We investigate the electromagnetically induced Talbot effects resulting from the gain-loss modulated optical lattices constructed in a coherent four-level $N$-type atomic system. Both integer and fractional Talbot effects are studied in a parity-time ($\mathcal{PT}$) symmetric optical lattice, quasi-$\mathcal{PT}$-symmetric optical lattices, and a conventional electromagnetically induced transparency (EIT) optical lattice. Additionally, the visibilities of Talbot images from a $\mathcal{PT}$-symmetric optical lattice, quasi-$\mathcal{PT}$-symmetric optical lattices, and a conventional EIT optical lattice are examined. This study provides insights for understanding the Talbot effects in experiments based on coherent atomic systems with gain and loss properties.

中文翻译：

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相干原子介质中增益损耗调制光晶格引起的 Talbot 效应

我们研究了由以相干四能级构造的增益损耗调制光学晶格产生的电磁感应 Talbot 效应 $N$型原子系统。整数和分数 Talbot 效应都在奇偶校验时间 ($\mathcal{PT}$) 对称光学晶格，准$\mathcal{PT}$-对称光学晶格，以及传统的电磁感应透明 (EIT) 光学晶格。此外，来自 Talbot 图像的可见性$\mathcal{PT}$-对称光学晶格，准$\mathcal{PT}$对对称光学晶格和传统的 EIT 光学晶格进行了检查。这项研究为理解基于具有增益和损耗特性的相干原子系统的实验中的 Talbot 效应提供了见解。