Michael V Berry, S Soskin, E Brasselet, I Freund, Boris A Malomed, Valerii P Aksenov, C Rosales Guzmán, C N Alexeyev, A N Alexeyev, M A Yavorsky, L Tryfonyuk, A Ushenko, D L Andrews, L Torner, A Desyatnikov, Y Miyamoto, O Angelsky, P Banzer, Nikolay N Rosanov, F S Roux, V Venediktov, R O Vlokh, A Volyar, Y Egorov, A Rubass, G Gbur, M A Alonso, E Karimi and Mark R Dennis 1 H H Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom 2 Department of Theoretical Physics, Institute of Semiconductor Physics, Kyiv, Ukraine 3 University of Bordeaux, CNRS, Laboratoire Ondes et Matière d’Aquitaine, F-33400 Talence, France 4 Physics Department, Bar Ilan University, Ramat Gan, Israel 5 Department of Physical Electronics, School of Electrical Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv, Israel 6 V.E. Zuev Institute of Atmospheric Optics SB RAS (IAO SB RAS), Tomsk, Russia 7 Wang Da-Heng Collaborative Innovation Center for Quantum Manipulation and Control, Harbin University of Science and Technology, Harbin 150080, People’s Republic of China 8 V. I. Vernadsky Crimean Federal University, Vernadsky Prospekt, 4, Simferopol 295007, Russia 9 V. M. Efetov Crimean Center for Oncology, Bespalova St. 45a, Simferopol 295008, Russia 10 Department of Urology, Rivne Regional Hospital, Rivne, Ukraine Knight of science

A detailed analysis of the stimulated parametric down-conversion (PDC) process is performed to investigate the effects of the spatiotemporal degrees of freedom. The analysis provides information that would be useful for PDC-based metrology applications. Using a Wigner functional approach, we obtain the parametric down-converted state as the Bogoliubov transformed input state, in terms of Bogoliubov kernel functions. The result is used to consider the case for a coherent state seeding stimulated PDC. We also compute the background which is obtained from spontaneous PDC.

We investigate the impact of Hilbert-space truncation upon the entanglement of an initially maximally entangled $m\times m$ bipartite quantum state, after propagation under an entanglement-preserving $n \times n$ ($n\geq m$) unitary. Truncation -- physically enforced, e.g., by a detector's finite cross section -- projects the state onto an $s \times s$-dimensional subspace ($3\leq s \leq n$). For a random local unitary evolution, we obtain a simple analytical formula that expresses the truncation-induced entanglement loss as a function of $n$, $m$ and $s$.

We provide an analytical expression for the entanglement decay of initially maximally entangled orbital-angular-momentum biphoton states, when scattered off an obstruction. We show that the decay is controlled by the diffraction-induced mutual overlap between the diffracted field modes, and quantify its dependence on the size and position of the obstruction.

Elementary thin optical components with phase-only transmission functions are used to perform coordinate transformations. Such point transforms, which are defined by sets of explicit equations, perform geometrical transformations on the transverse intensity distributions of optical beams. We discuss the procedure to determine the phase-only transmission function that would implemented a coordinate transformation and apply it to the rotation transformation. The Hough transform is a point transform that is defined in terms of an implicit equation. The implementation of the Hough transform in a linear optical system is also discussed.

We propose a simple method for the detection of Bessel beams with arbitrary radial and azimuthal indices, and then demon strate it in an all-digital setup with a spatial light modulator. We confirm that the fidelity of the detection method is very high, with modal cross-talk b elow 5%, even for high orbital angular momentum carrying fields with long p ro agation ranges. To illustrate the versatility of the approach we use it to observe the modal spectrum changes during the self-reconstruction pro cess of Bessel beams after encountering an obstruction, as well as to chara terize modal distortions of Bessel beams propagating through atmospher ic turbulence. © 2018 Optical Society of America OCIS codes: (090.1995) Digital holography; (070.6120) Spatial light m odulators; (0.50.4865) Optical vortices. References and links 1. J. Durnin,“Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651-654 (1987). 2. J. Durnin, J. J. Miceli, and J. H. 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Recently, the Hong-Ou-Mandel (HOM) effect, which incorporates second-order quantum interference, has been used for remote synchronization of clocks with a synchronization stability of less than a picosecond [R. Quan, et al., Sci. Rep. 6, 30453 (2016)]. However, this implementation has only been demonstrated over a few kilometers. When such a synchronization protocol is implemented over longer distances, the effect of the channel may start to deteriorate the second-order quantum interference in the HOM effect. For instance, if the channel is the atmosphere (see for instance [J.-D. Deschenes, et al., Phys. Rev. X 6, 021016 (2016)]), turbulence may affect the quantum interference observed in the HOM effect. Here we investigate the effect of turbulence on the HOM effect. In our experiment, turbulence is simulated for weak scintillation conditions by a single phase screen and the input state is prepared with spontaneous parametric down-conversion. We consider various scenarios allowing for different variations of the synchronization protocol. The experimental results, which agree with our theoretical calculations, show that for symmetric input states under particular conditions (in a one-sided turbulence channel) the HOM effect is independent of the scintillation strength. This result follows from a combination of the fact that the HOM dip is only observed if the input state is symmetric and the fact that a one-sided turbulent channel does not convert a symmetric state into an anti-symmetric state. In view of these results, it should be possible to use second-order quantum interference to synchronize remote clocks over longer distances.

