Photon position eigenvectors, Wigner's little group and Berry's phase

Abstract

We show that the cylindrical symmetry of the eigenvectors of the photon position operator with commuting components, x, reflects the E(2) symmetry of the photon little group. The eigenvectors of x form a basis of localized states that have definite angular momentum, J, parallel to their common axis of symmetry. This basis is well suited to the description of "twisted light" that has been the subject of many recent experiments and calculations. Rotation of the axis of symmetry of this basis results in the observed Berry phase displacement. We prove that {x1,x2,J3} is a realization of the two dimensional Euclidean e(2) algebra that effects genuine infinitesimal displacements in configuration space.

Revised, 6 pages, 2 figures

References in corpus (5)

• Twisted Photons: New Quantum Perspectives in High Dimensions
• Angular Momenta and Spin-Orbit Interaction of Nonparaxial Light in Free Space
• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
• Observation of Interaction of Spin and Intrinsic Orbital Angular Momentum of Light
• Wigner translations and the observer-dependence of the position of masslesss spinning particles

Cited by in corpus (5)

• Local photons
• The geometrical interpretation of the photon position operator
• Construction of a photon position operator with commuting components from natural axioms
• The explicit form of the unitary representation of the Poincaré group for vector-valued wave functions (massive and massless), with applications to photon's localization and position operators
• Note on rotational properties of position operators of massless particles