Interaction of spin and intrinsic orbital angular momentum of light is observed, as evidenced by length-dependent rotations of both spatial patterns and optical polarization in a cylindricallysymmetric isotropic optical fiber. Such rotations occur in straight few-mode fiber when superpositions of two modes with parallel and anti-parallel orientation of spin and intrinsic orbital angular momentum (IOAM=2 ) are excited, resulting from a degeneracy splitting of the propagation constants of the modes.

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 novel 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 wavefunction 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.PACS numbers: 42.50. Tx, 42.81.Qb, 03.65.Ge It is well known that when an electron propagates in an inhomogeneous potential, its spin angular momentum (SAM)Ŝ interacts with the orbital angular momentum (OAM)L associated with its own curvilinear motion. It is also known that when light propagates in a transparent medium with an inhomogeneous refractive index, an analogous effect can take place: its polarization and OAM can interact and alter the propagation characteristics 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 unified wave-picture description of this spin-orbit interaction (SOI) for both photons (electromagnetic fields) and electrons (matter waves) can be reached.In this work we study the dynamics of the SOI from within such a unified framework. Remarkably, we find that the SOI is quantitatively described by a single expression applying to either an electron or a photon propagating in a straight, cylindrically symmetric waveguide geometry. This leads to the prediction of several novel rotational effects for both particle types, in which the particle's spin and orbital degrees of freedom influence one another as it propagates down the waveguide. These phenomena allow for the reversible transfer of entanglement between the SAM and OAM degrees of freedom of two-particle states. To provide deeper insight, we show that the common origin of these effects in electrons and photons is a universal geometric (Berry) phase associated 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 between the geometric phase and the SOI for both particle types (cf. [6,7] and Refs. therein). However, the cylindrical geometry we treat here, which supports transversely stationary waves with well-defined OAM that propagate down a straight waveguide axis, contrasts with the ge-FIG. 1: (a) An OAM eigenstate with |m ℓ | = 2 in a balanced superposition of + and...

Solution of the Dirac equation predicts that when an electron with non-zero orbital angular momentum propagates in a cylindrically symmetric potential, its spin and orbital degrees of freedom interact, causing the electron's phase velocity to depend on whether its spin and orbital angular momenta vectors are oriented parallel or anti-parallel with respect to each other. This spin-orbit splitting of the electronic dispersion curves can result in a rotation of the electron's spatial state in a manner controlled by the electron's own spin z-component value. These effects persist at nonrelativistic velocities. To clarify the physical origin of this effect, we compare solutions of the Dirac equation to perturbative predictions of the Schrödinger-Pauli equation with a spin-orbit term, using the standard Foldy-Wouthuysen Hamiltonian. This clearly shows that the origin of the effect is the familiar relativistic spin-orbit interaction.

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG(nm) input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG(l)(p) modes depending upon whether they have an even or odd value of their orbital angular momentum l. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m = 1) spatial states, covering the entire Poincar e sphere of first-order transverse modes.

We show that when an electron or photon propagates in a cylindrically symmetric waveguide, it experiences both a zitterbewegung effect and a spin-orbit interaction leading to identical propagation dynamics for both particles. Applying a unified perturbative approach to both particles simultaneously, we find that to first-order in perturbation theory their Hamiltonians each contain identical Darwin (zitterbewegung) and spin-orbit terms, resulting in the unification of their dynamics. The presence of the zitterbewegung effect may be interpreted physically as the delocalization of the electron on the scale of its Compton wavelength, or the delocalization of the photon on the scale of its wavelength in the waveguide. The presence of the spin-orbit interaction leads to the prediction of several rotational effects: the spatial or time evolution of either particle's spin/polarization vector is controlled by the sign of its orbital angular momentum quantum number, or conversely, its spatial wave function is controlled by its spin angular momentum.