Quantum 2025 – scientific programme
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MON: Monday Contributed Sessions
MON 19: Foundational / Mathematical Aspects – Quantum Optics and Quantum Information
MON 19.2: Talk
Monday, September 8, 2025, 16:45–17:00, ZHG008
Preventing the Breakdown of the Tight Binding Approximation in Waveguide Quantum Optics — •Konrad Tschernig1, Florian Huber2, Janik Wolters1,3, and Jasmin Meinecke2,3 — 1Deutsches Zentrum für Luft- und Raumfahrt, Institut für Weltraumforschung, Berlin, Germany — 2Max-Planck-Institut für Quantenoptik, Garching, Germany — 3Technische Universität Berlin, Berlin, Germany
Many scientific advancements rely on the tight-binding approximation, which simplifies the description and prediction of complex system behaviors. In waveguide quantum optics, this approximation describes the dynamics of the single photon field by examining the coupling between the guided modes of individual single-mode waveguides. However, a crucial and often overlooked assumption in this framework is the mutual orthogonality of the guided modes. This assumption can fail when the waveguides are positioned very close to each other. We analyze the breakdown of the tight-binding approximation in scenarios involving small distances and then introduce the solution called Symmetric Löwdin Orthogonalization (SLO). By using SLO, we restore the orthogonality of the guided modes, leading to a closer alignment with the full continuous theory and improved agreement with experimental data compared to the standard tight-binding approach. Additionally, we explore the origin of nonreciprocal coupling in detuned waveguide systems within the SLO framework, which has previously been attributed to non-Hermitian effects.
Keywords: Quantum optics; Photonics; Tightbinding Approximation; Waveguides