AI 中文总结
本研究提出一种光子架构，使佩奇-伍特斯时钟自由度携带拓扑不变量，通过耦合微环阵列的双光子符合条纹测量该几何相位的拓扑缠绕，且参数需求可通过薄膜铌酸锂实现。
AI 中文摘要
佩奇-伍特斯构造赋予时间一个希尔伯特空间，将其表示为一个内部自由度，系统其余部分的演化相对于该自由度进行。我们探究这种时钟自由度是否能携带拓扑不变量，并提出一种光子架构，其中该自由度确实携带拓扑不变量，且该不变量可被测量。耦合微环阵列中自发四波混频产生的信号-闲频对构成时钟-系统划分，闲频占据赖斯-梅勒能带，其交错耦合与失谐在间隙闭合点周围绝热循环。一个周期对该能带的作用为：刚性平移\textit{C}个原胞，乘以晶体动量上周期的几何相位，再乘以动力学相位，在绝热极限下这是一个恒等式，且与它作用的状态无关。读出针对该几何相位在布里渊区的缠绕。反转泵浦回路的遍历可抵消动力学相位，并在双光子符合条纹中分离出两倍的几何相位，而能量反相关性使对信号的滤波能扫描时钟动量而不触碰时钟，并以关系方式提供相位参考，替代外部光学参考。该估计在两个独立层面受到保护：一是间隙免受平滑变形的影响，二是展开的数字特性免受阈值以下噪声的影响。以薄膜铌酸锂为基准的参数预算将需求置于保守工作点下可实现的范围内。
英文摘要
The Page--Wootters construction gives time a Hilbert space, representing it as an internal degree of freedom whose readings the rest of the system evolves with respect to. We ask whether such a clock degree of freedom can carry a topological invariant, and we propose a photonic architecture in which it does and in which the invariant can be measured. Signal--idler pairs from spontaneous four-wave mixing in a coupled microring array supply the clock--system partition, with the idler occupying a Rice--Mele band whose staggered coupling and detuning are cycled adiabatically around a gap-closing point. One cycle acts on that band as a rigid translation by \(C\) unit cells, times a geometric phase periodic in the crystal momentum, times a dynamical phase, an identity exact in the adiabatic limit and independent of the state on which it acts. The readout targets the winding of that geometric phase across the Brillouin zone. Reversing the traversal of the pump loop cancels the dynamical phase and isolates twice the geometric phase in a two-photon coincidence fringe, while energy anticorrelation lets a filter on the signal scan the clock momentum without touching the clock and supplies the phase reference relationally, in place of an external optical reference. The estimate is protected on two independent levels, by the gap against smooth deformation and by the digital character of the unwrapping against noise below a threshold. A parameter budget anchored to thin-film lithium niobate places the requirements within reach at a conservative operating point.
