Rotation of Canonical Orbital Angular Momentum of a Charged Particle Due to Effects of Global Geometric Phase

Pei-Song He

Cody C. Leary, M. G. Raymer, S. J. van Enk

We show that when an electron or photon propagates in a cylindrically symmetric waveguide, its spin angular momentum (SAM) and its orbital angular momentum (OAM) interact. Remarkably, we find that the dynamics resulting from this spin-orbit interaction are quantitatively described by a single expression applying to both electrons and photons. This leads to the prediction of several rotational effects: the spatial or time evolution of either particle's spin-polarization vector is controlled by its OAM quantum number or, conversely, its spatial wave function is controlled by its SAM. We show that the common origin of these effects in electrons and photons is a universal geometric phase. We demonstrate how these phenomena can be used to reversibly transfer entanglement between the SAM and OAM degrees of freedom of two-particle states.

Ioannes Rigas, Luis Lorenzo Sánchez-Soto, A. B. Klimov +2 more

Jean-Marc Lévy-Leblond

Constantine N. Alexeyev, M. A. Yavorsky

The propagation of a scalar field that satisfies the Schrodinger equation in a coiled helical potential well is studied. It is demonstrated that on propagation the scalar wave acquires an additional phase whose value is determined only by geometric parameters of the helix. It is established that this geometric phase is proportional to the orbital angular momentum of the particle and the solid angle subtended by the trajectory of the state on the orbital Poincare sphere. It is shown that this phase increment takes place for any state with well-defined orbital angular momentum and can be obtained through a simple rotational transformation of the Schrodinger equation into some effective rotating frame. A possible way of detection of such a phase in an interferometric experiment is also discussed. A connection is made with the propagation of optical vortices in coiled few-mode optical fibres.

Eric Palmerduca, Hong Qin

There has been an extended debate regarding the existence of a spin-orbital decomposition of the angular momentum of photons and other massless particles. It was recently shown that there are both geometric and topological obstructions preventing any such decomposition. Here we show that any geometric connection on a particle's state space induces a splitting of the angular momentum into two operators. These operators are well-defined angular momentum operators if and only if the connection has zero curvature. Massive particles have two canonical curved connections corresponding to boosts and rotations, respectively. These can be uniquely combined to produce a flat connection, and this gives a novel derivation of the Newton-Wigner position operator and the corresponding spin and orbital angular momenta for relativistic massive particles. When the mass is taken to zero, transverse boosts and rotations degenerate, leaving only a single connection for massless particles. This connection produces a commonly proposed splitting of the massless angular momentum into two operators. However, the connection is not flat, explaining why these operators do not satisfy the angular momentum commutation relations and are thus not true spin and orbital angular momentum operators.