  Understanding the entanglement of radiation in QFT has been a long standing
challenge, with implications ranging from black hole thermodynamics to quantum
information. We demonstrate how the case of the free fermion in $1 + 1$
dimensions reveals the details of the density matrix of the radiation produced
by a moving mirror. Using the resolvent method rather than standard CFT
techniques we derive the R\'enyi entropies, modular Hamiltonian and flow of the
radiation, and determine when mirrors generate unitary transformations.
