TITLE: Density matrix reconstruction in ultrafast free electron optics

ABSTRACT: Recent advancements in photon induced near-field electron microscopy (PINEM) enable the preparation,
coherent manipulation and characterization of free-electron quantum states. This talk will focus on the
mathematical aspects of the reconstruction of the corresponding density matrices from measured electron
energy spectrograms. This reconstruction requires the solution of an ill-posed inverse problem, where a
positive semi-definte trace-class operator is reconstructed given its diagonal in different bases. We will
discuss stability results, reconstruction algorithms and suitable penalty functionals in the quantum state
tomography context.