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

arXiv:0704.0893 · Physical Review Letters

Topological Phase for Spin-Orbit Transformations on a Laser Beam

C. E. R. Souza, J. A. O. Huguenin, P. Milman, Antonio Zelaquett Khoury

Published Oct 15, 2007• 102 citations
arXivHTMLPDF

Abstract

We investigate the topological phase associated with the double connectedness of the SO(3) representation in terms of maximally entangled states. An experimental demonstration is provided in the context of polarization and spatial mode transformations of a laser beam carrying orbital angular momentum. The topological phase is evidenced through interferometric measurements, and a quantitative relationship between the concurrence and the fringes visibility is derived. Both the quantum and the classical regimes were investigated.

DOI
10.1103/physrevlett.99.160401

Related papers

Topological Phase for Spin-Orbit Transformations on a Laser Beam

C. E. R. Souza, J. A. O. Huguenin, P. Milman +1 more

We investigate the topological phase associated with the SO(3) representation in terms of maximally entangled states. An experimental demonstration of this topological phase is provided for polarization and spatial mode transformations of a laser beam.

International Conference on Quantum Information•Jan 1, 2008•4 citations

Exprimental Demonstration of the Topological Phase for Entangled Qubits

C. E. R. Souza, J. A. O. Huguenin, P. Milman +1 more

We investigate the topological phase associated with the SO(3) representation in terms of maximally entangled states. An experimental demonstration of this topological phase is provided for polarization and spatial mode transformations of a laser beam.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2007•0 citations

Topological phase for entangled two-qubit states and the representation of theSO(3) group

F De Zela

We discuss the representation of the $SO(3)$ group by two-qubit maximally entangled states (MES). We analyze the correspondence between $SO(3)$ and the set of two-qubit MES which are experimentally realizable. As a result, we offer a new interpretation of some recently proposed experiments based on MES. Employing the tools of quantum optics we treat in terms of two-qubit MES some classical experiments in neutron interferometry, which showed the $π$-phase accrued by a spin-$1/2$ particle precessing in a magnetic field. By so doing, we can analyze the extent to which the recently proposed experiments - and future ones of the same sort - would involve essentially new physical aspects as compared with those performed in the past. We argue that the proposed experiments do extend the possibilities for displaying the double connectedness of $SO(3)$, although for that to be the case it results necessary to map elements of $SU(2)$ onto physical operations acting on two-level systems.

arXiv:quant-ph/0511034•Journal of Optics B Quantum and Semiclassical Optics•Oct 31, 2005•3 citations

Quantum walks and topological phenomena with structured light

Alessio D’Errico

The manipulation of the spatial structure of a light beam has many application in both classical and quantum physics. The possibility to exploit high dimensional degrees of freedom carried by a light beam can be employed, among the various applications, for simulating the dynamics on quantum particles in multidimensional spaces. Coupling these degrees of freedom, like the orbital angular momentum or the transverse linear momentum, with the polarization of light (also associated with the spin) allows to implement quantum walks on one and two dimensional lattices. This work presents a series of experiments where these implementations of photonic quantum walks were realized exploiting patterned liquid crystal devices. In particular, the experimental setup allows to investigate interesting effects of the non-trivial topological features of the simulated processes, and test methods for the experimental measurement of topological invariants. This research has also led to the introduction of a novel method of characterizing unknown structured light beams and to the study of the stability of polarization singularities in laser beams.

•Dec 3, 2018•0 citations

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

Spatial-state Stokes-operator squeezing and entanglement for optical beams

Magnus T. L. Hsu, Warwick P. Bowen, Ping Koy Lam

The transverse spatial attributes of an optical beam can be decomposed into the position, momentum, and orbital angular momentum observables. The position and momentum of a beam are directly related to the quadrature amplitudes, while the orbital angular momentum is related to the polarization (spin) variables. In this paper, we study the quantum properties of these spatial variables, using a representation in the Stokes-operator basis. We propose a spatial detection scheme to measure all three spatial variables and, consequently, propose a scheme for the generation of spatial Stokes-operator squeezing and entanglement.

arXiv:0901.4813•Physical Review A•Apr 23, 2009•26 citations
We investigate the topological phase associated with the double connectedness of the SO(3) representation in terms of maximally entangled states. An experimental demonstration is provided in the context of polarization and spatial mode transformations of a laser beam carrying orbital angular momentum. The topological phase is evidenced through interferometric measurements, and a quantitative relationship between the concurrence and the fringes visibility is derived. Both the quantum and the classical regimes were investigated.
We discuss the representation of the SO(3)SO(3)SO(3) group by two-qubit maximally entangled states (MES). We analyze the correspondence between SO(3)SO(3)SO(3) and the set of two-qubit MES which are experimentally realizable. As a result, we offer a new interpretation of some recently proposed experiments based on MES. Employing the tools of quantum optics we treat in terms of two-qubit MES some classical experiments in neutron interferometry, which showed the πππ-phase accrued by a spin-1/21/21/2 particle precessing in a magnetic field. By so doing, we can analyze the extent to which the recently proposed experiments - and future ones of the same sort - would involve essentially new physical aspects as compared with those performed in the past. We argue that the proposed experiments do extend the possibilities for displaying the double connectedness of SO(3)SO(3)SO(3), although for that to be the case it results necessary to map elements of SU(2)SU(2)SU(2) onto physical operations acting on two-level systems.
The manipulation of the spatial structure of a light beam has many application in both classical and quantum physics. The possibility to exploit high dimensional degrees of freedom carried by a light beam can be employed, among the various applications, for simulating the dynamics on quantum particles in multidimensional spaces. Coupling these degrees of freedom, like the orbital angular momentum or the transverse linear momentum, with the polarization of light (also associated with the spin) allows to implement quantum walks on one and two dimensional lattices. This work presents a series of experiments where these implementations of photonic quantum walks were realized exploiting patterned liquid crystal devices. In particular, the experimental setup allows to investigate interesting effects of the non-trivial topological features of the simulated processes, and test methods for the experimental measurement of topological invariants. This research has also led to the introduction of a novel method of characterizing unknown structured light beams and to the study of the stability of polarization singularities in laser beams.
The transverse spatial attributes of an optical beam can be decomposed into the position, momentum, and orbital angular momentum observables. The position and momentum of a beam are directly related to the quadrature amplitudes, while the orbital angular momentum is related to the polarization (spin) variables. In this paper, we study the quantum properties of these spatial variables, using a representation in the Stokes-operator basis. We propose a spatial detection scheme to measure all three spatial variables and, consequently, propose a scheme for the generation of spatial Stokes-operator squeezing and entanglement.