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International Conference on Transparent Optical Networks

Continuous Variable Entanglement over Different Degree of Freedom for Entanglement Multiplexing

A. Porzio, Adriana Pecoraro, Filippo Cardano, Lorenzo Marrucci

Published Jul 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1109/icton.2019.8840360

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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.
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.
We have generated a new quantum state of light composed of quadrature entangled Laguerre-Gaussian (LG) modes. For the generation we used an OPO operating in a new regime where all field parameters are degenerate except for its spatial degree of freedom for which it is two-fold degenerate. The entanglement is manifested in the squeezing of the rotated modes in the Hermite-Gauss (HG) basis, measured with a specially tailored local oscillator. The most promising application of CV orbital angular momentum (OAM) states is their compatibility with atoms, thus allowing for storage of CV quantum information.
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.
In the present dissertation we describe the generation of a Gaussian bipartite entangled state in which the two subsystems are multi-distinguishable thanks to the fact that they have different polarizations and carry an opposite amount of orbital angular momentum along the propagation direction. Polarization entangled states are produced by using an optical parametric oscillator as spontaneous parametric down conversion source. This is able to produce a bipartite state consisting of collinear thermal crossed polarized modes exhibiting entanglement. These two modes have the same frequency and constitute a continuous variable bipartite entangled system in which each of the modes can be labeled by the polarization degree of freedom. Once these two polarization entangled states are produced, the bipartite state is endowed with an additional degree of freedom constituted by orbital angular momentum, that makes possible to further distinguish between these two co-propagating modes. The two-dimensional Hilbert polarization space is mapped into the orbital angular momentum one by means of Gaussian operations i.e. physical trasformations that preserve Gaussianity. In order to achieve this task we used a liquid crystal optical device called q-plate. This device is able to couple polarization and orbital angular momentum degrees of freedom by making the passing through beam acquire orbital angular momentum that depends on the topological charge q of the device and on the polarization of the incoming beam. Moreover, the setup enginereed to achieve this task is also capable of generating squeezed vortex beams i.e. single mode states for which the quadrature noise is below the standard quantum limit. After producing the bipartite entangled state it enters the characterizaton stage. Its quantumness is investigated by witnessing both squeezing and non classical correlations via balanced optical homodyne, a phase sensitive detection method that permits, by measuring the electromagnetic field quadratures statistics, to reconstruct the state of the system. In order to retrieve the quantum state with a high fidelity, homodyne detector needs to be optimized. This, besides imposing stringent conditions on the optical components involved in the setup, forces to improve the mode matching between the signal and the local oscillator that plays a central role in determining the overall detector efficiency. Although homodyne is a consolidated detection scheme, herein it is proposed an innovative extension of this technique to structured modes that opens the doors for homodyning directly in the orbital angular momentum space. The very central role, in this detection method, is played by interference between the signal under investigation and a strong coherent reference beam called local oscillator. Besides behaving as an amplifier for the quadrature under scrutiny, local oscillator also acts as a spatial and frequency filter, selecting for the measure the part of the signal that shares with it the same spatio-temporal properties. Hence, in order to ensure interference, in case of a signal carrying orbital angular momentum a further effort is required. Indeed, also the local oscillator has to be in the same helical mode, in particular the two beams have to transport the same amount of orbital angular momentum along the propagation direction. So by suitably designing the overall experimental setup it is possible to homodyne the bipartite entangled state carrying orbital angular momentum directly in this degree of freedom Hilbert space. Once the covariance matrix of the bipartite Gaussian state has been reconstructed, thanks to Gaussianity, it is possible to assess entanglement between the vortex modes by means of entanglement criteria based on covariance matrix elements such as the Peres-Horodecki-Simon (PHS) and the Duan ones.
The orbital angular momentum of light, unlike spin, is an infinite-dimensional discrete variable and may hence offer enhanced performances for encoding, transmitting, and processing quantum information. Hitherto, this degree of freedom of light has been studied mainly in the context of quantum states with definite number of photons. On the other hand, field-quadrature continuous-variable quantum states of light allow implementing many important quantum protocols not accessible with photon-number states. Here, we realize a scheme based on a qqq-plate device for endowing a bipartite continuous-variable Gaussian entangled state with nonzero orbital angular momentum. We then apply a reconfigurable homodyne detector working directly with such nonzero orbital angular momentum modes in order to retrieve experimentally their entire quantum-state covariance matrix, thus providing a full characterization of their quantum fluctuation properties. Our work is a step towards generating multipartite continuous-variable entanglement in a single optical beam.