标题： 瞬子和稀疏波作为基于增益的光学网络中实现全局相位相干的途径 显示英文标题

标题： Instantons and Rarefaction Pulses as Pathways to Global Phase Coherence in Gain-Based Optical Networks

摘要： 我们研究了如何可靠地去除基于增益的光学振荡器网络中的不需要的全局相位缠绕，从而确保收敛到与XY哈密顿量全局最小值相对应的真实同步配置。 专注于一维环和二维环面格子，我们展示了两种关键策略大大提高了达到无缺陷状态的概率。 首先，在阈值以上较低的有效注入速率下运行，利用振幅自由度，使系统能够形成瞬态零振幅孔：一维的瞬子，或二维空间中的涡旋-反涡旋稀疏脉冲，这些可以使相位滑移。 其次，用振幅或相位不均匀性来准备初始条件可以直接播种这些振幅崩溃，并防止系统被困在具有非零缠绕的更高能量状态。 使用Stuart-Landau方程和Ginzburg-Landau方程作为快速储层激光器的模型，我们推导出分析和数值证据，表明即使相对较轻的振幅下降也能触发一维的全局解缠。 我们进一步证明，泵浦的慢速退火有利于这些由振幅驱动的事件，从而提高找到全局相干基态的成功率。 这些发现突显了振幅自由度在XY优化问题类比求解器中的关键作用，展示了局部振幅抑制如何提供直接途径以排出拓扑缺陷。 显示英文摘要

摘要： We investigate how to reliably remove unwanted global phase windings in gain-based optical oscillator networks, thereby ensuring convergence to the true synchronized configuration corresponding to the XY Hamiltonian's global minimum. Focusing on one-dimensional rings and two-dimensional toroidal lattices, we show that two key strategies greatly enhance the probability of reaching the defect-free state. First, operating at a low effective injection rate just above threshold, exploits the amplitude degree of freedom, allowing the system to form transient zero-amplitude holes: instantons in one dimension, or vortex-antivortex rarefaction pulses in two-dimensional space, that enable phase slips. Second, preparing the initial condition with amplitude or phase inhomogeneities can directly seed these amplitude collapses and prevent the system from getting trapped in higher-energy states with nonzero winding. Using the Stuart--Landau and Ginzburg--Landau equations as models for fast-reservoir lasers, we derive analytic and numerical evidence that even relatively minor amplitude dips can trigger global unwinding in 1D. We further demonstrate that the pump's slow annealing favours these amplitude-driven events, leading to improved success in finding the globally coherent ground state. These findings highlight the critical role of amplitude freedom in analogue solvers for XY optimization problems, showing how local amplitude suppression provides a direct route to ejecting topological defects.