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

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.

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• Analytic next-to-nearest neighbour XX models with perfect state transfer and fractional revival
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Cited by in corpus (9)

• Quantum state engineering in arrays of nonlinear waveguides
• Versatile photonic entanglement synthesizer in the spatial domain
• Quantum transport in non-Markovian dynamically-disordered photonic lattices
• A classical model for perfect transfer and fractional revival based on $q$-Racah polynomials
• Quantum Walks on Graphs of the Ordered Hamming Scheme and Spin Networks
• Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials
• Sklyanin-like algebras for ($q$-)linear grids and ($q$-)para-Krawtchouk polynomials
• Perfect State Transfer in a Spin Chain without Mirror Symmetry
• Analytic "Newton's cradles" with perfect transfer and fractional revival