Combining the multiple degrees of freedom of photons has become topical in quantum communication and information processes. This provides advantages such as increasing the amount of information that is be packed into a photon or probing the wave-particle nature of light through path-polarisation entanglement. Here we present two experiments that show the advantages of using hybrid entanglement between orbital angular moment (OAM) and polarisation. Firstly, we present results where high dimensional quantum key distribution is demonstrated with spatial modes that have non-separable polarisation-OAM DOF called vector modes. Secondly, we show that through OAM-polarisation entanglement, the traditional which-way experiment can be performed without using the traditional physical path interference approach.

We report the first quantum entanglement experiment in South Africa. The spatial modes of the entangled photon pair were investigated with their potential for high-dimensional entanglement. The generation, measurement and characterisation of the entangled states were examined in detail and we show high-dimensional entanglement in a Hilbert space of dimension 25. High-dimensional entanglement introduces the possibility for more secure communication and more efficient computations. We highlight the experimental challenges contained within each step and provide practical techniques for future experiments in the quantum regime.

By using digital holograms, we present a simple technique for performing a complete azimuthal decomposition of an arbitrary laser mode. The match-filter, used to perform the azimuthal decomposition, is bounded by an annular ring, allowing us to conduct a scale-independent decomposition on our selected mode. This technique therefore requires no prior knowledge of the mode structure, the mode phases, or the amplitude distribution. A basis comprising of the angular harmonics is used to express the spatial distribution of the selected mode in terms of spatially dependant coefficients. We use this to infer directly from the measured weightings of the azimuthally decomposed modes and their phase-delay measurements, the intensity of the selected field, its phase, and its orbital angular momentum (OAM) density. We illustrate the concept by executing a full decomposition of two examples: a superposition of two Bessel beams, with relative phase differences, and an off-axis vortex mode. We show a reconstruction of the amplitude, phase and OAM density of these fields with a high degree of accuracy.

We demonstrate the efficient sorter of Bessel beams separating both the azimuthal and radial components. This is based upon the recently reported transformation of angular to transverse momentum states. We separately identify over forty azimuthal and radial components, with a radial spacing of 1588 m(-1), and outline how the device could be used to identify the two spatial dimensions simultaneously.

Colloquium presented at School of Physics, National University of Ireland, Galway, Ireland, 21 September 2009Colloquium presented at School of Physics, National University of Ireland, Galway, Ireland, 21 September 2009

Phase singularities (optical vortices) that are produced in a strongly scintillated optical beam make it difficult to correct such a beam's phase distortions with a deformable mirror. It is found that even if vortices annihilate in pairs during propagation, they tend to be replaced by other vortices that are created in pairs. This property of vortex fields in scintillated beams is investigated by modeling them as polynomial Gaussian beams. The number of optical vortices that can exist in a polynomial Gaussian beam depends on the reducibility of the polynomial prefactor. During propagation, the reducibility of the prefactor is generally destroyed. However, if the morphologies of the vortices of a fully reducible prefactor are all the same, the reducibility is maintained during propagation. We compute expressions for the vortex trajectories in such an isomorphological Gaussian beam with a second-order prefactor, showing that the number of vortices stays the same all the way along the propagation direction. The theoretical predictions of the trajectories are confirmed with a numerical simulation. The morphology distributions (anisotropy and orientation) are constant over the entire beam. We also show that the dynamics for an isomorphological beam can be expressed in a Lagrangian formalism.

Vortex-bearing optical beams have a tendency to maintain the maximum number of vortices during propagation. This tendency is reminiscent of the concept of enstrophy, which is a conserved quantity in two-dimensional fluid dynamics, and which is given in terms of the vorticity in the fluid. We derive the optical equivalent for the fluid vorticity and show that it represents the optical topological charge density in paraxial beams. It then follows that the optical equivalent of the enstrophy represents the total number of optical vortices on a cross-section of the beam. We then argue that this concept forms an important part of the tendency of paraxial beams to maintain their maximum number of vortices. As part of the derivation we provide a summary of some of the pertinent topological properties of phase functions.