Nonstationary Laguerre-Gaussian states vs Landau ones: choose your fighter

Although the widely used stationary Landau states describe electrons with a definite orbital angular momentum (OAM) in a magnetic field, it is the lesser known nonstationary Laguerre-Gaussian (NSLG) states that appropriately characterize vortex electrons after their transfer from free space to the field. The reason is boundary conditions lead to oscillations of the r.m.s. radius (the transverse coherence length) of the electron packet that has entered a solenoid. We comprehensively investigate properties of the NSLG states and establish their connections with the Landau states. For instance, we show that the transverse coherence length of an electron in the field usually oscillates around a value greatly exceeding the Landau state coherence length. We also discuss sensitivity of the NSLG states to a small misalignment between the propagation axis of a free electron and the field direction, which is inevitable in a real experiment. It is shown that for any state-of-the-art parameters, the corrections to the observables are negligible, and the electron OAM stays robust to a small tilt of the propagation axis. Finally, we draw analogies between a quantum wave packet and a classical beam of many particles in phase space, calculating the mean emittance of the NSLG states, which acts as a measure of their quantum nature.