields are homogeneous. We indicate outlines of the calculation in the inhomogeneous case, and finally express our results in the active-sterile basis, where we find that the mixing induced by background fields can lead to corrections to the tree-level mixing in the zero field limit that is usually considered to probe such systems. Our results may find applications for probing photon-dark photon conversions in the vicinity of neutron stars and in table-top petawatt laser experiments.