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arXiv:1805.05105 · Physical Review A

Continuous-variable entangled states of light carrying orbital angular momentum

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

Published Jul 15, 2019• 19 citations
arXivHTMLPDF

Abstract

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 $q$-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.

DOI
10.1103/physreva.100.012321

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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.
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.
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.
In addition to carrying spin angular momentum (SAM), light can also possess orbital angular momentum (OAM), whose quantum number can, in principle, take any integer value. This property provides a new degree of freedom to expand the capacity of both classical and quantum information. In recent years, generating OAM multiplexed continuous-variable entanglement via four-wave mixing (FWM) has emerged as an effective approach to increasing the capacity of quantum information channels. Consequently, there is a growing demand for precise characterization of the OAM spectrum in such quantum beams. Here we present, to the best of our knowledge, the first experimental demonstration of OAM spectrum measurement in quantum optics using phase-shifting interferometry (PSI). This method enables accurate characterization of the OAM spectrum of both the probe and conjugate beams in OAM multiplexed continuous-variable entanglement generated via the FWM process. These results provide an experimental foundation for the reliable detection and utilization of multiplexed OAM degrees of freedom in quantum communication and quantum information processing.
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.
Multiplexing techniques combine multiple signals into one channel, in order to increase the channel capacity and speed. Here we propose a correlation-based imaging method to efficiently measure the quantum states of orbital-angular-momentum (OAM)-multiplexed Gaussian light. The covariance matrices for all OAM components of the multiplexed Gaussian light can be efficiently reconstructed by one homodyne measurement on each beam. We also show that the proposed scheme can be simplified and implemented with only two charge coupled device detectors.
The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly 25 years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here, we explain the intuition that led to the first quantum experiment with OAM 15 years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps to applying these properties in novel quantum protocols. At the end, we identify several interesting open questions that could form the subject of future investigations with OAM.This article is part of the themed issue 'Optical orbital angular momentum'.