Detecting vacuum birefringence with X-ray free electron lasers and high-power optical lasers: A feasibility study

We study the feasibility of measuring vacuum birefringence by probing the focus of a high-intensity optical laser with an X-ray free electron laser (XFEL). This amounts to performing a new type of QED precision experiment, employing only laser pulses, hence space- and time-dependent fields. To set the stage, we briefly review the status of QED precision tests and then focus on the example of vacuum birefringence. Adopting a realistic laser beam model in terms of pulsed Gaussian beams we calculate the induced phase shift and translate it into an experimental signal, counting the number of photons with flipped polarization. We carefully design a detailed experiment at the European XFEL operating in self-seeded mode, supplemented by a petawatt class optical laser via the HIBEF project. Assuming all components to represent the current state of the art, in particular the X-ray polarizers, realistic estimates of signal-to-noise ratios plus ensuing acquisition times are provided. This is accompanied by a statistical analysis of the impact of poor laser focus overlap either due to timing and pointing jitter as well as limited alignment accuracy. A number of parasitic effects are analyzed together with appropriate countermeasures. We conclude that vacuum birefringence can indeed be measured upon combining an XFEL with a high-power optical laser if depolarization effects in the x-ray lenses can be controlled.