We theoretically investigate one-dimensional localized gap modes in a coherent atomic gas where an optical lattice is formed by a pair of counterpropagating far-detuned Stark laser fields. The atomic ensembles under study emerge as Λ-type three-level configuration accompanying the effect of electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations and the multiple scales method, we derive a nonlinear equation governing the spatial-temporal evolution of the probe-field envelope. We then uncover the formation and properties of optical localized gap modes of two kinds, such as the fundamental gap solitons and dipole gap modes. Furthermore, we confirm the (in)stability regions of both localized gap modes in the respective band-gap spectrum with systematic numerical simulations relying on linear-stability analysis and direct perturbed propagation. The predicted results may enrich the nonlinear horizon to the realm of coherent atomic gases and open up a new door for optical communication and information processing.

中文翻译：

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光学晶格中相干俘获原子的局部能隙模式

我们从理论上研究了相干原子气体中的一维局部间隙模式，在该相干原子气体中，光学晶格是由一对反向传播的失谐的Stark激光场形成的。所研究的原子团簇以Λ型三能级结构出现，伴随着电磁感应透明性（EIT）的影响。基于Maxwell-Bloch方程和多尺度方法，我们得出了一个控制探测场包络线时空演化的非线性方程。然后，我们揭示了两种基本的光学局部缝隙模式的形成和性质，例如基本缝隙孤子和偶极缝隙模式。此外，我们通过依赖于线性稳定性分析和直接扰动传播的系统数值模拟，确认了各自带隙谱中两个局部间隙模式的（in）稳定性区域。预测结果可以丰富非线性视界到相干原子气体的领域，并为光通信和信息处理打开新的大门。