Moving mirrors, Page curves and bulk entropies in AdS$_2$

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.