Polarization of light beams is one of the most important physical phenomena. But up till now it was only described in the paraxial approximation in which it is considered to be a single degree of freedom that is characterized by the local Stokes parameters over the transverse plane. Based on such a description, vector vortex beams are considered to be entangled in polarization and spatial mode. Here we show that there is not any entanglement in a large class of representative vector vortex beams, including the well-known cylindrical-vector beams. This is achieved by developing an approach to exactly characterize the polarization of a general beam. It is found that the Stokes parameters, when generalized rigorously to a general beam in momentum space, are physical quantities with respect to a natural coordinate system. The so-called Stratton vector determining the natural coordinate system fixes a natural representation for the polarization in which the Pauli matrices represent the intrinsic degree of freedom of the polarization with respect to the natural coordinate system. As a result, the Stratton vector itself shows up as another degree of freedom of the polarization. From this point of view, the light beams specified by a Stratton vector parallel to the propagation axis as well as by the eigenvalues of the Pauli matrix $\hatσ_1$ are precisely vector vortex beams. They are not endowed with any entanglement.
We calculate the entanglement of a generalized elliptical vortex formed by quantized radiation field, using Wigner quasiprobability distribution function for such states. We find a critical squeezing parameter above which the entanglement is less for higher vorticity, which is counter intuitive.
The negativity of the Wigner function is discussed as a measure of the non classicality and the quantum interference pattern obtained therein as a possible measure of the entanglement between the two modes of the vortex states. This measure of entanglement is compared with the results obtained from concurrence.
In this article we report that the entanglement produced by single photon subtraction is maximum, by studying the entanglement of multi photon subtraction from two mode squeezed states. We argue that the single photon subtraction produces maximum entanglement as it is more non-classical in nature than many photon subtractions
We study the entanglement evolution of a quantum optical vortex state propagating through coupled lossless waveguides. We consider states generated by coupling two squeezed modes using a sequence of beam splitters and also by subtracting photons from the signal in spontaneous parametric down conversion. We reconstruct the Wigner function at a later time to study the correlation and quantify the entanglement after propagation using \emph{logarithmic negativity}.
We calculate the Wigner (quasi)probability distribution function of the quantum optical elliptical vortex (QEV), generated by coupling squeezed vacuum states of two modes. The coupling between the two modes is performed by using beam splitter (BS) or a dual channel directional coupler (DCDC). The quantum interference due to the coupling between the two modes promises the generation of controlled entanglement for quantum computation and quantum tomography. We compute the entanglement of such QEV formed by non-classical radiation field, using Wigner function. We report a critical squeezing param…
Light endowed with orbital angular momentum, commonly termed optical vortex light, has an azimuthal phase indexed by the orbital quantum number $l$. In contrast to the two basis states of the optical spin angular momentum, the interest in the information content of optical vortex beams is centred on the assumption that $\lvert{l}\rangle{}$ forms a countably infinite set of basis states. The recent experimental observation that group velocity is inversely proportional to $l$ provides a theoretical basis for a practical measure of information transfer. This Letter sets an upper bound on that mea…
Given the multitude of applications of vector vortex beams there is a need for robust tools to measure them. Here we exploit the non-separability of such beams, akin to entanglement of quantum states, to apply tools traditionally associated with quantum measurements to these classical fields. We apply three measures of non-separability: a Bell inequality, a concurrence, and an entanglement entropy to define the "vectorness" of such beams. In addition to providing novel tools for the analysis of vector beams, we also introduce the concept of classical entanglement to explain why these tools are…
One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle both, classically and in the quantum regime. Here we demonstrate that the local entanglement, or non-separability, between the spatial and polarisation degrees of freedom also experience self-healing. We measured and quantified the degree of non-separability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of non-separability …
We calculate the Wigner quasiprobability distribution function of quantum elliptical vortex in elliptical beam (EEV), produced by coupling squeezed coherent states of two modes. The coupling between the two modes is performed by using beam splitter (BS) or a dual channel directional coupler (DCDC). The quantum interference due to the coupling between the two modes promises the generation of controlled entanglement for quantum computation and quantum tomography.
We present an analytical means of quantifying the fractional accumulation of geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a Sphere of Modes is endowed with a Supplementary Product Space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of geometric phase across a single lens as a function of initial state and lens position within the beam. It can be readily applied to a series of lenses as well.
It is shown that the vector-vortex Laguerre-Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams with nonzero azimuthal and radial indices in a cylindrical graded-index medium is investigated. The wave shape variation with distance taking into account the spin-orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is dem…
Secret sharing is the art of securely sharing information between more than two people in such a way that its reconstruction requires the collaboration of a certain number of parties. Entanglement-based secret sharing schemes which utilise multi-particle entanglement are limited by their scalability. Recently, a high-dimensional single photon secret sharing protocol was proposed which has impressive advantages in scalability. However, the experimental realisation of this protocol remains elusive. Here, by taking advantage of the high-dimensional Hilbert space for orbital angular momentum and u…
Violating a nonlocality inequality enables the most powerful remote quantum information tasks and fundamental tests of quantum physics. Loophole-free photonic verification of nonlocality has been achieved with polarization-entangled photon pairs, but not with states entangled in other degrees of freedom. Here we demonstrate completion of the quantum steering nonlocality task, with the detection loophole closed, when entanglement is distributed by transmitting a photon in an optical vector vortex state, formed by optical orbital angular momentum (OAM) and polarization. As well as opening up a h…
It is well known that the entanglement of a quantum state is invariant under local unitary transformations. It dictates, for example, that the degree of entanglement of a photon pair in a Bell state remains maximally entangled during propagation in free-space. Here we outline a scenario where this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and pro…
We perform Bell's measurement and perform quantum Fourier transform with the classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and nonquantum entanglement between the polarization and orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally, which is the crucial final step in Shor's algorithm
Constant sensitivity birefringence metrology using vector vortex beams
ICFO – Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；Centro de Investigaciones en Óptica, A.C.（光学研究中心）；Department of Signal Theory and Communications, Universitat Politecnica de Catalunya（加泰罗尼亚理工大学信号理论与通信系）
The atom-photon entanglement using the Laguerre-Gaussian beams is studied in the closed-loop three-level $V$-type quantum systems. We consider two schemes with degenerated and non-degenerated upper levels: in the first, the effect of the quantum interference due to the spontaneous emission is taken into account and in the second, a microwave plane wave is applied to the upper levels transition for non-degenerated scheme. It is shown that the atom-photon entanglement in both schemes depends on the intensity profile as well as the orbital angular momentum (OAM) of applied fields so that the vari…
Laguerre-Gaussian (LG) beams reflected from a multi-layered dielectric experience a shift in their centroid that is different than that from a single interface. This has been previously investigated for linearly polarized beams and, to a much lesser extent, beams with spin angular momentum. Here a combination of perturbation and computational analyses is used to provide a unified quantification of these shifts in layered dielectrics with two parallel interfaces. The approach is then extended to consider the qualitatively new behavior that results when the light is endowed with an intrinsic orb…
