标题： 多孤子传播和相互作用在$Λ$类EIT介质中的可积方法 显示英文标题

标题： Multi-Soliton Propagation and Interaction in $Λ$-Type EIT Media: An Integrable Approach

摘要： 电磁诱导透明（EIT）是一种众所周知的量子光学现象，由于跃迁路径之间的量子干涉，使通常不透明的介质变得透明。 本工作研究了由可积Maxwell-Bloch（MB）方程描述的EIT系统中的多孤子动力学，该方程适用于三能级$\Lambda $型原子构型。 通过采用广义规范变换，我们系统地从相应的Lax对中构造出显式的N孤子解。 得到了一、二、三和四孤子解的显式形式并进行了分析。 所得脉冲结构揭示了各种非线性现象，如时间不对称性、能量捕获和孤子相互作用。 它们还突出了相干传播、弹性碰撞和脉冲的部分存储，这些现象在EIT介质中量子记忆、慢光和光子数据传输的设计方面具有潜在的应用价值。 此外，利用激发范数和哈密顿量等基本物理量的守恒，提供了构造的孤子解可积性和稳定性的直接证据。 显示英文摘要

摘要： Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dynamics in an EIT system modeled by the integrable Maxwell-Bloch (MB) equations for a three-level $\Lambda $-type atomic configuration. By employing a generalized gauge transformation, we systematically construct explicit N-soliton solutions from the corresponding Lax pair. Explicit forms of one-, two-, three-, and four-soliton solutions are derived and analyzed. The resulting pulse structures reveal various nonlinear phenomena, such as temporal asymmetry, energy trapping, and soliton interactions. They also highlight coherent propagation, elastic collisions, and partial storage of pulses, which have potential implications for the design of quantum memory, slow light and photonic data transport in EIT media. In addition, the conservation of fundamental physical quantities, such as the excitation norm and Hamiltonian, is used to provide direct evidence of the integrability and stability of the constructed soliton solutions.