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Continuous variable entanglement and optical orbital angular momentum: a hybrid route to quantum communication

Adriana Pecoraro

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

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.

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Continuous-variable entangled states of light carrying orbital angular momentum

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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 $q$-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.

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Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.

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CV entangled beams carrying OAM are successfully generated by converting entangled polarization modes into vortex beams. Entanglement is detected by homodyning in the OAM space with the homodyne local oscillator switching between different OAM states.

Quantum Information and Measurement (QIM)•Jan 1, 2017•0 citations
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.
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.
Orbital angular momentum (OAM) is one of the most recently discovered properties of light, and it is only in the past decade its quantum properties have been the subject of experimental investigations and have found applications. Unlike polarization, which is only bidimensional, orbital angular momentum provides, with relative ease, unprecedented access to a theoretically unbounded discrete state space. The process of spontaneous parametric down-conversion has long been used as a source of two-photon states that can be entangled in several degrees of freedom, including OAM. In this thesis, the properties of the natural OAM spectrum associated with the entangled states produced by parametric down-conversion were investigated. Chapters 2 and 3 describe the production and detection of tunable high-dimensional OAM entanglement in a down-conversion system. By tuning the phase-matching conditions and improving the detection stage, a substantial increase in the half-width of the OAM correlation spectrum was observed. The conjugate variable of OAM, angular position, was also considered when examining high-dimensional states entangled in OAM. In order to efficiently determine their dimension, high-dimensional entangled states were probed by implementing a technique based on phase masks composed of multiple angular sectors, as opposed to narrow single-sector analysers. Presented in chapter 4, this technique allows the measurements of tight angular correlations while maintaining high optical throughput. The states so produced were then used for a number of applications centred around the concept of mutually unbiased bases. One can define sets of mutually unbiased bases for arbitrary subspaces of the OAM state space. Two bases are mutually unbiased if the measurement of a state in one basis provides no information about the state as described in the other basis. Complete measurements in mutually unbiased bases of high-dimensional OAM spaces are presented in chapter 5. Measurements in sets of mutually unbiased bases are integral to quantum science and can be used in a variety of protocols that fully exploit the large size of the OAM state space; we describe their use in efficient quantum state tomography, quantum key distribution and entanglement detection. Caution is however necessary when dealing with state spaces embedded in higher-dimensional spaces, such as that provided by OAM. Experimental tests of Bell-type inequalities allow us to rule out local hidden variable theories in the description of quantum correlations. Correlations inconsistent with the states observed, or even with quantum mechanics, known as super-quantum correlations, have however been recorded previously in experiments that fail to comply with the fair-sampling conditions. Chapter 6 describes an experiment that uses a particular choice of transverse spatial modes for which super-quantum correlations persist even if the detection is made perfectly efficient. The sets of modes carrying OAM allow a complete description of the transverse field. The ability to control and combine additional degrees of freedom provides the possibility for richer varieties of entanglement and can make quantum protocols more powerful and versatile. One such property of light, associated with transverse modes possessing radial nodes in the field distribution, can be accessed within the same type of experimental apparatus used for OAM. In chapter 7, the radial degree of freedom is explored, together with OAM, in the context of Hong-Ou-Mandel interference.
Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the corresponding covariance matrix. Here we describe in detail and experimentally demonstrate a robust and reliable method to fully characterize bipartite optical Gaussian states by means of a single homodyne detector. We have successfully applied our method to the bipartite states generated by a sub-threshold type-II optical parametric oscillator which produces a pair of thermal cross-polarized entangled cw frequency degenerate beams. The method provides a reliable reconstruction of the covariance matrix and allows us to retrieve all the physical information about the state under investigation. These include observable quantities, such as energy and squeezing, as well as nonobservable ones such as purity, entropy, and entanglement. Our procedure also includes advanced tests for the Gaussianity of the state and, overall, represents a powerful tool to study the bipartite Gaussian state from the generation stage to the detection one.
Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.