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arXiv:0905.3778 · Physical Review A

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

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

Published Dec 8, 2009• 18 citations
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Abstract

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.

DOI
10.1103/physreva.80.061804

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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.
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 or 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.
We investigate two-photon entangled states using two important degrees of freedom of the electromagnetic field, namely orbital angular momentum (OAM) and spin angular momentum. For photons propagating in the same direction we apply the idea of entanglement duality and develop schemes to do entanglement sorting based on either OAM or polarization. In each case the entanglement is tested using appropriate witnesses. We finally present generalizations of these ideas to three- and four-photon entangled states.
The optical "spin-orbit" coupling occurring in a suitably patterned nonuniform birefringent plate known as a "q plate" allows entangling the polarization of a single photon with its orbital angular momentum (OAM). This process, in turn, can be exploited for building a bidirectional "spin-OAM interface," capable of transposing the quantum information from the spin to the OAM degree of freedom of photons and vice versa. Here, we experimentally demonstrate this process by single-photon quantum tomographic analysis. Moreover, we show that two-photon quantum correlations such as those resulting from coalescence interference can be successfully transferred into the OAM degree of freedom.
In this paper, we provide a consistent framework to address the notorious difficult decomposition of the single-photon total angular momentum (TAM) into a spin (SAM) and an orbital (OAM) component.We discuss the canonical decomposition into SAM and OAM components, which are the generators of internal and spatial rotations in the space of physical states.We find that those operators are mutually compatible but unsharp quantum observables, therefore Positive Operator-Valued Measures describe their joint measurements.We present another decomposition of the TAM, which we denote as a non-canonical one.The operators resulting from this decomposition are mutually incompatible but sharp quantum observables, thus Projector-Valued Measurements.This fact reflects their consistency with the transversality condition of single-photon wavefunctions, thus explains the underlying physics from a quantum information theoretic view.Furthermore, we discuss the implementations on joint measurements for both decompositions and provide an explicit calculation of all these quantities for circularly polarized Gaussian single-photon states.The difference between the canonical and non-canonical momenta leads to observable differences in higher-order statistical moments.
Photons can carry spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used to realize a qubit system and a high-dimension system, respectively. This spin-orbital system is very suitable for implementing one-dimensional discrete-time quantum random walks. We propose a simple scheme of quantum walks on the spin-orbital angular momentum space of photons, where photons walk on the infinite OAM space controlled by their SAM. By employing the recent invention of an optical device, the so-called ``qqq-plate,'' our scheme is more simple and efficient than others because there is no Mach-Zehnder interferometer in the scheme.