Nonstationary Laguerre-Gaussian states vs Landau ones: choose your fighter
arXiv (Cornell University)(2023)
摘要
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.
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关键词
landau ones,laguerre-gaussian
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