Analytic Evolution for Complex Coupled Tight-Binding Models: Applications to Quantum Light Manipulation

• URL: http://arxiv.org/abs/2310.12366v2
• Date: Mon, 20 Nov 2023 17:03:46 GMT
• Title: Analytic Evolution for Complex Coupled Tight-Binding Models: Applications to Quantum Light Manipulation
• Authors: Santiago Rojas-Rojas and Camila Mu\~noz and Edgar Barriga and Pablo Solano and Aldo Delgado and Carla Hermann-Avigliano
• Abstract summary: We present analytic solutions to the evolution in generalized tight-binding models. We apply our results to relevant examples in quantum light manipulation. Our study paves the way for a comprehensive mathematical framework describing the spatial evolution of quantum states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 for efficiently calculating 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.

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