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We show that when an electron or photon propagates in a cylindricallysymmetric waveguide, its spin angular momentum (SAM) and its orbital angularmomentum (OAM) interact. Remarkably, we find that the dynamics resulting fromthis spin-orbit interaction are quantitatively described by a single expressionapplying to both electrons and photons. This leads to the prediction of severalnovel rotational effects: the spatial or time evolution of either particle'sspin/polarization vector is controlled by the sign of its OAM quantum number,or conversely, its spatial wavefunction is controlled by its SAM. We show thatthe common origin of these effects in electrons and photons is a universalgeometric phase. We demonstrate how these phenomena can be used to reversiblytransfer entanglement between the SAM and OAM degrees of freedom oftwo-particle states.

Spin and Orbital Rotation of Electrons and Photons via Spin-Orbit Interaction