Geometric Criteria for Complete Mode Conversion in Detuned Systems via Piecewise-Coherent Modulation

• URL: http://arxiv.org/abs/2601.10066v1
• Date: Thu, 15 Jan 2026 04:44:28 GMT
• Title: Geometric Criteria for Complete Mode Conversion in Detuned Systems via Piecewise-Coherent Modulation
• Abstract summary: Static phase detuning constrains coherent state transfer in asymmetric classical and quantum systems.<n>We introduce a Bloch-sphere formulation for piecewise-coherent modulation that recasts coupled-mode dynamics as geometric trajectories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Static phase detuning fundamentally constrains coherent state transfer in asymmetric classical and quantum systems. We introduce a Bloch-sphere formulation for piecewise-coherent modulation that recasts coupled-mode dynamics as geometric trajectories, transforming algebraic control into path optimization. The approach reveals a cone of inaccessibility at the target pole and yields exact geodesic criteria for complete mode conversion in detuned systems. Leveraging this framework, we break time-reversal symmetry to realize a magnet-free optical isolator with near-unity contrast. Furthermore, for detuning larger than coupling between modes, we develop a recursive multi-step protocol enabling deterministic transfer for arbitrary detunings and derive a universal geometric lower bound on the required number of coupling-switching events.

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