This Conceptual Design Report describes LUXE (Laser Und XFEL Experiment), an experimental campaign that aims to combine the high-quality and high-energy electron beam of the European XFEL with a powerful laser to explore the uncharted terrain of quantum electrodynamics characterised by both high energy and high intensity. We will reach this hitherto inaccessible regime of quantum physics by analysing high-energy electron-photon and photon-photon interactions in the extreme environment provided by an intense laser focus. The physics background and its relevance are presented in the science case which in turn leads to, and justifies, the ensuing plan for all aspects of the experiment: Our choice of experimental parameters allows (i) field strengths to be probed where the coupling to charges becomes non-perturbative and (ii) a precision to be achieved that permits a detailed comparison of the measured data with calculations. In addition, the high photon flux predicted will enable a sensitive search for new physics beyond the Standard Model. The initial phase of the experiment will employ an existing 40 TW laser, whereas the second phase will utilise an upgraded laser power of 350 TW. All expectations regarding the performance of the experimental set-up as well as the expected physics results are based on detailed numerical simulations throughout.

A factor that limits the use of multiphoton microscopy (MPM) in clinical and preclinical studies is the lack of a compact and flexible probe. We report on a miniaturized MPM probe employing a microelectromechanical system (MEMS) scanning mirror and a double-clad photonic crystal fiber (DCPCF). The use of a MEMS mirror and a DCPCF provides many advantages, such as size reduction, rapid and precise scanning, efficient delivery of short pulses, and high collection efficiency of fluorescent signals. The completed probe was 1 cm in outer diameter and 14 cm in length. The developed probe was integrated into an MPM system and used to image fluorescent beads, paper, and biological specimens.

Radiative and nonradiative electron spin-flip probabilities are analyzed in both plane wave and focused laser backgrounds. We provide a simple and physically transparent description of spin dynamics in plane waves, and demonstrate that there exists a kinematic regime in which the usual leading-order perturbative hierarchy of quantum electrodynamics is reversed, and nonradiative loop effects dominate over radiative tree-level spin flips. We show that while this loop dominance becomes suppressed in focused laser pulses due to a high sensitivity to field geometry, there is nevertheless a regime in which, in principle, loop effects on spin transitions can be discerned.

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