The intermodal entanglement in a two-channel symmetric nonlinear coupler, operated with Kerr nonlinearity was investigated using the analytical method based on the Heisenberg picture in quantum mechanics. The Heisenberg equations of motion of the propagating modes were solved based on the Baker-Hausdorff (BH) formula. The entanglement expressions were then derived following the Hillery-Zubairy criteria of two-modes state. The time evolution of entanglement was examined at different values of design parameters. Theoretical results from both the HZ-I and HZ-II criteria show that the system exhibits entangled states of light which can be improved by increasing the coupling constants and the initial amplitude of the input field. On the contrary, the increment in frequency mismatch weakens the HZ-I entanglement, while improving the HZ-II entanglement up to a certain mismatch value. The study provides a new theory of entanglement detection in Kerr nonlinear couplers, which opens up the avenues of a new class of applications based on entanglement.

使用基于量子力学中的海森堡图的解析方法研究了以克尔非线性操作的双通道对称非线性耦合器中的模间纠缠。基于 Baker-Hausdorff (BH) 公式求解了传播模式的海森堡运动方程。然后根据双模式状态的 Hillery-Zubairy 标准推导出纠缠表达式。在不同的设计参数值下检查了纠缠的时间演变。HZ-I 和 HZ-II 标准的理论结果表明，系统表现出光的纠缠态，可以通过增加耦合常数和输入场的初始幅度来改善这种纠缠态。相反，频率失配的增加削弱了 HZ-I 纠缠，同时将 HZ-II 纠缠提高到一定的失配值。该研究提供了克尔非线性耦合器中纠缠检测的新理论，为基于纠缠的一类新应用开辟了道路。