State-resolved quantum transport of vortex electrons in accelerators

Abstract

Vortex electrons carry a quantized orbital angular momentum (OAM) degree of freedom, but whether this internal structure can survive repeated transport through an accelerator lattice remains unclear. Here we formulate a density-matrix theory for periodic round lattices and show that the symmetry-protected quantity is a Lewis-Floquet OAM invariant, rather than the instantaneous kinetic OAM. The classical transfer map lifts to unitary state evolution, while stochastic field errors generate a Lindblad channel. This framework exposes a sharp separation between visibility and state survival. Dipole jitter displaces the wavepacket, rapidly smearing a vortex signature measured about a fixed origin without altering its recentered internal OAM distribution. Quadrupole fluctuations instead drive genuine $\Delta\ell=\pm2$ leakage. For a matched $n=0$, $|\ell|=1$ mode, white-noise estimates based on representative IOTA and PETRA III parameters give fixed-frame smearing scales of $4.9\times10^2$ and $3.3$ turns, but intrinsic-leakage scales of $2.1\times10^5$ and $2.2\times10^6$ turns, respectively. Thus loss of an unrecentered vortex image need not signal destruction of the vortex state: its internal OAM structure can persist hundreds to hundreds of thousands of times longer. Centroid tracking and quadrupole stability are therefore distinct experimental requirements for observability and state survival, respectively.