Angular EPR paradox

The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum correlations for the conjugate variables of orbital angular momentum and angular position. We determine an experimentally testable criterion for the demonstration of an angular version of the EPR paradox. For the interpretation of future experimental results from our proposed setup, we include a model for the indeterminacies inherent to the angular position measurement. For this measurement angular apertures are used to determine the probability density of the angle. We show that for a class of aperture functions a demonstration of an angular EPR paradox, according to our criterion, is to be expected.Comment: 21 pages, 9 figures, to be published in J. Mod. Opt. special issue on quantum imagin

Instantaneous modulations in time-varying complex optical potentials

We study the impact of a spatially homogeneous yet non-stationary dielectric permittivity on the dynamical and spectral properties of light. Our choice of potential is motivated by the interest in PT-symmetric systems as an extension of quantum mechanics. Because we consider a homogeneous and non-stationary medium, PT symmetry reduces to time-reversal symmetry in the presence of balanced gain and loss. We construct the instantaneous amplitude and angular frequency of waves within the framework of Maxwell's equations and demonstrate the modulation of light amplification and attenuation associated with the well-defined temporal domains of gain and loss, respectively. Moreover, we predict the splitting of extrema of the angular frequency modulation and demonstrate the associated shrinkage of the modulation period. Our theory can be extended for investigating similar time-dependent effects with matter and acoustic waves in PT-symmetric structures.Comment: 13 pages, 4 figure

Matter-wave grating distinguishing conservative and dissipative interactions

We propose an optical grating for matter waves that separates molecules depending on whether their interaction with the light is conservative or dissipative. Potential applications include fundamental tests of quantum mechanics, measurement of molecular properties and the ability to selectively prepare matter waves with different internal temperatures

On lines of constant polarisation in structured light beams

We show that Skyrmion field lines, constructed from the local Stokes parameters, trace out lines of constant optical polarisation

Optical helicity and chirality: conservation and sources

We consider the helicity and chirality of the free electromagnetic field, and advocate the former as a means of characterising the interaction of chiral light with matter. This is in view of the intuitive quantum form of the helicity density operator, and of the dual symmetry transformation generated by its conservation. We go on to review the form of the helicity density and its associated continuity equation in free space, in the presence of local currents and charges, and upon interaction with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity

A Topological Approach to Characterising Optical Skyrmions

Skyrmions are topologically protected field configurations characterised by a topological index, the skyrmion number. Optical skyrmions are ideally suited to investigate topological structures due to the ease of generating arbitrary light fields, and the freedom from energy constraints encountered by, for example, magnetic skyrmions. Building on our previous work of a topologically defined skyrmion number,1 here we demonstrate the conservation of the skyrmion number of hedgehog skyrmions and bimerons under propagation. We furthermore generate tunable multi-skyrmions from superpositions of oppositely polarised Gaussian and split-vortex beams of different waists, and find that the skyrmion number is conserved as a function of waist scaling. For both cases, the topological definition of the skyrmion number forms an intuitive geometric approach to understanding the underlying topology and to identifying the individual skyrmion structures