Spin and orbital rotation of electrons and photons via spin-orbit interaction

S interacts with the orbital angular momentum (OAM) ^ L associated with its own curvilinear motion. It is also known that when light propagates in a trans- parent medium with an inhomogeneous refractive index, an analogous eect can take place: its polarization and OAM can interact and alter the propagation character- istics of the light. Several instances of this have been predicted (cf. (1, 2, 3)), and a few experiments have been done (4, 5, 6). What has not yet been made clear is the extent to which a unied wave-picture description of this spin-orbit interaction (SOI) for both photons (elec- tromagneticelds) and electrons (matter waves) can be reached. In this work we study the dynamics of the SOI from within such a unied framework. Remarkably, wend that the SOI is quantitatively described by a single ex- pression applying to either an electron or a photon prop- agating in a straight, cylindrically symmetric waveguide geometry. This leads to the prediction of several novel rotational eects for both particle types, in which the particle's spin and orbital degrees of freedom inuence one another as it propagates down the waveguide. These phenomena allow for the reversible transfer of entangle- ment between the SAM and OAM degrees of freedom of two-particle states. To provide deeper insight, we show that the common origin of these eects in electrons and photons is a universal geometric (Berry) phase associ- ated with the interplay between either particle's spin and OAM. This implies that the SOI occurs for any particle with spin, and thereby exists independently of whether or not the particle has mass, charge, or magnetic moment. Previous authors have examined the connection be- tween the geometric phase and the SOI for both particle types (cf. (6, 7) and Refs. therein). However, the cylindri- cal geometry we treat here, which supports transversely stationary waves with well-dened OAM that propagate down a straight waveguide axis, contrasts with the ge-