Analytic evolution for complex coupled tight-binding models: Applications to quantum light manipulation

doi:10.1103/PhysRevResearch.6.033224

Analytic evolution for complex coupled tight-binding models: Applications to quantum light manipulation

2024-08-27

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Santiago Rojas-Rojas *

Carla Hermann-Avigliano

DOI：10.1103/PhysRevResearch.6.033224

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We present analytic solutions to the evolution in generalized tight-binding models, which consider complex first-neighbor couplings with equal amplitude and arbitrary phases. Our findings provide a powerful tool to efficiently calculate expectation values and correlations within the system, which are otherwise difficult to compute numerically. We apply our results to relevant examples in quantum light manipulation using N-port linear couplers, describing the evolution of single (multi)-mode squeezing, single-photon added (subtracted) Gaussian states, and second-order site-to-site photon correlations. Significantly, our analytic results outperform standard numerical calculations. Our study paves the way for a comprehensive mathematical framework describing the spatial evolution of quantum states across a wide range of physical systems governed by the tight-binding model.

Keywords:

WIGNER FUNCTION

STATES

NEGATIVITY

LATTICES

Analytic evolution for complex coupled tight-binding models: Applications to quantum light manipulation

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