Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Science China Physics Mechanics and Astronomy

Geometric transformations of optical orbital angular momentum spatial modes

Rui He, Xin An

Published Nov 21, 2017• 5 citations
Publisher
DOI
10.1007/s11433-017-9099-0

Related papers

Wigner representation and geometric transformations of optical orbital angular momentum spatial modes

Gabriel F. Calvo

An exact Wigner representation of optical spatial modes carrying orbital angular momentum is found in closed form by exploiting the underlying SU(2) Lie-group algebra of their associated Poincaré sphere. Orthogonality relations and observables of these states are obtained within the phase space picture. Development of geometric phases on mode transformations is also elucidated.

Optics Letters•May 15, 2005•64 citations

Optical Gaussian States Carrying Orbital Angular Momentum

Elena D. Zhebrak

Journal of Russian Laser Research•May 1, 2016•1 citation

Cyclic transformation of orbital angular momentum modes

Florian Schlederer, Mario Krenn, Robert Fickler +2 more

The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D -dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D -dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states.

arXiv:1512.02696•New Journal of Physics•Apr 14, 2016•48 citations

Transformations of angular momentum coherent states under coordinate rotations

V.V. Mikhailov

Physics Letters A•Apr 1, 1971•6 citations

Orbital angular momentum in phase space

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

arXiv:1011.6184•Annals of Physics•Nov 27, 2010•46 citations

Topological phase evolving from the orbital angular momentum of ‘coiled’ quantum vortices

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.

Journal of Optics A Pure and Applied Optics•Jul 13, 2006•28 citations
The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D -dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D -dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states.
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.