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 $\Delta \ell =\pm 2$ 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 $4.9\times 10^2$ and $3.3$ turns, but intrinsic-leakage scales of $2.1\times 10^5$ and $2.2\times 10^6$ 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.

13 pages