Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 074, 19 pages      arXiv:1705.04841      https://doi.org/10.3842/SIGMA.2017.074
Contribution to the Special Issue on Symmetries and Integrability of Difference Equations

Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results

Éric-Olivier Bossé and Luc Vinet
Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal, QC, Canada, H3C 3J7

Received May 13, 2017, in final form September 09, 2017; Published online September 14, 2017

Abstract
The analytic specifications of photonic lattices with fractional revival (FR) and perfect state transfer (PST) are reviewed. The approach to their design which is based on orthogonal polynomials is highlighted. A compendium of analytic models with PST is offered. New results on their FR properties are included. The nearest-neighbour approximation is adopted in most of the review; one analytic example with next-to-nearest neighbour interactions is also presented.

Key words: perfect state transfer; fractional revival; quantum information.

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