Quantum Field Framework for Structured Light Interactions (17w5079)

Arriving in Banff, Alberta Sunday, April 23 and departing Friday April 28, 2017

Organizers

Konstantin Bliokh (RIKEN and ANU)

(McMaster University)

Robert Boyd (University of Ottawa)

(University of Bristol)

(University of Calgary)

(University of East Anglia)

Objectives

The ultimate objectives are to achieve a more cohesive formulation of structured light quantization, and a consistent framework with which to describe the fundamental photon interactions of such light – in a form that is suitable and amenable to technical and experimental application. The course of discussion will also aim to identify flaws, shortcomings, oversights and physically unsupportable assumptions in some existing areas of theory.

The community has identified a wide range of issues demanding attention. To expedite progress during the week, the plan is to begin the workshop by agreeing on terms of reference, and uniform terms and symbology for key parameters, operators and spaces. Brief presentations by different participants will then introduce each of the following issues, following which the workshop attendees will prioritise and order them for consideration in discussions and work sessions. Although it is a substantial list, the subject it represents is a very well-focused and interconnected area of mathematical optics:

a) Identification of a robust, physically meaningful and generically applicable measure of the information-conveying capacity of a photon, and factors fundamentally limiting that capacity. Exploring potential connections with Majorana quantization.

b) Resolving the information capacity achievable through the entanglement of structured light beams, (as may be produced by parametric down-conversion), with potential links to Bohm photon trajectories.

c) Formulating a fully quantum-based representation of photon interactions in systems of fluctuating density and turbulence. Considering informational aspects of optical helicity and its potential for transfer on scattering by chiral molecules or particles.

d) Considering how or whether the correspondence principle extends to the quantum number represented by topological charge, accounting for the quantitative limitation of the latter to surface intersections of lines of optical phase singularity. Whereas a quantum-to-classical transition in the orbital quantum number has been observed directly for Rydberg atoms, there has been no such progress in singularities in optical fields.

e) Developing the quantum theory of vector polarization (Poincaré) beam interactions, accommodating polarization entanglement. In quantum vector fields, the polarization and spatial degrees of freedom are coupled and an exchange of entanglement can occur during propagation. It is currently unclear how this might affect the time evolution of quantum entanglement between two such fields.

f) Establishing a robust formulation of the optical momentum associated with structured light and its connection to Hamiltonian ray optics; consideration of the electromagnetic field stress tensors, and their consequences for field momentum and the laws governing force and torque; elucidation of the concept of ‘hidden momentum’ in electromagnetic systems.

g) Addressing the connectivity of catastrophe theory with singular optics, addressing both the singularities of scalar wave optics (optical vortices) and the singularities of vector wave optics.

h) Constructing a quantum electrodynamical formulation of cavity modes and virtual photon representations of the fields in low-index and negative-index materials. Also addressing the quantum aspects of light-matter interaction in the near-field vicinity of metamaterials with holey lattices and other surface structures.

i) Addressing quantum aspects of interactions between structured light-and matter, such as ultracold atomic or molecular ensembles, incorporating issues of non-locality and topological phase. To identify a means of forging strong interactions with structured light would pave the way for high-dimensional quantum hybrids, with matter mediating interactions between the structured light beams.

j) To consider where a scalar field representation of singular light becomes an invalid representation of physical interactions and observations.

k) Establishing a limit of spatial dimensions below which quantum phenomena emerge in the field of topological photonics. Whereas optical wavelength sets a natural length scale, the conundrum with structured light is that its optical singularities are usually points or lines of unlimited extent. It is a challenge to find out whether the established concepts remain valid in the progressive reduction of length scales, or if new phenomena might emerge.

By mid-week it is intended that a small number of working groups can begin to develop presentations for delivery to the whole workshop on the Thursday and Friday, resolving a number of the issues identified above. The intention is that the ensuing proceedings and discussions will deliver materials that can be used subsequently, to develop a resource for release to the ever growing community working in this area of optical physics. The benefits will support many of the most promising and potentially transformative developments in modern optics, photonics and information technology.