International Conference on Quantum Information

Topological Phase for Spin-Orbit Transformations on a Laser Beam

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

Published Jan 1, 2008• 4 citations

Abstract

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.

DOI: 10.1364/icqi.2008.jmb45

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International Conference on Quantum Information

Topological Phase for Spin-Orbit Transformations on a Laser Beam

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

Published Jan 1, 2008• 4 citations

Publisher

Abstract

DOI: 10.1364/icqi.2008.jmb45

Related papers

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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 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 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.

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Representation of the SO(3) group by a maximally entangled state

W. LiMing, Zhilie Tang, Cai-Hong Liao

A representation of the $\mathrm{SO}(3)$ group is mapped into a maximally entangled two qubit state according to the literature. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the $\mathrm{SO}(3)$ sphere breaks an odd or even number of times, corresponding to the double connectedness of the $\mathrm{SO}(3)$ group. An odd number of breaks leads to an additional $\ensuremath{\pi}$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\ensuremath{\pi}$ phase.A representation of the $\mathrm{SO}(3)$ group is mapped into a maximally entangled two qubit state according to the literature. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the $\mathrm{SO}(3)$ sphere breaks an odd or even number of times, corresponding to the double connectedness of the $\mathrm{SO}(3)$ group. An odd number of breaks leads to an additional $\ensuremath{\pi}$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\ensuremath{\pi}$ phase.

arXiv:quant-ph/0403099Physical Review AJun 11, 200415 citations

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.

A representation of the

\mathrm{SO}(3)

group is mapped into a maximally entangled two qubit state according to the literature. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the

\mathrm{SO}(3)

sphere breaks an odd or even number of times, corresponding to the double connectedness of the

\mathrm{SO}(3)

group. An odd number of breaks leads to an additional $\ensuremath{\pi}$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\ensuremath{\pi}$ phase.