Entanglement of the properties of two separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum information science. We demonstrate strong Einstein, Podolsky, and Rosen correlations between the angular position and orbital angular momentum of two photons created by the nonlinear optical process of spontaneous parametric down-conversion. The discrete nature of orbital angular momentum and the continuous but periodic nature of angular position give rise to a special sort of entanglement between these two variables. The resulting correlations are found to be an order of magnitude stronger than those allowed by the uncertainty principle for independent (nonentangled) particles. Our results suggest that angular position and orbital angular momentum may find important applications in quantum information science.

We observe entanglement between photons in controlled super-position states of orbital angular momentum (OAM). By drawing a direct analogy between OAM and polarization states of light, we demonstrate the entangled nature of high order OAM states generated by spontaneous downconversion through violation of a suitable Clauser Horne Shimony Holt (CHSH)-Bell inequality. We demonstrate this violation in a number of two-dimensional subspaces of the higher dimensional OAM Hilbert space.

The physical process of generation of waves by wind is extremely complex, uncertain and not yet fully understood. Despite a variety of deterministic models presented to predict the heights and periods of waves from the characteristics of the generating wind, a large scope still exists to improve on the existing models or to provide alternatives to them. This paper explores the possibility of employing the relatively recent technique of neural networks for this purpose. A simple 3-layered feed forward type of network is developed to obtain the output of significant wave heights and average wave periods from the input of generating wind speeds. The network is trained with different algorithms and using three sets of data. The results show that an appropriately trained network could provide satisfactory results in open wider areas, in deep water and also when the sampling and prediction interval is large, such as a week. A proper choice of training patterns is found to be crucial in achieving adequate training.

We study the effects of atmospheric turbulence on the entanglement of spatial two-qubit states that are prepared using the signal and idler photons produced by parametric down-conversion. Such states are the basic ingredients of quantum information protocols and can be prepared, for example, by making down-converted photons pass through a pair of double-apertures. We make use of the Kolmogorov model for atmospheric turbulence and quantify the entanglement of the two-qubit state in terms of Wootters's concurrence. We restrict our analysis to the two-qubit states that can be represented by density matrices having only two nonzero diagonal elements.

We show that the use of path-entangled states of photons, having nonzero orbital angular momentum (OAM), increases the resolution and sensitivity of angular-displacement measurements performed using an interferometer. In the ideal case of maximally path-entangled states, the resolution of angular-displacement measurements increases by a factor of Nl, while the uncertainty in the measurement of angular displacements scales as 1/N l, where N is the number of entangled photons, half of which carry, on average, an OAM of +lh per photon and the other half carry an OAM of −lh per photon. We analyze measurement schemes for two-and four-photon entangled states produced by parametric down-conversion and, by employing a 4×4 matrix formalism to study the propagation of entangled OAM modes, obtain explicit expressions for the resolution and sensitivity in these schemes. These results constitute an improvement over what could be obtained with N nonentangled photons carrying an orbital angular momentum of |l|h per photon. −l ). Using Eqs. (25)-(27), we solve Eq. (30) to obtain the following operator relations:

We study the spatial coherence properties of the entangled two-photon field produced by parametric downconversion (PDC) when the pump field is, spatially, a partially coherent beam. By explicitly treating the case of a pump beam of the Gaussian Schell-model type, we show that in PDC the spatial coherence properties of the pump field get entirely transferred to the spatial coherence properties of the down-converted two-photon field. As one important consequence of this study, we find that, for two-qubit states based on the position correlations of the two-photon field, the maximum achievable entanglement, as quantified by concurrence, is bounded by the degree of spatial coherence of the pump field. These results could be important by providing a means of controlling the entanglement of down-converted photons by tailoring the degree of coherence of the pump field.

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The existing methods for measuring the orbital-angular-momentum (OAM) spectrum suffer from issues such as poor efficiency, strict interferometric stability requirements, and too much loss. Furthermore, most techniques inevitably discard part of the field and measure only a post-selected portion of the true spectrum. Here, we propose and demonstrate an interferometric technique for measuring the true OAM spectrum of optical fields in a single-shot manner. Our technique directly encodes the OAM-spectrum information in the azimuthal intensity profile of the output interferogram. In the absence of noise, the spectrum can be fully decoded using a single acquisition of the output interferogram, and, in the presence of noise, acquisition of two suitable interferograms is sufficient for the purpose. As an important application of our technique, we demonstrate measurements of the angular Schmidt spectrum of the entangled photons produced by parametric down-conversion and report a broad spectrum with the angular Schmidt number 82.1.