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Physical Review Letters

Continuous-Variable Hyperentanglement in a Parametric Oscillator with Orbital Angular Momentum

B. Coutinho dos Santos, K. Dechoum, Antonio Zelaquett Khoury

Published Dec 3, 2009• 57 citations
Publisher

Abstract

We describe continuous-variable hyperentanglement in polarization and orbital angular momentum modes of an optical parametric oscillator. The quantum stochastic equations for the multimode parametric interaction are derived and solved allowing for calculation of the quadrature noise spectra that characterize continuous-variable entanglement. As a main result, we predict simultaneous entanglement between different combinations of amplitude and phase quadratures of the interacting modes. We also propose experimental setups to access the different kinds of entanglement.

DOI
10.1103/physrevlett.103.230503

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We describe continuous-variable hyperentanglement in polarization and orbital angular momentum modes of an optical parametric oscillator. The quantum stochastic equations for the multimode parametric interaction are derived and solved allowing for calculation of the quadrature noise spectra that characterize continuous-variable entanglement. As a main result, we predict simultaneous entanglement between different combinations of amplitude and phase quadratures of the interacting modes. We also propose experimental setups to access the different kinds of entanglement.
We report on the generation of continuous-variable hyperentanglement of polarization and orbital angular momentum with a type II optical parametric oscillator. By compensating for the astigmatism between spatial modes, we produce an entangled pair of Hermite-Gauss beams. From correlations measurements, we verify the existence of continuous-variable hyperentanglement by the general entanglement criterion as well as by the continuous-variable version of the Peres-Horodecki criterion visualized on an equivalent Poincaré sphere.
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital angular momentum modes is mapped on an orbital Poincaré sphere, where the mode's position on the sphere is spanned by the three orbital parameters. Using a nondegenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincaré sphere.
Orbital angular momentum is a discrete degree of freedom that can access an infinite dimensional Hilbert space, thus enhancing the information capacity of a single optical beam. Continuous variables field quadratures allow achieving some quantum tasks in a more advantageous way with respect to the use of photon-number states. Here, we use a hybrid approach realizing bipartite continuous-variable Gaussian entangled state made up of two electromagnetic modes carrying orbital angular momentum. A q-plate is used for endowing a pair of entangled beams with such a degree of freedom. This quantum state is then completely characterized thanks to a novel design of a homodyne detector in which also the local oscillator is an orbital angular momentum-carrying beams so allowing the direct detection of vortex modes quadratures.
Continuous variable entanglement is usually set between pairs of optical modes sharing the same geometrical property where distinguishability is demanded to polarization and/or frequency. Thus, the inherent non-local correlation shows-up in quantum quadratures relative to two distinct e.m. modes. In this contribution we will show how the polarization d.o.f. of a pair of entangled modes is coupled to the optical orbital angular momentum giving, at the end, a pair of entangled modes that have orthogonal OAM and polarization. We also show how this experimental scheme can be extended to give more than a pair of entangled modes paving the way to CV entanglement multiplexing.