  Radiation reaction is the influence of the electromagnetic field emitted by a
charged particle on the dynamics of the particle itself. Here we report
experimental radiation emission spectra from ultrarelativistic positrons in
silicon in a regime where both quantum and radiation-reaction effects dominate
the dynamics of the positrons. We found that each positron emits multiple
photons with energy comparable to its own energy, revealing the importance of
quantum photon recoil. Moreover, the shape of the emission spectra indicates
that photon emissions occur in a nonlinear regime where positrons absorb
several quanta from the crystal field. Our theoretical analysis shows that only
a full quantum theory of radiation reaction is capable of explaining the
experimental results, with radiation-reaction effects arising from the recoils
undergone by the positrons during multiple photon emissions. This experiment is
the first fundamental test of quantum electrodynamics in a new regime where the
dynamics of charged particles is determined not only by the external
electromagnetic fields but also by the radiation-field generated by the charges
themselves. Future experiments carried out in the same line will be able to, in
principle, also shed light on the fundamental question about the structure of
the electromagnetic field close to elementary charges.
